ATS Native XML Input Specification V-dev
About the Specification
ATS, and Amanzi’s “native” specificiation, is an xml file following Trilinos’s Teuchos ParameterList schema. There are only two types of tags used – “Parameter” and “ParameterList”. “Parameter” elements consist of “name”, “type”, and “value” attributes. “ParameterList” elements use the “name” attribute and include subelements that are other “ParameterList” and “Parameter” elements.
The top-most, “main” list is read by the code and used to provide all information needed to run the simulation. This input spec is designed for the code, not necessarily for the user. In general, avoid writing input files from scratch, and prefer to modify existing demos or examples.
Here we document the input spec by defining what each possible element used by the code needs to be well posed.
Specs
In many cases, the input specifies data for a particular parameterized model, and ATS supports a number of parameterizations. For example, initial data might be uniform (the value is required), or linear in y (the value and its gradient are required). Where ATS supports a number of parameterized models for quantity Z, the available models will be listed by name, and then will be described in the subsequent section. For example, the specification for an “X” list might look like:
X-spec
“Y”
[string]default_value Documentation desribing Y.“Z”
[Z-spec]Model for Z, One of “z1” or “z2” (see below)
Here, an “X” is defined by a “Y” and a “Z”. The “Y” is a string parameter but the “Z” is given by a model (which will require its own set of parameters). The options for “Z” will then be described seperately as a “Z-spec”
An example of using such a specification:
<ParameterList name="X">
<Parameter name="Y" type="string" value="hello"/>
<ParameterList name="z2">
<Parameter name="z2a" type="double" value="0.7"/>
<Parameter name="z2b" type="int" value="3"/>
</ParameterList>
</ParameterList>
Syntax
Reserved keywords and labels are “quoted and italicized” – these labels or values of parameters in user-generated input files must match (using XML matching rules) the specified or allowable values.
User-defined labels are indicated with ALL-CAPS, and are meant to represent a typical or default name given by a user - these can be names or numbers or whatever serves best the organization of the user input data. Things liked PRESSURE or SURFACE-PONDED_DEPTH can be renamed from their defaults if it makes sense to the problem.
Bold values are default values, and are used if the Parameter is not provided.
Naming
Variables are named according to a very strong convention. While some variables may be overridden by the user, users should choose to follow these conventions or things like visualization scripts may not behave as expected.
A variable name looks like one of:
SUFFIX
DOMAIN-SUFFIX
DOMAIN_SET:ID-VARNAME
where:
When DOMAIN is supplied, it is the “default” mesh, called “domain” in the mesh list, and otherwise is the name of the mesh (e.g. “surface”).
DOMAIN_SET:ID is itself a DOMAIN, where the set defines the collection as a whole (from the mesh list) and the ID is defined by an index across the collection, e.g. “column:4”
Tags indicate the use of a variable at a specific time in the discretized time interval. Default tags include “current” and “next” indicating the variable at the beginning and end of the interval, respectively. Often subcycling and other schemes will designate special-purpose tags which may be used internally by a subset of the equations begin solved. Tags are combined with variables to indicate a specific data structure, e.g. “surface-pressure@NEXT”.
Lastly, derivatives are named using the “d” and the “|” character, e.g. “dsurface-water_content|dsurface-pressure” is the derivative of the “water_content” variable on the “surface” domain with respect to the “pressure” on the same domain.
As a result of these conventions, none of the above individual strings, (suffixes, domains, domain sets, or IDs) can contain any of the following reserved characters: :, -, |, @.
Symbol Index
Symbol |
Description |
|---|---|
\(E\) |
extensive energy of a cell \([\mathop{\mathrm{MJ}}]\) |
\(e\) |
specific enthalpy \([\mathop{\mathrm{MJ}} \mathop{\mathrm{mol}}^{-1}]\) |
\(g\) |
gravitational acceleration vector \([m s^{-2}]\) |
\(h\) |
ponded depth, or the water head over the surface \([m]\) |
alternative, in context of the subsurface, water head \([m]\) |
|
\(h_{snow}\) |
snow depth \([m]\) |
\(K\) |
absolute permeability \([m^2]\) |
\(\kappa\) |
thermal conductivity \([\mathop{\mathrm{MW}} m^{-1} K^{-1}]\) |
\(k_r\) |
relative permeability \([-]\) |
\(n_X\) |
molar density of phase X \([\mathop{\mathrm{mol}} m^{-3}]\) |
\(\vert \partial \Omega \vert\) |
volume of a discrete element \(\partial \Omega\) |
\(p\) |
pressure of the liquid phase \([\mathop{\mathrm{Pa}}]\) |
\(P_{r}\) |
precipitation of rain \([m s^{-1}]\) |
\(P_{s}\) |
precipitation of snow, in snow-water-equivalent (SWE) \([m \mathop{\mathrm{SWE}} s^{-1}]\) |
\(Q_e\) |
source of energy \([\mathop{\mathrm{MJ}} s^{-1}]\) |
\(Q_w\) |
mass source of water \([\mathop{\mathrm{mol}} s^{-1}]\) |
\(s_X\) |
saturation of phase X \([-]\) |
\(t\) |
time variable \([s]\) |
\(z\) |
elevation \([m]\) |
\(\nu\) |
dynamic viscosity of water \([\mathop{\mathrm{Pa}} s]\) |
\(\phi\) |
porosity of the soil \([-]\) |
\(\mathbf{q}\) |
Darcy flux vector \([\mathop{\mathrm{mol}} m^{-2} s^{-1}]\) |
\(\mathbf{q_s}\) |
surface flux vector \([\mathop{\mathrm{mol}} m s^{-1}]\) |
\(\rho\) |
mass density of a phase \([\mathop{\mathrm{kg}} m^{-3}]\) |
\(t\) |
time variable \([s]\) |
\(T\) |
temperature \([K]\) |
\(\Theta\) |
extensive water content of a cell \([\mathop{\mathrm{mol}}]\) |
\(u_X\) |
specific internal energy of phase X \([\mathop{\mathrm{MJ}} \mathop{\mathrm{mol}}^{-1}]\) |
\(\mathbf{V}\) |
Darcy velocity vector \([m s^{-1}]\) |
\(\mathbf{V_s}\) |
surface velocity vector \([m s^{-1}]\) |
\(x\), \(y\), \(z\) |
spatial coordinates \([m]\) |
Main
ATS’s top level driver is provided the entire input spec as a single list called “main”. That list contains the following required elements:
main-spec
“cycle driver”
[coordinator-spec]See below.“mesh”
[mesh-typed-spec-list]A list of Mesh objects.“regions”
[region-typedinline-spec-list]A list of Region objects.“visualization”
[visualization-spec-list]A list of Visualization objects.“observations”
[observation-spec-list]An list of Observation objects.“checkpoint”
[checkpoint-spec]A Checkpoint spec.“PKs”
[pk-typedinline-spec-list]A list of Process Kernels.“state”
[state-spec]A State spec.
Coordinator
In the “cycle driver” sublist, the user specifies global control of the simulation, including starting and ending times and restart options.
coordinator-spec
“start time”
[double]0. Specifies the start of time in model time.“start time units”
[string]“s” One of “s”, “d”, or “yr”
ONE OF
“end time”
[double]Specifies the end of the simulation in model time.“end time units”
[string]“s” One of “s”, “d”, or “yr”
OR
“end cycle”
[int]optional If provided, specifies the end of the simulation in timestep cycles.END
“subcycled timestep”
[bool]false If true, this coordinator creates a third State object to store intermediate solutions, allowing for failed steps.“restart from checkpoint file”
[string]optional If provided, specifies a path to the checkpoint file to continue a stopped simulation.“wallclock duration [hrs]”
[double]optional After this time, the simulation will checkpoint and end.“required times”
[io-event-spec]optional An IOEvent spec that sets a collection of times/cycles at which the simulation is guaranteed to hit exactly. This is useful for situations such as where data is provided at a regular interval, and interpolation error related to that data is to be minimized.“PK tree”
[pk-typed-spec-list]List of length one, the top level PK spec.
Note: Either “end cycle” or “end time” are required, and if both are present, the simulation will stop with whichever arrives first. An “end cycle” is commonly used to ensure that, in the case of a time step crash, we do not continue on forever spewing output.
Example:
<ParameterList name="cycle driver">
<Parameter name="end cycle" type="int" value="6000"/>
<Parameter name="start time" type="double" value="0."/>
<Parameter name="start time units" type="string" value="s"/>
<Parameter name="end time" type="double" value="1"/>
<Parameter name="end time units" type="string" value="yr"/>
<ParameterList name="required times">
<Parameter name="start period stop" type="Array(double)" value="{0,-1,86400}" />
</ParameterList>
<ParameterList name="PK tree">
<ParameterList name="my richards pk">
<Parameter name="PK type" type="string" value="richards" />
</ParameterList>
</ParameterList>
</ParameterList>
Mesh
A list of mesh objects and their domain names.
All processes are simulated on a domain, which is discretized through a mesh.
Multiple domains and therefore meshes can be used in a single simulation, and
multiple meshes can be constructed on the fly. The top level “mesh” is a
list of [mesh-typed-spec] sublists whose name indicate the mesh or domain
name.
Included in that list is at least one mesh: the “domain” mesh. The “domain” mesh represents the primary domain of simulation – usually the subsurface. Simple, structured meshes may be generated on the fly, or complex unstructured meshes are provided as Exodus II files. The “domain” mesh list includes either a Generated Mesh, Read Mesh File, or Logical Mesh spec, as described below.
Additionally, a Surface Mesh may be formed by lifting the surface of a provided mesh and then flattening that mesh to a 2D surface. Column Meshes which split a base mesh into vertical columns of cells for use in 1D models may also be generated automatically.
Finally, mesh generation is hard and error-prone. A mesh audit is provided, which checks for many common geometric and topologic errors in mesh generation. This is reasonably fast, even for big meshes, and can be done through providing a “verify mesh” option.
mesh-typed-spec
“mesh type”
[string]One of:“generate mesh” See Generated Mesh.
“read mesh file” See Read Mesh File.
“logical” See Logical Mesh.
“surface” See Surface Mesh.
“extracted” See Extracted Mesh.
“domain set indexed” See Domain Set Meshes.
“domain set regions” See Domain Set Meshes.
“column” See Column Meshes.
“column surface” See Column Surface Meshes.
“_mesh_type_ parameters”
[_mesh_type_-spec]List of parameters associated with the type.“verify mesh”
[bool]false Perform a mesh audit.“deformable mesh”
[bool]false Will this mesh be deformed?“build columns from set”
[string]optional If provided, build columnar structures from the provided set.“partitioner”
[string]zoltan_rcb Method to partition the mesh. Note this only makes sense on the domain mesh. One of:“zoltan_rcb” a “map view” partitioning that keeps columns of cells together
“metis” uses the METIS graph partitioner
“zoltan” uses the default Zoltan graph-based partitioner.
Generated Mesh
Generated mesh are by definition structured, with uniform dx, dy, and dz. Such a mesh is specified by a bounding box high and low coordinate, and a list of number of cells in each direction.
Specified by “mesh type” of “generate mesh”.
mesh-generate-mesh-spec
“domain low coordinate”
[Array(double)]Location of low corner of domain“domain high coordinate”
[Array(double)]Location of high corner of domain“number of cells”
[Array(int)]the number of uniform cells in each coordinate direction
Example:
<ParameterList name="mesh">
<ParameterList name="domain">
<Parameter name="mesh type" type="string" value="generate mesh"/>
<ParameterList name="generate mesh parameters"/>
<Parameter name="number of cells" type="Array(int)" value="{100, 1, 100}"/>
<Parameter name="domain low coordinate" type="Array(double)" value="{0.0, 0.0, 0.0}" />
<Parameter name="domain high coordinate" type="Array(double)" value="{100.0, 1.0, 10.0}" />
</ParameterList>
</ParameterList>
</ParameterList>
Read Mesh File
Meshes can be pre-generated in a multitude of ways, then written to file, and loaded in ATS. Note that in the case of an Exodus II mesh file, the suffix of the serial mesh file must be .exo and the suffix of the parallel mesh file must be .par. When running in serial the code will read this the indicated file directly. When running in parallel with a prepartitioned mesh, the suffix is .par and the code will instead read the partitioned files that have been generated with a Nemesis tool and named as filename.par.N.r where N is the number of processors and r is the rank. When running in parallel and the suffix is .exo, the code will partition automatically the serial file.
Specified by “mesh type” of “read mesh file”.
mesh-read-mesh-file-spec
“file”
[string]filename of a pre-generated mesh file
Example:
<ParameterList name="mesh">
<ParameterList name="domain">
<Parameter name="mesh type" type="string" value="read mesh file"/>
<ParameterList name="read mesh file parameters">
<Parameter name="file" type="string" value="mesh_filename.exo"/>
</ParameterList>
<Parameter name="verify mesh" type="bool" value="true" />
</ParameterList>
</ParameterList>
Logical Mesh
Logical meshes are meshes for whom nodal coordinates may not be specified, but sufficient information about the geometry of the conceptual domain can be specified to allow solving problems. This allows for the conceptual generation of domains that “act” like a mesh and can be used like a mesh, but don’t fit MSTK’s view of an unstructured mesh.
This is an active research and development area, and is used most frequently for river networks, root networks, and crack networks.
Specified by “mesh type” of “logical”.
mesh-logical-spec
Not yet completed…
Surface Mesh
To lift a surface off of the mesh, a side-set specifying all surface faces must be given. These faces are lifted locally, so the partitioning of the surface cells will be identical to the partitioning of the subsurface faces that correspond to these cells. All communication and ghost cells are set up. The mesh is flattened, so all surface faces must have non-zero area when projected in the z-direction. No checks for holes are performed. Surface meshes may similarly be audited to make sure they are reasonable for computation.
Specified by “mesh type” of “surface”.
mesh-surface-spec
“parent domain”
[string]domain Parent mesh’s name.
ONE OF
“surface sideset name”
[string]The Region name containing all surface faces.
OR
“surface sideset names”
[Array(string)]A list of Region names containing the surface faces.
END
“verify mesh”
[bool]false Verify validity of surface mesh.“export mesh to file”
[string]optional Export the lifted surface mesh to this filename.“create subcommunicator”
[bool]false If false, the communicator of this mesh is the same as the parent mesh. If true, the communicator of this mesh is the subset of the parent mesh comm that has entries on the surface.
Example:
<ParameterList name="mesh" type="ParameterList">
<ParameterList name="surface" type="ParameterList">
<Parameter name="mesh type" type="string" value="surface" />
<ParameterList name="surface parameters" type="ParameterList">
<Parameter name="surface sideset name" type="string" value="{surface_region}" />
<Parameter name="verify mesh" type="bool" value="true" />
<Parameter name="export mesh to file" type="string" value="surface_mesh.exo" />
</ParameterList>
</ParameterList>
<ParameterList name="domain" type="ParameterList">
<Parameter name="mesh type" type="string" value="read mesh file" />
<ParameterList name="read mesh file parameters" type="ParameterList">
<Parameter name="file" type="string" value="../data/open-book-2D.exo" />
<Parameter name="format" type="string" value="Exodus II" />
</ParameterList>
</ParameterList>
</ParameterList>
Extracted Mesh
A mesh is created by lifting a subset of entities from a parent mesh. Locality is preserved, so all local entities in this mesh have parents whose entities are local on the parent mesh, so that no communication is ever done when passing info between an parent mesh and an extracted mesh.
Specified by “mesh type” of “extracted”.
mesh-extracted-spec
“parent domain”
[string]domain Parent mesh’s name.
ONE OF
“region”
[string]The Region name containing all surface faces.
OR
“regions”
[Array(string)]A list of Region names containing the surface faces.
END
“verify mesh”
[bool]false Verify validity of surface mesh.“export mesh to file”
[string]optional Export the lifted surface mesh to this filename.“create subcommunicator”
[bool]false If false, the communicator of this mesh is the same as the parent mesh. If true, the communicator of this mesh is the subset of the parent mesh comm that has entries on the surface.
Aliased Mesh
Aliased domains are simply domains that share a mesh with another domain. For instance, one might find it useful to define both a “surface water” and a “snow” domain that share a common “surface” mesh. In that case, typically the “surface” domain would point to the “surface” mesh, and the “snow” domain would be an “aliased” domain whose target is the “surface” mesh.
Specified by “mesh type” of “aliased”.
mesh-aliased-spec
“target”
[string]Mesh that this alias points to.
Domain Set Meshes
A collection of meshes formed by associating a new mesh with each entity of a region or set of indices. This includes generating a 1D column for each surface face of a semi-structured subsurface mesh, or for hanging logical meshes off of each surface cell as a subgrid model, etc.
The domain set meshes are then named “MESH_NAME:X” for each X, which can be a local ID of an entity (in the case of “domain set indexed”) or a region name (in the case of “domain set regions”).
Indexed domain set meshes are specified by “mesh type” of “domain set indexed”.
mesh-domain-set-indexed-spec
“regions”
[Array(string)]Regions from which indices are created.“entity kind”
[string]One of “cell”, “face”, etc. Entity of the region (usually “cell”) on which each mesh will be associated.“indexing parent domain”
[string]domain Mesh which includes the above region.“referencing parent domain”
[string]optional Mesh from which the entities of the mesh will be extracted. For instance, columns may be indexed from a surface mesh and referenced from the volume mesh below that surface.
Note, additionally, there must be a sublist of the name of the domain set, which itself is a “mesh-typed-spec”_, but may be missing some info (e.g. “entity LID”) that is filled in by this index.
Example:
<ParameterList name="column:*" type="ParameterList">
<Parameter name="mesh type" type="string" value="domain set indexed" />
<ParameterList name="domain set indexed parameters" type="ParameterList">
<Parameter name="indexing parent domain" type="string" value="surface" />
<Parameter name="entity kind" type="string" value="cell" />
<Parameter name="referencing parent domain" type="string" value="domain" />
<Parameter name="regions" type="Array(string)" value="{surface}" />
<ParameterList name="column:*" type="ParameterList">
<Parameter name="mesh type" type="string" value="column" />
<ParameterList name="column parameters" type="ParameterList">
<Parameter name="parent domain" type="string" value="domain" />
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Region-based domain set meshes are specified by “mesh type” of “domain set regions”.
mesh-domain-set-regions-spec
“regions”
[Array(string)]Regions from which indices are created.“entity kind”
[string]One of “cell”, “face”, etc. Entity of the region (usually “cell”) on which each mesh will be associated.“indexing parent domain”
[string]domain Mesh which includes the above region.“referencing parent domain”
[string]optional Mesh from which the entities of the mesh will be extracted. For instance, columns may be indexed from a surface mesh and referenced from the volume mesh below that surface.
Note, additionally, there must be a sublist of the name of the domain set, which itself is a “mesh-typed-spec”_, but may be missing some info (e.g. “region”) that is filled in by this domain set.
Example: the below example shows how to extract two subdomains, making them each a proper mesh whose communicators only live where they have cells, thereby decomposing the domain mesh into two subdomains.
<ParameterList name="watershed:*" type="ParameterList">
<Parameter name="mesh type" type="string" value="domain set regions" />
<ParameterList name="domain set regions parameters" type="ParameterList">
<Parameter name="indexing parent domain" type="string" value="domain" />
<Parameter name="entity kind" type="string" value="cell" />
<Parameter name="referencing parent domain" type="string" value="domain" />
<Parameter name="regions" type="Array(string)" value="{upstream, downstream}" />
<ParameterList name="watershed:*" type="ParameterList">
<Parameter name="mesh type" type="string" value="extracted" />
<ParameterList name="extracted parameters" type="ParameterList">
<Parameter name="parent domain" type="string" value="domain" />
<Parameter name="create subcommunicator" type="bool" value="true" />
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Column Meshes
Warning
Note these are rarely if ever created manually by a user. Instead use Domain Set Meshes, which generate a column mesh spec for every face of a set.
Specified by “mesh type” of “column”.
mesh-column-spec
“parent domain”
[string]The name of the 3D mesh from which columns are generated. Note that the “build columns from set” parameter must be set in that mesh.“entity LID”
[int]Local ID of the surface cell that is the top of the column.“verify mesh”
[bool]false Verify validity of surface mesh.“deformable mesh”
[bool]false Used for deformation PKs to allow non-const access.
Example:
<ParameterList name="mesh" type="ParameterList">
<ParameterList name="column" type="ParameterList">
<ParameterList name="column parameters" type="ParameterList">
<Parameter name="parent domain" type="string" value="domain" />
<Parameter name="entity LID" type="int" value="0" />
</ParameterList>
</ParameterList>
<ParameterList name="domain" type="ParameterList">
<Parameter name="mesh type" type="string" value="read mesh file" />
<ParameterList name="read mesh file parameters" type="ParameterList">
<Parameter name="file" type="string" value="../data/open-book-2D.exo" />
<Parameter name="format" type="string" value="Exodus II" />
</ParameterList>
</ParameterList>
</ParameterList>
Column Surface Meshes
Warning
Note these are rarely if ever created manually by a user. Instead use Domain Set Meshes, which generate a column surface mesh spec for every face of a set.
Specified by “mesh type” of “column surface”.
mesh-column-surface-spec
“parent domain”
[string]The name of the 3D mesh from which columns are generated. Note that the “build columns from set” parameter must be set in that mesh.“surface region”
[string]Region of the surface of the parent mesh.“verify mesh”
[bool]false Verify validity of surface mesh.“deformable mesh”
[bool]false Used for deformation PKs to allow non-const access.
Region
A geometric or discrete subdomain of the full domain.
Regions are geometrical constructs used to define subsets of the computational domain in order to specify the problem to be solved, and the output desired. Regions may represents zero-, one-, two- or three-dimensional subsets of physical space. For a three-dimensional problem, the simulation domain will be a three-dimensional region bounded by a set of two-dimensional regions. If the simulation domain is N-dimensional, the boundary conditions must be specified over a set of regions are (N-1)-dimensional.
Warning
Surface files contain labeled triangulated face sets. The user is responsible for ensuring that the intersections with other surfaces in the problem, including the boundaries, are exact (i.e. that surface intersections are watertight where applicable), and that the surfaces are contained within the computational domain. If nodes in the surface fall outside the domain, the elements they define are ignored.
Examples of surface files are given in the Exodus II file format here.
Warning
Region names must NOT be repeated.
Example:
<ParameterList> <!-- parent list -->
<ParameterList name="regions">
<ParameterList name="TOP SECTION">
<ParameterList name="region: box">
<Parameter name="low coordinate" type="Array(double)" value="{2, 3, 5}"/>
<Parameter name="high coordinate" type="Array(double)" value="{4, 5, 8}"/>
</ParameterList>
</ParameterList>
<ParameterList name="MIDDLE SECTION">
<ParameterList name="region: box">
<Parameter name="low coordinate" type="Array(double)" value="{2, 3, 3}"/>
<Parameter name="high coordinate" type="Array(double)" value="{4, 5, 5}"/>
</ParameterList>
</ParameterList>
<ParameterList name="BOTTOM SECTION">
<ParameterList name="region: box">
<Parameter name="low coordinate" type="Array(double)" value="{2, 3, 0}"/>
<Parameter name="high coordinate" type="Array(double)" value="{4, 5, 3}"/>
</ParameterList>
</ParameterList>
<ParameterList name="INFLOW SURFACE">
<ParameterList name="region: labeled set">
<Parameter name="label" type="string" value="sideset_2"/>
<Parameter name="file" type="string" value="F_area_mesh.exo"/>
<Parameter name="format" type="string" value="Exodus II"/>
<Parameter name="entity" type="string" value="face"/>
</ParameterList>
</ParameterList>
<ParameterList name="OUTFLOW PLANE">
<ParameterList name="region: plane">
<Parameter name="point" type="Array(double)" value="{0.5, 0.5, 0.5}"/>
<Parameter name="normal" type="Array(double)" value="{0, 0, 1}"/>
</ParameterList>
</ParameterList>
<ParameterList name="BLOODY SAND">
<ParameterList name="region: color function">
<Parameter name="file" type="string" value="F_area_col.txt"/>
<Parameter name="value" type="int" value="25"/>
</ParameterList>
</ParameterList>
<ParameterList name="FLUX PLANE">
<ParameterList name="region: polygon">
<Parameter name="number of points" type="int" value="5"/>
<Parameter name="points" type="Array(double)" value="{-0.5, -0.5, -0.5,
0.5, -0.5, -0.5,
0.8, 0.0, 0.0,
0.5, 0.5, 0.5,
-0.5, 0.5, 0.5}"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
In this example, TOP SECTION, MIDDLE SECTION and BOTTOM SECTION are three box-shaped volumetric regions. INFLOW SURFACE is a surface region defined in an Exodus II-formatted labeled set file and OUTFLOW PLANE is a planar region. BLOODY SAND is a volumetric region defined by the value 25 in color function file.
All
A region consisting of all entities on a mesh.
No parameters required.
[region-all-spec]
“empty”
[bool]True This is simply here to avoid issues with empty lists.
Example:
<ParameterList name="domain"> <!-- parent list -->
<ParameterList name="region: all">
</ParameterList>
</ParameterList>
Box
RegionBox: a rectangular region in space, defined by two corners
List region: box defines a region bounded by coordinate-aligned planes. Boxes are allowed to be of zero thickness in only one direction in which case they are equivalent to planes.
region-box-spec
“low coordinate”
[Array(double)]Location of the boundary point with the lowest coordinates.“high coordinate”
[Array(double)]Location of the boundary points with the highest coordinates.
Example:
<ParameterList name="WELL"> <!-- parent list -->
<ParameterList name="region: box">
<Parameter name="low coordinate" type="Array(double)" value="{-5.0,-5.0, -5.0}"/>
<Parameter name="high coordinate" type="Array(double)" value="{5.0, 5.0, 5.0}"/>
</ParameterList>
</ParameterList>
Plane
RegionPlane: A planar (infinite) region in space, defined by a point and a normal.
List region: plane defines a plane using a point lying on the plane and normal to the plane.
region-plane-spec
“normal”
[Array(double)]Normal to the plane.“point”
[Array(double)]Point in space.
Example:
<ParameterList name="TOP_SECTION"> <!-- parent list -->
<ParameterList name="region: plane">
<Parameter name="point" type="Array(double)" value="{2, 3, 5}"/>
<Parameter name="normal" type="Array(double)" value="{1, 1, 0}"/>
<ParameterList name="expert parameters">
<Parameter name="tolerance" type="double" value="1.0e-05"/>
</ParameterList>
</ParameterList>
</ParameterList>
Labeled Set
RegionLabeledSet: A region defined by a set of mesh entities in a mesh file
The list region: labeled set defines a named set of mesh entities existing in an input mesh file. This is the same file that contains the computational mesh. The name of the entity set is given by label. For example, a mesh file in the Exodus II format can be processed to tag cells, faces and/or nodes with specific labels, using a variety of external tools. Regions based on such sets are assigned a user-defined label for Amanzi, which may or may not correspond to the original label in the exodus file. Note that the file used to express this labeled set may be in any Amanzi-supported mesh format (the mesh format is specified in the parameters for this option). The entity parameter may be necessary to specify a unique set. For example, an Exodus file requires cell, face or node as well as a label (which is an integer). The resulting region will have the dimensionality associated with the entities in the indicated set.
region-labeled-set-spec
“label”
[string]Set per label defined in the mesh file.“file”
[string]File name.“format”
[string]Currently, we only support mesh files in the “Exodus II” format.“entity”
[string]Type of the mesh object (cell, face, etc).
Example:
<ParameterList name="AQUIFER">
<ParameterList name="region: labeled set">
<Parameter name="entity" type="string" value="cell"/>
<Parameter name="file" type="string" value="porflow4_4.exo"/>
<Parameter name="format" type="string" value="Exodus II"/>
<Parameter name="label" type="string" value="1"/>
</ParameterList>
</ParameterList>
Function Color
RegionFunctionColor: A region defined by the value of an indicator function in a file.
The list region: color function defines a region based a specified integer color, value, in a structured color function file, file. The format of the color function file is given below in the “Tabulated function file format” section. As shown in the file, the color values may be specified at the nodes or cells of the color function grid. A computational cell is assigned the ‘color’ of the data grid cell containing its cell centroid (cell-based colors) or the data grid nearest its cell-centroid (node-based colors). Computational cells sets are then built from all cells with the specified color Value.
In order to avoid, gaps and overlaps in specifying materials, it is strongly recommended that regions be defined using a single color function file.
region-color-function-spec
“file”
[string]File name containing color function.“value”
[int]Color that defines the set in the tabulated function file.
Example:
<ParameterList name="SOIL_TOP">
<ParameterList name="region: color function">
<Parameter name="file" type="string" value="geology_resamp_2D.tf3"/>
<Parameter name="value" type="int" value="1"/>
</ParameterList>
</ParameterList>
Point
RegionPoint: a point in space.
List region: point defines a point in space. This region consists of cells containing this point.
region-point-spec
“coordinate”
[Array(double)]Location of point in space.
Example:
<ParameterList name="DOWN_WIND150"> <!-- parent list defining the name -->
<ParameterList name="region: point">
<Parameter name="coordinate" type="Array(double)" value="{-150.0, 0.0, 0.0}"/>
</ParameterList>
</ParameterList>
Logical
RegionLogical: A region defined by a logical operation on one or two other regions
The list region: logical defines logical operations on regions allow for more advanced region definitions. At this time the logical region allows for logical operations on a list of regions. union and intersection are self-evident. In the case of subtraction, subtraction is performed from the first region in the list. The complement is a special case in that it is the only case that operates on single region, and returns the complement to it within the domain ENTIRE_DOMAIN. Currently, multi-region booleans are not supported in the same expression.
region-logical-spec
“operation”
[string]defines operation on the list of regions. One of: “union”, “intersect”, “subtract”, “complement”“regions”
[Array(string)]specifies the list of involved regions.
Example:
<ParameterList name="LOWER_LAYERs">
<ParameterList name="region: logical">
<Parameter name="operation" type="string" value="union"/>
<Parameter name="regions" type="Array(string)" value="{Middle1, Middle2, Bottom}"/>
</ParameterList>
</ParameterList>
Polygon
RegionPolygon: A closed polygonal segment of a plane.
The list region: polygon defines a polygonal region on which mesh faces and nodes can be queried. NOTE that one cannot ask for cells in a polygonal surface region. In 2D, the polygonal region is a line and is specified by 2 points. In 3D, the polygonal region is specified by an arbitrary number of points. In both cases the point coordinates are given as a linear array. The polygon can be non-convex.
This provides a set of faces with a normal for computing flux.
The polygonal surface region can be queried for a normal. In 2D, the normal is defined as [Vy,-Vx] where [Vx,Vy] is the vector from point 1 to point 2. In 3D, the normal of the polygon is defined by the order in which points are specified.
[region-polygon-spec]
“number of points”
[int]Number of polygon points.“points”
[Array(double)]Point coordinates in a linear array.
Example:
<ParameterList name="XY_PENTAGON">
<ParameterList name="region: polygon">
<Parameter name="number of points" type="int" value="5"/>
<Parameter name="points" type="Array(double)" value="{-0.5, -0.5, -0.5,
0.5, -0.5, -0.5,
0.8, 0.0, 0.0,
0.5, 0.5, 0.5,
-0.5, 0.5, 0.5}"/>
<ParameterList name="expert parameters">
<Parameter name="tolerance" type="double" value="1.0e-3"/>
</ParameterList>
</ParameterList>
</ParameterList>
Enumerated
RegionEnumerated: A region enumerated as a list of IDs.
List region: enumerated set defines a set of mesh entities via the list of input global ids. Note that global ids are not defined correctly when parallel mesh is created on a fly.
region-enumerated-spec
“entity”
[string]Type of the mesh object. One of: “cell”, “face”, “edge”, “node”“entity gids”
[Array(int)]List of the global IDs of the entities.
Example:
<ParameterList name="WELL"> <!-- parent list -->
<ParameterList name="region: enumerated set">
<Parameter name="entity" type="string" value="face"/>
<Parameter name="entity gids" type="Array(int)" value="{1, 12, 23, 34}"/>
</ParameterList>
</ParameterList>
Boundary
RegionBoundary: A region consisting of all entities on the domain boundary
List region: boundary defines a set of all boundary faces. Using this definition, faces located on the domain boundary are extracted.
region-boundary-spec
“entity”
[string]Type of the mesh object. Unclear whether this is used or can be other things than “face”?
Example:
<ParameterList name="DOMAIN_BOUNDARY"> <!-- parent list names the region -->
<ParameterList name="region: boundary">
<Parameter name="entity" type="string" value="face"/>
</ParameterList>
</ParameterList>
Box Volume Fractions
RegionBoxVolumeFractions: A rectangular region in space, defined by two corner points and normals to sides.
List region: box volume fraction defines a region bounded by a box not aligned with coordinate axes. Boxes are allowed to be of zero thickness in only one direction in which case they are equivalent to rectangles on a plane or segments on a line.
region-box-volume-fractions-spec
“corner coordinate”
[Array(double)]Location of one box corner.“opposite corner coordinate”
[Array(double)]Location of the opposite box corner.“normals”
[Array(double)]Normals to sides in a linear array. Default is columns of the identity matrix. The normals may be scaled arbitrarily but must be orthogonal to one another and form the right coordinate frame.
Example:
<ParameterList name="BASIN"> <!-- parent list -->
<ParameterList name="region: box volume fractions">
<Parameter name="corner coordinate" type="Array(double)" value="{-1.0,-1.0, 1.0}"/>
<Parameter name="opposite corner coordinate" type="Array(double)" value="{1.0, 1.0, 1.0}"/>
<Parameter name="normals" type="Array(double)" value="{1.0, 0.0, 0.0
0.0, 2.0, 0.0,
0.0, 0.0, 3.0}"/>
</ParameterList>
</ParameterList>
This example defines a degenerate box, a square on a surface z=1.
Line Segment
RegionLineSegment: A line segment, defined by two points in space.
List region: line segment desribes a region defined by a line segment. This region is a set of cells which intersect with a line segment. The line segment is allowed to intersect with one or more cells. Zero length line segments are allowed. The line segment is defined by its ends points.
region-line-segment-spec
“end coordinate”
[Array(double)]Location of one end of a line segment.“opposite end coordinate”
[Array(double)]Location of the opposite end of a line segment.
Example:
<ParameterList name="WELL"> <!-- parent list -->
<ParameterList name="region: line segment">
<Parameter name="end coordinate" type="Array(double)" value="{497542.44, 5393755.77, 0.0}"/>
<Parameter name="opposite end coordinate" type="Array(double)" value="{497542.44, 5393755.77, 100.0}"/>
</ParameterList>
</ParameterList>
Visualization
Manages simulation output to disk.
A user may request periodic writes of field data for the purposes of visualization in the “visualization” sublists.
ATS accepts a visualization list for each domain/mesh, including surface and column meshes. These are in separate ParameterLists, entitled “visualization” for the main mesh, and “visualization surface” on the surface mesh. It is expected that, for any addition meshes, each will have a domain name and therefore admit a spec of the form: “visualization DOMAIN-NAME”.
visualization-spec
“file name base”
[string]visdump_DOMAIN_data“dynamic mesh”
[bool]false Write mesh data for every visualization dump; this facilitates visualizing deforming meshes.“time unit”
[string]s A valid time unit to convert time into for output files. One of “s”, “d”, “y”, or “yr 365”
INCLUDES:
- [io-event-spec] An IOEvent spec
Example:
<ParameterList name="visualization">
<Parameter name="file name base" type="string" value="visdump_data"/>
<Parameter name="cycles start period stop" type="Array(int)" value="{0, 100, -1}" />
<Parameter name="cycles" type="Array(int)" value="{999, 1001}" />
<Parameter name="times start period stop 0" type="Array(double)" value="{0.0, 10.0, 100.0}"/>
<Parameter name="times start period stop 1" type="Array(double)" value="{100.0, 25.0, -1.0}"/>
<Parameter name="times" type="Array(double)" value="{101.0, 303.0, 422.0}"/>
<Parameter name="dynamic mesh" type="bool" value="false"/>
</ParameterList>
Checkpoint
Manages checkpoint/restart capability.
A user may request periodic dumps of ATS Checkpoint Data in the “checkpoint” sublist. The user has no explicit control over the content of these files, but has the guarantee that the ATS run will be reproducible (with accuracies determined by machine round errors and randomness due to execution in a parallel computing environment). Therefore, output controls for Checkpoint Data are limited to file name generation and writing frequency, by numerical cycle number. Unlike “visualization”, there is only one “checkpoint” list for all domains/meshes.
checkpoint-spec
“file name base”
[string]“checkpoint”“file name digits”
[int]5“single file checkpoint”
[bool]true If true, writes all checkpoint to one file. If false, uses a subdirectory with one file per mesh. false is required if meshes exist on other communicators than MPI_COMM_WORLD, but this is toggled if the code detects that this is necessary.
INCLUDES:
- [io-event-spec] An IOEvent spec
Example:
<ParameterList name="checkpoint">
<Parameter name="cycles start period stop" type="Array(int)" value="{0, 100, -1}" />
<Parameter name="cycles" type="Array(int)" value="{999, 1001}" />
<Parameter name="times start period stop 0" type="Array(double)" value="{0.0, 10.0, 100.0}"/>
<Parameter name="times start period stop 1" type="Array(double)" value="{100.0, 25.0, -1.0}"/>
<Parameter name="times" type="Array(double)" value="{101.0, 303.0, 422.0}"/>
</ParameterList>
In this example, checkpoint files are written when the cycle number is a multiple of 100, every 10 seconds for the first 100 seconds, and every 25 seconds thereafter, along with times 101, 303, and 422. Files will be written in the form: “checkpoint00000.h5”.
Observation
observation-spec
“observation output filename”
[string]user-defined name for the file that the observations are written to.“delimiter”
[string]COMMA Delimiter to split columns of the file“write interval”
[int]1 Interval of observations on which to flush IO files.“time units”
[string]s Controls the unit of the time column in the observation file.“domain”
[string]“domain” Can be used to set the communicator which writes (defaults to the standard subsurface domain).“observed quantities”
[observable-spec-list]A list of Observable objects that are all put in the same file.
INCLUDES:
[io-event-spec]An IOEvent spec
Note, for backwards compatibility, an observable-spec may be directly
included within the observation-spec if it is the only variable to be
observed in this file.
Observations are a localized-in-space but frequent-in-time view of simulation output, designed to get at useful diagnostic quantities such as hydrographs, total water content, quantities at a point, etc. These allow frequent collection in time without saving huge numbers of visualization files to do postprocessing. In fact, these should be though of as orthogonal data queries to visualization – vis is pointwise in time but complete in space, while observations are pointwise/finite in space but complete in time.
Observables describe what is observed – the variable, region, integration/averaging scheme, etc.
A user may request any number of specific observables. Each observable spec involves a field quantity, a reduction reduction operator, a region from which it will extract its source data, and a list of discrete times for its evaluation. The observations are evaluated during the simulation and written to disk by the UnstructuredObservation object.
observable-spec
“variable”
[string]any ATS variable used by any PK, e.g. “pressure” or “surface-water_content”“region”
[string]the label of a user-defined region“location name”
[string]cell The mesh location of the thing to be measured, i.e. “cell”, “face”, or “node”“number of vectors”
[int]1 Number of vector components to write.“degree of freedom”
[int]-1 Degree of freedom to write. Default of -1 implies writing all degrees of freedom.“reduction”
[string]the type of function to apply to the variable on the region. One of:“point” returns the value of the field quantity at a point. The region and location name should result in a single entity being selected.
“average” returns the volume-weighted average of the field across all entities in the region selected. This is likely what you want for intensive state variables such as “temperature” or “saturation_liquid”.
“integral” returns the volume-weighted sum of a variable over the region. This should be used for example on intensive sources, for instance “surface-precipitation”, to get the total source/sink.
“extensive integral” returns the sum of an variable over the region. This should be used for extensive quantities such as “water_content” or “energy” which already include the volume in their value.
“minimum” returns the min value over the region
“maximum” returns the max value over the region
“modifier”
[function-typedinline-spec]optional If provided, defines a function used to modify the “variable” prior to applying the “reduction”.“direction normalized flux”
[bool]false For flux observations, dots the face-normal flux with a vector to ensure fluxes are integrated pointing the same direction.“direction normalized flux direction”
[Array(double)]optional For flux observations, provides the vector to dot the face normal with. If this is not provided, then it is assumed that the faces integrated over are all boundary faces and that the default vector is the outward normal direction for each face.“direction normalized flux relative to region”
[string]optional If provided, the flux observation is assumed to be on a set of faces which are the exterior of a volumetric region. This region provides that volume, and fluxes are oriented in the “outward normal” direction relative to this region’s interior.“time integrated”
[bool]false If true, observe the time-integral, observing on all cycles and accumulating the backwards-Euler product of dt times the observable at the new time.
Process Kernels
Process Kernels, or PKs, are the fundamental unit of a model, and represent a single or system of Partial Differential Equations (PDEs) or Differential Algebraic Equations (DAEs). PKs are broadly split into individual equations (Physical PKs) and systems of equations, called Multi-Process Coordinators (MPCs).
The PK tree forms the fundamental definition of the entire system of equations to be solved by the simulator, and is represented by a single PK or a single MPC which couples other MPCs and/or Physical PKs.
Base PKs
There are several types of PKs, and each PK has its own valid input spec. However, there are three main types of PKs, from which nearly all PKs derive. Note that none of these are true PKs and cannot stand alone.
PK base class
The interface for a Process Kernel, an equation or system of equations.
A process kernel represents a single or system of partial/ordinary differential equation(s) or conservation law(s), and is used as the fundamental unit for coupling strategies.
Implementations of this interface typically are either an MPC (multi-process coupler) whose job is to heirarchically couple several other PKs and represent the system of equations, or a Physical PK, which represents a single equation.
Note there are two PK specs – the first is the “typed” spec, which appears in the “cycle driver” list in the PK tree and has no other parameters other than its type and its children. The second is the spec for the base class PK, which is inherited and included by each actual PK, lives in the “PKs” sublist of “main”, and has all needed parameters.
pk-typed-spec
“PK type”
[string]One of the registered PK types
Example:
<ParameterList name="PK tree">
<ParameterList name="Top level MPC">
<Parameter name="PK type" type="string" value="strong MPC"/>
<ParameterList name="sub PK 1">
...
</ParameterList>
<ParameterList name="sub PK 2">
...
</ParameterList>
...
</ParameterList>
</ParameterList>
pk-spec
“PK type”
[string]One of the registered PK types. Note this must match the corresponding entry in the[pk-typed-spec]“verbose object”
[verbose-object-spec]optional See Verbose Object
Example:
<ParameterList name="PKs">
<ParameterList name="my cool PK">
<Parameter name="PK type" type="string" value="my cool PK"/>
...
</ParameterList>
</ParameterList>
PK: Physical
A base class with default implementations of methods for a leaf of the PK tree (a conservation equation, or similar).
PKPhysicalBase is a base class providing some functionality for PKs which are defined on a single mesh, and represent a single process model. Typically all leaves of the PK tree will inherit from PKPhysicalBase.
pk-physical-default-spec
“domain name”
[string]Name from the Mesh list on which this PK is defined.“primary variable key”
[string]The primary variable e.g. “pressure”, or “temperature”. Most PKs supply sane defaults.“initial condition”
[initial-conditions-spec]See InitialConditions.“max valid change”
[double]-1 Sets a limiter on what is a valid change in a single timestep. Changes larger than this are declared invalid and the timestep shrinks. By default, any change is valid. Units are the same as the primary variable.
INCLUDES:
PK: BDF
A base class with default implementations of methods for a PK that can be implicitly integrated in time.
PKBDFBase is a base class from which PKs that want to use the BDF series of implicit time integrators must derive. It specifies both the BDFFnBase interface and implements some basic functionality for BDF PKs.
pk-bdf-default-spec
“initial time step [s]”
[double]1. Initial time step size [s]“assemble preconditioner”
[bool]true A flag, typically not set by user but by an MPC.“time integrator”
[bdf1-ti-spec]optional A TimeIntegrator. Note that this is only required if this PK is not strongly coupled to other PKs.“inverse”
[inverse-typed-spec]optional A Preconditioner. Note that this is only used if this PK is not strongly coupled to other PKs.
INCLUDES:
[pk-spec]This is a PK.
PK: Physical and BDF
Default implementation of both BDF and Physical PKs.
A base class for all PKs that are both physical, in the sense that they implement an equation and are not couplers, and BDF, in the sense that they support the implicit integration interface. This largely just supplies a default error norm based on error in conservation relative to the extent of the conserved quantity.
By default, the error norm used by solvers is given by:
\(ENORM(u, du) = |du| / ( a_tol + r_tol * |u| )\)
The defaults here are typically good, or else good defaults are set in the code, so usually are not supplied by the user.
pk-physical-bdf-default-spec
“conserved quantity key”
[string]Name of the conserved quantity. Usually a sane default is set by the PK.“absolute error tolerance”
[double]1.0 Absolute tolerance, \(a_tol\) in the equation above. Unit are the same as the conserved quantity. Note that this default is often overridden by PKs with more physical values, and very rarely are these set by the user.“relative error tolerance”
[double]1.0 Relative tolerance, \(r_tol\) in the equation above.[-]Note that this default can be overridden by PKs with more physical values, and very rarely are these set by the user.“flux error tolerance”
[double]1.0 Relative tolerance on the flux. Note that this default is often overridden by PKs with more physical values, and very rarely are these set by the user.
INCLUDES:
[pk-bdf-default-spec]Is a PK: BDF[pk-physical-default-spec]Is a PK: Physical
Physical PKs
Physical PKs are the physical capability implemented within ATS.
Flow PKs
Flow PKs describe the conservation of mass of water as it flows both above and below-ground. Subsurface flow PKs are based on 3D Richards equation, which describes variably saturated flow in porous media. Minor variations to this include the incorporation of freeze-thaw processes. Surface flow PKs are based on a diffusion wave equation and Manning’s model for sheet flow. Variations to this also include the incorporation of freeze-thaw processes. Finally we include in flow a “snow distribution” algorithm which takes as input precipitation and applies it based on the existing surface level (elevation + water + snowpack), thereby “filling in” low-lying areas preferentially. This makes for more accurate snowpacks at fine scales.
Richards PK
Two-phase, variable density Richards equation.
Solves Richards equation:
richards-spec
“domain”
[string]“domain” Defaults to the subsurface mesh.“primary variable key”
[string]The primary variable associated with this PK, typically “DOMAIN-pressure” Note there is no default – this must be provided by the user.“boundary conditions”
[list]Defaults to Neuman, 0 normal flux. See Flow-specific Boundary Conditions“permeability type”
[string]scalar This controls the number of values needed to specify the absolute permeability. One of:“scalar” Requires one scalar value.
“horizontal and vertical” Requires two values, horizontal then vertical.
“diagonal tensor” Requires dim values: {xx, yy} or {xx, yy, zz}
“full tensor”. (Note symmetry is required.) Either {xx, yy, xy} or {xx,yy,zz,xy,xz,yz}.
“water retention evaluator”
[wrm-evaluator-spec]The water retention curve. This needs to go away, and should get moved to State.
IF
“source term”
[bool]false Is there a source term?
THEN
“source key”
[string]DOMAIN-water_source Typically not set, as the default is good.[mol s^-1]“source term is differentiable”
[bool]true Can the source term be differentiated with respect to the primary variable?“explicit source term”
[bool]false Apply the source term from the previous time step.
END
Math and solver algorithm options:
“diffusion”
[pde-diffusion-spec]The (forward) diffusion operator, see PDE_Diffusion.“diffusion preconditioner”
[pde-diffusion-spec]optional The inverse of the diffusion operator. See PDE_Diffusion. Typically this is only needed to set Jacobian options, as all others probably should match those in “diffusion”, and default to those values.“surface rel perm strategy”
[string]none Approach for specifying the relative permeabiilty on the surface face. “clobber” is frequently used for cases where a surface rel perm will be provided. One of:“none” : use the upwind direction to determine whether to use the boundary face or internal cell
“clobber” : always use the boundary face rel perm
“max” : use the max of the boundary face and internal cell values
“unsaturated” : Uses the boundary face when the internal cell is not saturated.
“relative permeability method”
[string]upwind with Darcy flux Relative permeability is defined on cells, but must be calculated on faces to multiply a flux. There are several methods commonly used. Note these can significantly change answers – you don’t want to change these unless you know what they mean. One of:“upwind with Darcy flux” First-order upwind method that is most common
“upwind with gravity” Upwinds according to the gravitational flux direction
“cell centered” This corresponds to the harmonic mean, and is most accurate if the problem is always wet, but has issues when it is dry.
“arithmetic mean” Face value is the mean of the neighboring cells. Not a good method.
Globalization and other process-based hacks:
“modify predictor with consistent faces”
[bool]false In a face+cell diffusion discretization, this modifies the predictor to make sure that faces, which are a DAE, are consistent with the predicted cells (i.e. face fluxes from each sides match).“modify predictor for flux BCs”
[bool]false Infiltration into dry ground can be hard on solvers – this tries to do the local nonlinear problem to ensure that face pressures are consistent with the prescribed flux in a predictor.“modify predictor via water content”
[bool]false Modifies the predictor using the method of Krabbenhoft [??] paper. Effectively does a change of variables, extrapolating not in pressure but in water content, then takes the smaller of the two extrapolants.“max valid change in saturation in a time step [-]”
[double]-1 Rejects timesteps whose max saturation change is greater than this value. This can be useful to ensure temporally resolved solutions. Usually a good value is 0.1 or 0.2.“max valid change in ice saturation in a time step [-]”
[double]-1 Rejects timesteps whose max ice saturation change is greater than this value. This can be useful to ensure temporally resolved solutions. Usually a good value is 0.1 or 0.2.“limit correction to pressure change [Pa]”
[double]-1 If > 0, this limits an iterate’s max pressure change to this value. Not usually helpful.“limit correction to pressure change when crossing atmospheric [Pa]”
[double]-1 If > 0, this limits an iterate’s max pressure change to this value when they cross atmospheric pressure. Not usually helpful.
Discretization / operators / solver controls:
“accumulation preconditioner”
[pde-accumulation-spec]optional The inverse of the accumulation operator. See PDE_Accumulation. Typically not provided by users, as defaults are correct.“absolute error tolerance”
[double]2750.0 in units of [mol].“compute boundary values”
[bool]false Used to include boundary face unknowns on discretizations that are cell-only (e.g. FV). This can be useful for surface flow or other wierd boundary conditions. Usually provided by MPCs that need them.
Physics control:
“permeability rescaling”
[double]1e7 Typically 1e7 or order \(sqrt(K)\) is about right. This rescales things to stop from multiplying by small numbers (permeability) and then by large number (\(\rho / \mu\)).
IF
“coupled to surface via flux”
[bool]false If true, apply surface boundary conditions from an exchange flux. Note, if this is a coupled problem, it is probably set by the MPC. No need for a user to set it.
THEN
“surface-subsurface flux key”
[string]DOMAIN-surface_subsurface_flux
END
“coupled to surface via head”
[bool]false If true, apply surface boundary conditions from the surface pressure (Dirichlet).
Permafrost Flow PK
A three-phase, thermal Richard’s equation with water, water vapor, and ice for permafrost applications.
Note that the only difference between permafrost and richards is in constitutive relations – the WRM changes to provide three saturations, while the water content changes to account for water in ice phase. As these are now drop-in field evaluators, there is very little to change in the PK.
In the future, this should not even need a different PK.
permafrost-spec
“saturation ice key”
[string]“DOMAIN-saturation_ice” volume fraction of the ice phase (only when relevant)[-]Typically the default is correct.
INCLUDES:
[richards-spec]See Richards PK
Overland Flow PK
Overland flow using the diffusion wave equation.
Solves the diffusion wave equation for overland flow with pressure as a primary variable:
overland-pressure-spec
Keys name variables:
“domain”
[string]“surface” Defaults to the extracted surface mesh.“primary variable”
[string]The primary variable associated with this PK, typically “DOMAIN-pressure” Note there is no default – this must be provided by the user.“boundary conditions”
[list]Defaults to Neuman, 0 normal flux.“overland conductivity evaluator”
[list]See Overland Conductivity Evaluator.
IF
“source term”
[bool]false Is there a source term?
THEN
“source key”
[string]DOMAIN-water_source Typically not set, as the default is good.[m s^-1]or[mol s^-1]“water source in meters”
[bool]true Is the source term in[m s^-1]?“source term is differentiable”
[bool]true Can the source term be differentiated with respect to the primary variable?
END
Math and solver algorithm options:
“diffusion”
[pde-diffusion-spec]The (forward) diffusion operator, see PDE_Diffusion.“diffusion preconditioner”
[pde-diffusion-spec]optional The inverse of the diffusion operator. See PDE_Diffusion. Typically this is only needed to set Jacobian options, as all others probably should match those in “diffusion”, and default to those values.“absolute error tolerance”
[double]550. Defaults to 1 cm of water. A small, but significant, amount of water.“limit correction to pressure change [Pa]”
[double]-1 If > 0, this limits an iterate’s max pressure change to this value. Not usually helpful.“limit correction to pressure change when crossing atmospheric [Pa]”
[double]-1 If > 0, this limits an iterate’s max pressure change to this value when they cross atmospheric pressure. Not usually helpful.“allow no negative ponded depths”
[bool]false Modifies all correction updates to ensure only positive ponded depth is allowed.“min ponded depth for velocity calculation”
[double]1.e-2 For ponded depth below this height, declare the velocity 0.“min ponded depth for tidal bc”
[double]0.02 Control on the tidal boundary condition. TODO: This should live in the BC spec?
INCLUDES:
[pk-physical-bdf-default-spec]A PK: Physical and BDF spec.
Everything below this point is usually not provided by the user, but are documented here for completeness.
Keys name variables:
“conserved quantity key”
[string]DOMAIN-water_content Typically not set, as the default is good.[mol]“elevation key”
[string]DOMAIN-elevation Typically not set, as the default is good.[mol]“slope magnitude key”
[string]DOMAIN-slope_magnitude Typically not set, as the default is good.[mol]
Algorithmic parameters:
“coupled to subsurface via flux”
[bool]false Set by MPC.“coupled to subsurface via head”
[bool]false Set by MPC.“accumulation preconditioner”
[pde-accumulation-spec]optional The inverse of the accumulation operator. See PDE_Accumulation. Typically not provided by users, as defaults are correct.
EVALUATORS:
“conserved quantity”
“water content”
“cell volume”
“surface_subsurface_flux”
“elevation”
“slope magnitude”
“overland_conductivity”
“ponded_depth”
“pres_elev”
“source”
Overland Flow with Ice
Two-phase overland flow equation.
This modifies the diffusion wave equation for overland flow that includes freeze-thaw processes. This class could completely go away, but it does some error checking on the input file to make sure freeze-thaw processes are done correctly. In the future this service should be done by a preprocessor generating the input file, and this class would go away.
Snow Distribution PK
Preferential distribution of snow precip in low-lying areas.
This PK is a heuristic PK that distributes incoming snow precipitation using a diffusion wave equation. Think of it as an analogue to overland flow – it effectively ensures that new snow “flows downhill,” due to a uniformly random direction and strength wind, and lands on the lowest lying areas.
Tweaking the snow-manning_coefficient lets you play with how uniform the snow layer ends up. Most of the parameters are set by your snow precipitation input data interval. The details of this are a bit tricky mathematically, and it may take some fiddling with parameters to do this correctly if your data is not daily (which all defaults are set for).
snow-distribution-spec
“distribution time”
[double]86400. Interval of snow precip input dataset. [s]“precipitation function”
[function-spec]Snow precipitation function, see Functions.“diffusion”
[pde-diffusion-spec]Diffusion drives the distribution. Typically we use finite volume here. See PDE_Diffusion“diffusion preconditioner”
[pde-diffusion-spec]Inverse of the above. Likely only Jacobian term options are needed here, as the others default to the same as the “diffusion” list. See PDE_Diffusion.“inverse”
[inverse-typed-spec]Inverse method for the solve.
Not typically provided by the user, defaults are good:
“accumulation preconditioner”
[pde-accumulation-spec]See PDE_Accumulation.
Transport PK
The Transport PK describes the conservation of mass of components transported with water as it flows. The transport PK is based on the advection-diffusion equation, applies to one or more components that are dissolved in the aqueous phase, and is currently used in both surface and subsurface compartments. The key difference between surface and subsurface transport is in capturing the volume of water. In the subsurface, the volume of water is set by the porosity and saturation of the porous medium, while in the surface it is set by the ponded depth.
The advection-diffusion equation for component i in partially saturated porous media may be written as
The advection-diffusion equation for component i in the surface may be written as
transport-spec
“PK type”
[string]“transport ats”“domain name”
[string]domain specifies mesh name that defines the domain of this PK.“component names”
[Array(string)]No default. Provides the names of the components that will be transported. Must be in the order: aqueous, gaseous, solid.“number of aqueous components”
[int]-1 The total number of aqueous components. Default value is the length of “component names”“number of gaseous components”
[int]0 The total number of gaseous components.“boundary conditions”
[transport-bc-spec]Boundary conditions for transport are dependent on the boundary conditions for flow. See Flow-specific Boundary Conditions and Transport-specific Boundary Conditions“component molar masses”
[Array(double)]No default. Molar mass of each component.“molecular diffusion”
[molecular-diffusion-spec]defines names of solutes in aqueous and gaseous phases and related diffusivity values.“material properties”
[material-properties-spec-list]Defines material properties see below).
Source terms:
“source terms”
[transport-source-spec-list]Provides solute source.
Physical model and assumptions:
“physical models and assumptions” [material-properties-spec] Defines material properties.
“effective transport porosity”
[bool]false If true, effective transport porosity will be used by dispersive-diffusive fluxes instead of total porosity.
Math and solver algorithm options:
“diffusion”
[pde-diffusion-spec]Diffusion drives the distribution. Typically we use finite volume here. See PDE_Diffusion“diffusion preconditioner”
[pde-diffusion-spec]Inverse of the above. Likely only Jacobian term options are needed here, as the others default to the same as the “diffusion” list. See PDE_Diffusion.“inverse”
[inverse-typed-spec]Inverse method for the solve.“cfl” [double] Time step limiter, a number less than 1. Default value is 1.
“spatial discretization order” [int] defines accuracy of spatial discretization. It permits values 1 or 2. Default value is 1.
“temporal discretization order” [int] defines accuracy of temporal discretization. It permits values 1 or 2 and values 3 or 4 when expert parameter “generic RK implementation” is set to true. Note that RK3 is not monotone. Default value is 1.
- “reconstruction” [list] collects reconstruction parameters. The available options are
describe in the separate section below.
- “transport subcycling”
[bool]true The code will default to subcycling for transport within the master PK if there is one.
- “transport subcycling”
Developer parameters:
- “enable internal tests” [bool] turns on various internal tests during
run time. Default value is “false”.
- “generic RK implementation” [bool] leads to generic implementation of
all Runge-Kutta methods. Default value is “false”.
- “internal tests tolerance” [double] tolerance for internal tests such as the
divergence-free condition. The default value is 1e-6.
- “runtime diagnostics: solute names” [Array(string)] defines solutes that will be
tracked closely each time step if verbosity “high”. Default value is the first solute in the global list of “aqueous names” and the first gas in the global list of “gaseous names”.
- “runtime diagnostics: regions” [Array(string)] defines a boundary region for
tracking solutes. Default value is a seepage face boundary, see Flow PK.
KEYS
- “saturation liquid” This variable is a multiplier in in the
accumulation term. For subsurface transport, this will typically be the saturation (“saturation_liquid”). For surface transport, this will typically be the ponded depth (“ponded_depth”).
“previous saturation liquid”
- “molar density liquid” Transport is solved
for concentrations in units of mol fractions. Molar density is needed for conversion.
“water flux”
- “water source” Defines the water injection rate [mol H2O m^-2 s^-1] in
surface and [mol H2O m^-3 s^-1] in subsurface) which applies to concentrations specified by the “geochemical conditions”. Note that if this PK is coupled to a surface flow PK, the unit of the water source there must be in [mol m^-2 s^-1], not in [m s^-1] as is an option for that PK (e.g. “water source in meters” must be set to “false” in the overland flow PK).
The injection rate of a solute [molC s^-1], when given as the product of a concentration and a water source, is evaluated as:
- Concentration [mol C L^-1] *
1000 [L m^-3] of water * water source [mol H2O m^-3 s^-1] * volume of injection domain [m^3] / molar density of water [mol H2O m^-3]
molecular-diffusion-spec
“aqueous names”
[Array(string)]List of aqueous component names to be diffused.“aqueous values”
[Array(string)]Diffusivities of each component.
<ParameterList name="molecular diffusion">
<Parameter name="aqueous names" type=Array(string)" value="{CO2(l),Tc-99}"/>
<Parameter name="aqueous values" type=Array(double)" value="{1e-8,1e-9}"/>
</ParameterList>
material-properties-spec
“region”
[Array(string)]Defines geometric regions for material SOIL.“model”
[string]scalar Defines dispersivity model. One of:“scalar” : scalar dispersivity
“Bear” : dispersion split into along- and across- velocity
“Burnett-Frind”
“Lichtner-Kelkar-Robinson”
“parameters for MODEL”
[list]where “MODEL” is the model name.
IF model == scalar
ONE OF
“alpha”
[double]defines dispersivity in all directions, [m].
OR
“dispersion coefficient”
[double]defines dispersion coefficient [m^2 s^-1].
END
ELSE IF model == Bear
“alpha_l”
[double]defines dispersion in the direction of Darcy velocity, [m].“alpha_t”
[double]defines dispersion in the orthogonal direction, [m].
ELSE IF model == Burnett-Frind
“alphaL”
[double]defines the longitudinal dispersion in the direction of Darcy velocity, [m].“alpha_th”
[double]Defines the transverse dispersion in the horizonal direction orthogonal directions, [m].“alpha_tv”
[double]Defines dispersion in the orthogonal directions, [m]. When “alpha_th” equals to “alpha_tv”, we obtain dispersion in the direction of the Darcy velocity.
ELSE IF model == Lichtner-Kelker-Robinson
“alpha_lh”
[double]defines the longitudinal dispersion in the horizontal direction, [m].“alpha_lv”
[double]Defines the longitudinal dispersion in the vertical direction, [m]. When “alpha_lh” equals to “alpha_lv”, we obtain dispersion in the direction of the Darcy velocity.“alpha_th”
[double]Defines the transverse dispersion in the horizontal direction orthogonal directions, [m].“alpha_tv” ``[double]` Defines dispersion in the orthogonal directions. When “alpha_th” equals to “alpha_tv”, we obtain dispersion in the direction of the Darcy velocity.
END
“aqueous tortuosity”
[double]Defines tortuosity for calculating diffusivity of liquid solutes, [-].“gaseous tortuosity”
[double]Defines tortuosity for calculating diffusivity of gas solutes, [-].
transport-source-spec
“component mass source”
[list]Defines solute source injection rate.“spatial distribution method”
[string]One of:“volume”, source is considered as extensive quantity [molC s^-1] and is evenly distributed across the region.
“none”, source is considered as intensive quantity. [molC m^-2 s^-1] in surface and [molC m^-3 s^-1] in subsurface
“geochemical”
[list]Defines a source by setting solute concentration for all components (in moles/L) and an injection rate given by the water source. Currently, this option is only available for Alquimia provided geochemical conditions.“geochemical conditions”
[Array(string)]List of geochemical constraints providing concentration for solute injection.
Energy PKs
Energy PKs describe the conservation of energy as it is advected and diffuses both above and below-ground. Both surface and subsurface energy equations are based on a simple advection-diffusion equation, and include variants with and without freeze-thaw processes.
Energy Base PK
An advection-diffusion equation for energy.
Solves an advection-diffusion equation for energy:
energy-pk-spec
“domain”
[string]“domain” Defaults to the subsurface mesh.“primary variable”
[string]The primary variable associated with this PK, typically “DOMAIN-temperature” Note there is no default – this must be provided by the user.“boundary conditions”
[list]Defaults to 0 diffusive flux boundary condition. See Energy-specific Boundary Conditions“thermal conductivity evaluator”
[list]The thermal conductivity. This needs to go away, and should get moved to State.“absolute error tolerance”
[double]76.e-6 A small amount of energy, see error norm. [MJ]“upwind conductivity method”
[string]arithmetic mean Method of moving cell-based thermal conductivities onto faces. One of:“arithmetic mean” the default, average of neighboring cells
“cell centered” harmonic mean
IF
“explicit advection”
[bool]false Treat the advection term implicitly.
ELSE
“supress advective terms in preconditioner”
[bool]false Typically subsurface energy equations are strongly diffusion dominated, and the advective terms may add little. With this flag on, we ignore theem in the preconditioner, making an easier linear solve and often not negatively impacting the nonlinear solve.“advection preconditioner”
[list]optional Typically defaults are correct.
END
“diffusion”
[pde-diffusion-spec]See PDE_Diffusion, the diffusion operator.“diffusion preconditioner”
[pde-diffusion-spec]See PDE_Diffusion, the inverse operator. Typically only adds Jacobian terms, as all the rest default to those values from “diffusion”.
IF
“source term”
[bool]false Is there a source term?
THEN
“source key”
[string]DOMAIN-total_energy_source Typically not set, as the default is good.[MJ s^-1]“source term is differentiable”
[bool]true Can the source term be differentiated with respect to the primary variable?“source term finite difference”
[bool]false If the source term is not diffferentiable, we can do a finite difference approximation of this derivative anyway. This is useful for difficult-to-differentiate terms like a surface energy balance, which includes many terms.
END
Globalization:
“modify predictor with consistent faces”
[bool]false In a face+cell diffusion discretization, this modifies the predictor to make sure that faces, which are a DAE, are consistent with the predicted cells (i.e. face fluxes from each sides match).“modify predictor for freezing”
[bool]false A simple limiter that keeps temperature corrections from jumping over the phase change.“limit correction to temperature change [K]”
[double]-1.0 If > 0, stops nonlinear updates from being too big through clipping.
The following are rarely set by the user, as the defaults are typically right.
“advection”
[list]optional The PDE_Advection spec. Only one current implementation, so defaults are typically fine.“accumulation preconditioner”
[pde-accumulation-spec]optional The inverse of the accumulation operator. See PDE_Accumulation. Typically not provided by users, as defaults are correct.
IF
“coupled to surface via flux”
[bool]false If true, apply surface boundary conditions from an exchange flux. Note, if this is a coupled problem, it is probably set by the MPC. No need for a user to set it.
THEN
“surface-subsurface energy flux key”
[string]DOMAIN-surface_subsurface_energy_flux
END
“coupled to surface via temperature”
[bool]false If true, apply surface boundary conditions from the surface temperature (Dirichlet).
KEYS:
“conserved quantity” DOMAIN-energy The total energy \(E\) [MJ]
“energy” DOMAIN-energy The total energy \(E\), also the conserved quantity. [MJ]
“water content” DOMAIN-water_content The total mass \(\Theta\), used in error norm [mol]
“enthalpy” DOMAIN-enthalpy The specific enthalpy :math`e` [MJ mol^-1]
“flux” DOMAIN-water_flux The water flux \(\mathbf{q}\) used in advection. [mol s^-1]
“diffusive energy” DOMAIN-diffusive_energy_flux \(\mathbf{q_e}\) [MJ s^-1]
“advected energy” DOMAIN-advected_energy_flux \(\mathbf{q_e^{adv}} = q e\) [MJ s^-1]
“thermal conductivity” DOMAIN-thermal_conductivity Thermal conductivity on cells [W m^-1 K^-1]
“upwinded thermal conductivity” DOMAIN-upwinded_thermal_conductivity Thermal conductivity on faces [W m^-1 K^-1]
EVALUATORS:
“source term” optional If source key is provided.
“enthalpy”
“cell volume”
“thermal conductivity”
“conserved quantity”
“energy”
Two-Phase subsurface Energy PK
An advection-diffusion equation for energy in two phases.
This is simply a subsurface energy equation that places a few more requirements on the base class. It could probably go away if we refactor to remove hard-coded evaluators.
Three-Phase subsurface Energy PK
An advection-diffusion equation for energy in three phases.
This is simply a subsurface energy equation that places a few more requirements on the base class. It could probably go away if we refactor to remove hard-coded evaluators.
Overland energy with Ice
An advection-diffusion equation for surface energy in two phases.
This is simply a surface energy equation that places a few more requirements on the base class. It could probably go away if we refactor to remove hard-coded evaluators.
energy-surface-ice-pk-spec
These are typically not set by the user:
“coupled to subsurface via temperature”
[bool]false A coupling scheme, provided by MPC.“coupled to subsurface via flux”
[bool]false A coupling scheme, provided by MPC.“subsurface domain name”
[string]optional If one of the above coupling schemes is turned on, we need to know the subsurface mesh. Provided by MPC.
INCLUDES:
[energy-pk-spec]See Energy Base PK
Surface Energy Balance PKs
Integrated hydrology is not much use without significant process complexity in source terms coming from the ecohydrologic environment. These include straightforward sources, like precipitation, but also more complicated ones such as evaporation and transpiration.
These terms are almost always tied up in a surface energy balance – evaporation and transpiration are driven by vapor pressure gradients between the atmosphere and the surface (either snow, ponded water, soil, or leaf). Solving a surface energy balance often requires providing a bunch of terms, including radiated energy, conducted energy, latent and sensible heat models, etc.
ATS currently has several approaches to calculating these – see ats-demos examples on ecohydrology for a more in-depth discussion.
Balance Equation
A simple conservation ODE.
This is a very simple vector of ODEs, useful in balance equations, where the time derivative of a conserved quantity is determined by a bunch of sources and sinks.
balance-pk-spec
“primary variable key”
[string]The primary variable associated with this PK. Note there is no default – this must be provided by the user.“conserved quantity key”
[string]The conserved quantity \(\Phi\)“source key”
[string]DOMAIN-source_sink Units are in conserved quantity per second per cell volume.“time discretization theta”
[double]1.0 \(\theta\) in a Crank-Nicholson time integration scheme. 1.0 implies fully implicit, 0.0 implies explicit, 0.5 implies C-N.“modify predictor positivity preserving”
[bool]false If true, predictors are modified to ensure that the conserved quantity is always > 0.“absolute error tolerance”
[double]550.0 a_tol in the standard error norm calculation. Defaults to a small amount of water. Units are the same as the conserved quantity.
INCLUDES:
[pk-physical-bdf-default-spec]
Snow Balance Equation
An implicit PK for surface balance snow SWE conservation.
This is a balance PK whose conserved quantity is snow SWE. The energy balance comes in as it provides the energy needed to melt snow. So source terms include snow precipitation and snowmelt. It also manages snow density, which should get rethought a bit.
There is also some wierd hackiness here about area fractions – see ATS Issue #8
subgrid-balance-pk-spec
“absolute error tolerance”
[double]0.01[m]
INCLUDES:
[balance-pk-spec]This is a Balance Equation
Not typically set by user, defaults work:
“conserved quantity key”
[string]DOMAIN-snow_water_equivalent Sets the default conserved quantity key, so this is likely not supplied by the user. [m]“snow density key”
[string]DOMAIN-density Default snow density key. [kg m^-3]“snow age key”
[string]DOMAIN-age Default snow age key. [d]“new snow key”
[string]DOMAIN-source Default new snow key. [m SWE s^-1]“area fractions key”
[string]DOMAIN-fractional_areas Subgrid model fractional areas, see note above. [-]“snow death rate key”
[string]DOMAIN-death_rate Deals with last tiny bit of snowmelt.
Biogeochemistry
To accurately predict watershed ecohydrology, a carbon cycle model is needed to predict transpiration. By simulating a carbon cycle, we are able to predict the rate of photosynthesis as a function of space and time, and photosynthesis governs root water uptake. Currently only one big-leaf model is available, but ongoing work is wrapping a generalized Common/Colorado Land Model based on that developed within the ParFlow team, and another ongoing project is working on wrapping kernels from E3SM’s Land Model.
Biogeochemistry – Monolithic Version
Above and below-ground carbon cycle model.
This is a multi-leaf layer, big-leaf vegetation model coupled to a Century model for belowground carbon decomposition.
It leverages a PFT-based structure which allows multiple height-sorted PFTs to coexist on the same grid cells, with the shorter PFTs getting whatever light is left in the understory.
The implementation is based on an old, standalone code by Chonggang Xu, and adapted for ATS. While this is not simple, it is called BGC simple as it is about the least amount of complexity required to get a reasonable carbon cycle into ATS.
Outputs of this include transpiration, a critical sink for hydrology, as it solves photosynthesis based on water availability.
Note this is an “explicit update PK,” or effectively a forward Euler timestep that is not written in ODE form.
Note this works on both the surface (vegetation) and subsurface (decomposition) meshes. It is required that the subsurface mesh is a “columnar” mesh, and that build_columns in the subsurface Mesh spec has been supplied.
bgc-simple-spec
“initial time step”
[double]1.0 Initial time step size [s]“number of carbon pools”
[int]7 Unclear whether this can actually change?“soil carbon parameters”
[soil-carbon-spec-list]List of soil carbon parameters by soil mesh partition region name.“pft parameters”
[pft-spec-list]List of PFT parameters by PFT name.“latitude [degrees]”
[double]60 Latitude of the simulation in degrees. Used in radiation balance.“wind speed reference height [m]”
[double]2.0 Reference height of the wind speed dataset.“cryoturbation mixing coefficient [cm^2/yr]”
[double]5.0 Controls diffusion of carbon into the subsurface via cryoturbation.“leaf biomass initial condition”
[initial-conditions-spec]Sets the leaf biomass IC.“domain name”
[string]domain“surface domain name”
[string]surface“transpiration key”
[string]DOMAIN-transpiration The distributed transpiration flux [mol s^-1]“shaded shortwave radiation key”
[string]SURFACE_DOMAIN-shaded_shortwave_radiation Shortwave radiation that gets past the canopy and teo the bare ground for soil evaporation. [W m^-2]“total leaf area index key”
[string]SURFACE_DOMAIN-total_leaf_area_index Total LAI across all PFTs.
EVALUATORS:
“temperature” The soil temperature [K]
“pressure” soil mafic potential [Pa]
“surface-cell_volume” [m^2]
“surface-incoming shortwave radiation” [W m^-2]
“surface-air_temperature” [K]
“surface-vapor_pressure_air” [Pa]
“surface-wind_speed” [m s^-1]
“surface-co2_concentration” [ppm]
Deformation
The unstructured mesh framework we use provides the opportunity to include deformation of the mesh. This deformation can be done in two ways – either node coordinate changes are provided, or volumetric changes are provided, and the code attempts to iterate toward a global coordinate change that satisfies these volumetric changes. The latter can be somewhat fragile for large deformation, but it does allow simple deformation such as small, somewhat uniform subsidence. The volumetric deformation PK below does this based on a volumetric change given by loss of bulk ice.
Volumetric Deformation
Subsidence through bulk ice loss and cell volumetric change.
This process kernel provides for going from a cell volumetric change to an updated unstructured mesh, and can be coupled sequentially with flow to solve problems of flow in a subsiding porous media.
Note that this PK is slaved to the flow PK. This PK must be advanced first, and be weakly coupled to the flow PK (or an MPC that advances the flow PK), and the timestep of this PK must match that of the flow PK (e.g. do not try to subcyle one or the other). This uses a rather hacky, unconventional use of time tags, where we use saturations and porosities at the NEXT time, but ASSUME they are actually the values of the CURRENT time. This saves having to stash a copy of these variables at the CURRENT time, which would otherwise not be used.
Note that all deformation here is vertical, and we assume that the subsurface mesh is perfectly columnar and that the “build columns” parameter has been given to the subsurface mesh. See the Mesh spec for more.
The process here is governed through two options, the “deformation mode” and the “deformation strategy.”
The deformation mode describes how the cell volume change is calculated. There are three options here:
“prescribed” uses a function to precribe the volume changes as a function of (t,x,y,z).
“structural” decreases the cell volume if the porosity is above a prescribed “structurally connected matrix” porosity. Think of this as bulk ice “propping up” the soil grains – as that bulk ice melts, it reduces porosity toward the porosity in at which grains start to touch again and can be structurally sound.
“saturation” is a heuristic that considers the liquid saturation directly, and tries to relax the liquid saturation back toward a value that is consistent with what the thawed soil should be.
The deformation strategy describes how the cell volume change is turned into node coordinate changes. Three options are available:
“average” simply takes the average of volume change/surface area and horizontally averages this quantity across all neighbors. While this has the advantage of being simple, it has issues when thaw gradients in the horizontal are not zero, as it may result in the loss of volume in a fully frozen cell, blowing up the pressure and breaking the code. This is great when it works, but it almost never works in real problems, except in column-based models, where it is perfect.
“mstk implementation” MSTK implements an iterated, local optimization method that, one-at-a-time, moves nodes to try and match the volumes. This has fewer issues with overfitting, but doesn’t always do sane things, and can be expensive if iterations don’t work well. This is not particularly robust either, but it seems to be the preferred method for 2D/3D problems.
“global optimization” attempts to directly form and solve the minimization problem to find the nodal changes that result in the target volumetric changes. Note this has issues with overfitting, so penalty methods are used to smooth the solution of the problem. This is currently disabled.
NOTE: all deformation options are treated EXPLICITLY, and depend only upon values from the old time.
volumetric-deformation-pk-spec
“max time step [s]”
[double]inf Sets a maximum time step size.“deformation mode”
[string]prescribed See above for descriptions. One of: “prescribed”, “structural”, or “saturation”.“deformation strategy”
[string]global optimization See above for descriptions. One of “average”, “global optimization”, or “mstk implementation”“domain name”
[string]domain The mesh to deform.“surface domain name”
[string]surface The surface mesh.“deformation function”
[function-spec]optional Only used if “deformation mode” == “prescribed”
EVALUATORS:
“saturation_ice” DOMAIN-saturation_ice
“saturation_liquid” DOMAIN-saturation_liquid
“saturation_gas” DOMAIN-saturation_gas
“porosity” DOMAIN-porosity
“cell volume” DOMAIN-cell_volume
INCLUDES:
[pk-physical-default-spec]
MPC
Multi-process-couplers or MPCs couple other PKs. They also are PKs themselves, in that they implement the PK interface. So MPCs can also couple other MPCs. There are a few common “base” MPCs which do the simplest form of coupling – sequential and globally implicit (with a diagonal preconditioner). Then there are specific couplers which know more about their coupled sub-PKs, and can do more complicated things (for instance, adding off-diagonal block entries to the preconditioner).
MPCs are also used to couple across domains – for instance integrated hydrology is a surface+subsurface flow coupler. They also can do fancier things like drape a bunch of subgrid columns off of a mesh, or other things. Think of these as the custom couplers.
Base MPC
Multi process coupler base class.
A multi process coupler is a PK (process kernel) which coordinates and couples several PKs. Each of these coordinated PKs may be MPCs themselves, or physical PKs. Note this does NOT provide a full implementation of PK – it does not supply the AdvanceStep() method. Therefore this class cannot be instantiated, but must be inherited by derived classes which finish supplying the functionality. Instead, this provides the data structures and methods (which may be overridden by derived classes) for managing multiple PKs.
Most of these methods simply loop through the coordinated PKs, calling their respective methods.
mpc-spec
“PKs order”
[Array(string)]Provide a specific order to the sub-PKs; most methods loop over all sub-PKs, and will call the sub-PK method in this order.
INCLUDES:
[pk-spec]Is a PK.
WeakMPC
Multi process coupler for sequential coupling.
Noniterative sequential coupling simply calls each PK’s AdvanceStep() method in order.
StrongMPC
Multi process coupler for globally implicit (strong) coupling.
Globally implicit coupling solves all sub-PKs as a single system of equations. This can be completely automated when all PKs are also PK: BDF PKs, using a block-diagonal preconditioner where each diagonal block is provided by its own sub-PK.
Physical MPCs
Coupling is an art, and often requires special off-diagonal work for globally implicit coupling, and fancy games can be played with domains to couple across domain interfaces both implicitly and sequentially. Physical MPCs derive from default MPCs to provide special implementations of some methods.
Coupled Water MPC
A coupler which integrates surface and subsurface flow implicitly.
Couples Richards equation to surface water through continuity of both pressure and fluxes. This leverages subsurface discretizations that include face-based unknowns, and notes that those face unknowns that correspond to surface faces are co-located with the surface cell pressure, and therefore are equivalent. In this approach (described in detail in a paper that is in review), the surface equations are directly assembled into the subsurface discrete operator.
mpc-coupled-water-spec
“PKs order”
[Array(string)]The use supplies the names of the coupled PKs. The order must be {subsurface_flow_pk, surface_flow_pk} (subsurface first).“subsurface domain name”
[string]domain“surface domain name”
[string]surface“water delegate”
[mpc-delegate-water-spec]A Coupled Water Globalization Delegate spec.
INCLUDES:
[strong-mpc-spec]Is a StrongMPC
Coupled Cells MPC
A coupler which solves two PDEs on the same domain.
This is a StrongMPC which uses a preconditioner in which the block-diagonal cell-local matrix is dense. If the system looks something like:
A( y1, y2, x, t ) = 0 B( y1, y2, x, t ) = 0
where y1,y2 are spatially varying unknowns that are discretized using the MFD method (and therefore have both cell and face unknowns), an approximation to the Jacobian is written as
[ dA_c/dy1_c dA_c/dy1_f dA_c/dy2_c 0 ] [ dA_f/dy1_c dA_f/dy1_f 0 0 ] [ dB_c/dy1_c 0 dB_c/dy2_c dB_c/dy2_f ] [ 0 0 dB_f/dy2_c dB_f/dy2_f ]
Note that the upper left block is the standard preconditioner for the A system, and the lower right block is the standard precon for the B system, and we have simply added cell-based couplings, dA_c/dy2_c and dB_c/dy1_c.
Most commonly this is used to couple flow and energy equations on the same mesh. In the temperature/pressure system, these extra blocks correspond to
mpc-coupled-cells-spec
“domain name”
[string]Domain of simulation“conserved quantity A”
[string]Key of the first sub-PK’s conserved quantity.“conserved quantity B”
[string]Key of the second sub-PK’s conserved quantity.“primary variable A”
[string]Key of the first sub-PK’s primary variable.“primary variable B”
[string]Key of the second sub-PK’s primary variable.“no dA/dy2 block”
[bool]false Excludes the dA_c/dy2_c block above.“no dB/dy1 block”
[bool]false Excludes the dB_c/dy1_c block above.
INCLUDES:
[strong-mpc-spec]Is a StrongMPC.
Subsurface MPC
A coupler which solves flow and energy in the subsurface.
This MPC provides most nearly all terms for an approximate Jacobian for coupling three-phase Richards equation (the Permafrost Flow PK) to the three-phase Energy equation (the Three-Phase subsurface Energy PK).
Many options are provided for turning on and off various aspects of this Jacobian, so it is useful to mathematically write out these terms. The equations are:
Note that all of the following are dependent on \(p\) and/or \(T\):
Also, both source terms \(Q_w\) and \(Q_e\) may or may not depend on \(p\) and \(T\).
Note also that the Darcy flux \(\mathbf{q}\) used in the advection of energy is given by the Darcy flux:
Differentiating these two equations in their two unknowns gives the following four blocks in the approximate Jacobian:
\(\frac{\partial F_1}{\partial p}\): this is the Richards equation diagonal block, and is controlled inside that PK.
\(\frac{\partial F_1}{\partial T}\) includes terms for:
\(\frac{\partial \Theta}{\partial T}\) This term is the cell-local diagonal block.
The partial derivative of the divergence of the Darcy flux with respect to temperature is dominated by \(\frac{\partial}{\partial T} \frac{k_r n_l}{\mu}\). This is because the relative permeability is strongly dependent upon phase change (the freezing equals drying approximation). This term is referred to as the “d div q / dT” term.
\(\frac{\partial F_2}{\partial p}\) includes terms for:
\(\frac{\partial E}{\partial p}\) This term is the cell-local diagonal block.
The partial derivative of the energy diffusion term with respect to pressure is dominated by \(\frac{\partial \kappa}{\partial p}\) through phase change – at a constant temperature, but changing pressure, phase change can result in large changes to thermal conductivity. This is referred to as the “div K grad T / dp” term.
\(\frac{\partial F_2}{\partial T}\): this is the energy equation diagonal block, and is controlled inside that PK.
Also, at this level, where we know more about the flux used in the energy equation (it is the Darcy flux), we can do a better approximation of the derivative of the advection of energy term with respect to both temperature and pressure. For instance, enthalpy is only weakly dependent on pressure, so we can use the derivative of the divergence of the Darcy flux with respect to pressure (from the Richards block) in the advection term in the \(\frac{\partial F_2}{\partial p}\) block, and approximate \(\frac{\partial k_r}{\partial T}\) in the advection term as well. These terms are referred to as “div hq / dp,T terms”. Note the missing initial “d” here relative to other terms.
The behavior of this MPC’s preconditioner can be set by an option, “preconditioner type”. Really users should not change this from the default, except in expert cases or for comparison’s sake, but the options are:
“picard” is the default, this uses all available terms, and enables the “suppress” options for finer-grained control.
“none” No preconditioner never works.
“block diagonal” This is what one would get from the default StrongMPC. This probably never works.
“no flow coupling” This keeps the accumulation terms, but turns off all the non-local blocks. This is equivalent to Coupled Cells MPC.
“ewc” CURRENTLY DEPRECATED/BROKEN/DISABLED In addition to the “picard” coupling, this also always does a change of variables, whereby we first invert to calculate primary variable corrections, then do a change of variables to calculate the linearized corrections in energy and water content space. We then apply those corrections, and invert to find the primary variable changes that would have made those corrections. This is called the “energy and water content” algorithm, and is related to similar variable changing approaches by Krabbenhoft (for flow) and Knoll (for energy), but in the multivariate approach. This is somewhat bad, becuase while it fixes some corrections, it breaks others.
“smart ewc” CURRENTLY DEPRECATED/BROKEN/DISABLED Does the “ewc” algorithm above, but tries to be smart about when to do it. This algorithm helps when we are about to fall off of the latent heat cliff. If we can guess when to do it, we have a better chance of not breaking things. This seems like it ought to be helpful, but often doesn’t do as much as one might hope.
Note this “ewc” algorithm is just as valid, and more useful, in the predictor (where it is not deprecated/disabled). There, we extrapolate a change in pressure and temperature, but often do better to extrapolate in water content and energy space, then invert (locally) for pressure and temperature corrections that meet that extrapolation. Both of these globalization algorithms are supported by the EWC Globalization Delegate object.
mpc-subsurface-spec
“domain name”
[string]Domain of simulation“preconditioner type”
[string]picard See the above for detailed descriptions of the choices. One of: “none”, “block diagonal”, “no flow coupling”, “picard”, “ewc”, and “smart ewc”.“supress Jacobian terms: div hq / dp,T”
[bool]false If using picard or ewc, do not include this block in the preconditioner.“supress Jacobian terms: d div q / dT”
[bool]false If using picard or ewc, do not include this block in the preconditioner.“supress Jacobian terms: d div K grad T / dp”
[bool]false If using picard or ewc, do not include this block in the preconditioner.“ewc delegate”
[mpc-delegate-ewc-spec]A EWC Globalization Delegate spec.
INCLUDES:
[strong-mpc-spec]Is a StrongMPC.
Surface MPC
Permafrost MPC
A coupler which solves flow and energy both surface and subsurface.
This MPC handles the coupling of surface energy and flow to subsurface energy and flow for integrated hydrology with freeze/thaw processes.
mpc-permafrost-spec
“PKs order”
[Array(string)]The user supplies the names of the coupled PKs. The order must be {subsurface_flow_pk, subsurface_energy_pk, surface_flow_pk, surface_energy_pk}.“subsurface domain name”
[string]domain“surface domain name”
[string]surface“mass exchange flux key”
[string]SURFACE_DOMAIN-surface_subsurface_flux“energy exchange flux key”
[string]SURFACE_DOMAIN-surface_subsurface_energy_flux“water delegate”
[mpc-delegate-water-spec]A Coupled Water Globalization Delegate spec.
INCLUDES:
[mpc-subsurface-spec]Is a Subsurface MPC
Globalization Delegates
Globalization is the art of convincing a solver to find the solution. Remember – physics typically cares very little about how you get to a solution, only that you get there. If you can guess or otherwise find the solution physically, without doing fancy math, go for it! These delegates are handy utility classes which are used by MPCs to effeciently leverage physics understanding in the mathematical solvers to nudge the solver in the direction of a reasonable solution, or to keep a solver from going off into a part of space which is totally unphysical. These can often make the difference between converging and not converging.
Much of the efficiency of ATS comes from these delegates, and more of them are always welcome contributions.
Coupled Water Globalization Delegate
EWC Globalization Delegate
Globalization for nonlinearity associated with phase change and latent heat.
The EWC delegate works to deal with strong nonlinearities associated with latent heat and phase change. Provided a change in primary variables pressure and temperature, it works by first multiplying those changes by the local Jacobian matrix, \(\frac{\partial \left\{ \Theta, E \right\} }{ \partial \left\{ p, T \right\} }\) to calculate changes in water content and energy, then calculating the new water content and energy and inverting the functions \(\Theta(p,T), E(p,T)\) to determine what pressure and temperature would have resulted in those values. This provides a corrected change in the primary variables.
Conceptually, this is a “more robust” choice in nonlinearities associated with phase change, where the derivatives go from small to large to small again, and small changes in pressure and temperature result in large changes in water content and energy.
This delegate manages these globalization strategies, which can be used both in modifying the correction supplied by a nonlinear iterate, and in modifying a predictor, the extrapolated projection (from previous timesteps) that provides the initial guess to the nonlinear solve.
mpc-delegate-ewc-spec
“verbose object”
[verbose-object-spec]See Verbose Object.“PK name”
[string]Name of the owning PK – simply for logging and debugging.“domain name”
[string]“domain” The mesh.“preconditioner type”
[string]When to use EWC on the nonlinear iterate’s correction. One of:“none” Never do EWC
“ewc” Always do EWC
“smart ewc” Attempt EWC when it seems likely it will be useful and take the EWC correction if it is smaller than the standard correction.
“predictor type”
[string]When to use EWC on the predictor. One of:“none” Never do EWC
“ewc” Always do EWC
“smart ewc” Attempt EWC when it seems likely it will be useful and take the EWC correction if it is smaller than the standard correction.
“freeze-thaw cusp width [K]”
[double]Controls a width over which to assume we are close to the latent heat cliff, and begins applying the EWC algorithm in “ewc smarter”.“freeze-thaw cusp width (freezing) [K]”
[double]Controls a width over which to assume we are close to the latent heat cliff as we get colder, and begins applying the EWC algorithm in “ewc smarter”.“freeze-thaw cusp width (thawing) [K]”
[double]Controls a width over which to assume we are close to the latent heat cliff as we get warmer, and begins applying the EWC algorithm in “ewc smarter”.“pressure key”
[string]DOMAIN-pressure“temperature key”
[string]DOMAIN-temperature“water content key”
[string]DOMAIN-water_content“energy key”
[string]DOMAIN-energy“cell volume key”
[string]DOMAIN-cell_volume
INCLUDES
[debugger-spec]Uses a Debugger
State
State, a container for data.
State is a simple data-manager, allowing PKs to require, read, and write various fields.
Acts as a factory for data through the various require methods.
Provides some data protection by providing both const and non-const data pointers to PKs.
Provides some initialization capability – this is where all independent variables can be initialized (as independent variables are owned by state, not by any PK).
state-spec
“evaluators”
[evaluator-typedinline-spec-list]A list of evaluators.“initial conditions”
[list]A list of constant-in-time data. Note that “initial conditions” is not a particularly descriptive name here – PDE initial conditions are generally not here. This list consists of“model parameters”
[list]A list of shared model parameters that can be used across all evaluators.
evaluator-typedinline-spec
“evaluator type”
[string]Type of the evaluator Included for convenience in defining data that is not in the dependency graph, constants are things (like gravity, or atmospheric pressure) which are stored in state but never change. Typically they’re limited to scalars and dense, local vectors.
Example:
<ParameterList name="state">
<Parameter name="initialization filename" type="string" value="_CHECK00123.h5"/>
<ParameterList name="evaluators">
<ParameterList name="pressure">
<Parameter name="evaluator type" type="string" value="primary variable" />
</ParameterList>
</ParameterList>
<ParameterList name="initial conditions">
<Parameter name="time" type="double" value="0.0">
<ParameterList name="atmospheric pressure">
<Parameter name="value" type="double" value="101325.0" />
</ParameterList>
<ParameterList name="gravity">
<Parameter name="value" type="Array(double)" value="{0.0,0.0,-9.80665}" />
</ParameterList>
</ParameterList>
</ParameterList>
State consists of two sublists, one for evaluators and the other for atomic constants. The latter is currently called “initial conditions”, which is a terrible name which must be fixed.
example:
<ParameterList name="state">
<ParameterList name="field evaluators">
...
</ParameterList>
<ParameterList name="initial conditions">
...
</ParameterList>
</ParameterList>
Evaluators
Evaluators are individual terms used to build up a PK or MPCs. Each term represents a variable in the equation, and can consist of primary variables (those that are solved for by a PK solver), independent variables (those that have no dependent variables but are provided by the user as data), and secondary variables (those that are functions of other variables). Note that all three may be variable in space and/or time.
Primary Variables
An evaluator with no dependencies that serves as the primary variable to be solved for by a PK. Note that users almost never are required to write an input spec for these – they are controlled by the PK and therefore the input spec for this evaluator is written by that PK.
evaluator-primary-spec
“tag”
[string]“” Time tag at which this primary variable is used.
Independent Variables
Independent variables are variables which do not depend upon other dependent variables but are provided as data by the user. Examples include material properties, forcing datasets, etc. These can be provided in a few forms:
Constant
This evaluator is typically used for providing data that is a simple constant value.
This evaluator is used by providing the option:
“evaluator type” = “independent variable constant”
independent-variable-constant-evaluator-spec
“value”
[double]The value.
From Function
This evaluator is typically used for providing data that are functions of space and time. The evaluator consists of a list of region,function pairs, and the functions are evaluated across that region at each timestep. If the problem is time-independent, the “constant in time” option results in a performance improvement (as the functions need only be evaluated once). This leverages the exaustive functional format capability provided in Amanzi’s Functions library.
This evaluator is used by providing the option:
“evaluator type” == “independent variable”
independent-variable-function-evaluator-spec
“constant in time”
[bool]false If true, only evaluate the functions once as they are time-independent.“function”
[composite-vector-function-spec-list]
From File
An evaluator with no dependencies specified by discrete data in a file.
This evaluator is typically used for providing data that are functions of space and time. Data is provided, discretely (e.g. with one data point per cell/face/node), at a series of time slices. The time slices are interpolated linearly in time to provide the value.
Within the file, data is expected to meet the following (HDF5) layout:
/time : a 1D array of length NTIMES, providing the time in seconds.
/variable_name.ENTITY.DOF (group)
/0 : a 1D array of length NENTITIES, providing the values for each entity
at time /time[0]
/1 : ...
/NTIMES-1 : 1D array at time /time[NTIMES-1]
This evaluator is used by providing the option:
“evaluator type” == “independent variable”
independent-variable-from-file-evaluator-spec
“filename”
[string]Path to the file.“variable name”
[string]Name of the dataset to read from the file.- “domain name”
[string]domain Name of the domain on which the field is defined.
- “domain name”
“component name”
[string]cell Name of the component in the field to populate.“mesh entity”
[string]cell Name of the entity on which the component is defined.“number of dofs”
[int]1 Number of degrees of freedom to read.“time function”
[function-spec]optional If provided, time is first manipulated by this function before interpolation. This is useful for things like cyclic data, which can use a modulo time function to repeat the same data.
<ParameterList name="field_evaluators"> <!-- parent list -->
<ParameterList name="porosity">
<Parameter name="field evaluator type" type="string" value="independent variable from file"/>
<Parameter name="filename" type="string" value="_DATA_FILE.h5"/>
<Parameter name="domain name" type="string" value="domain"/>
<Parameter name="variable name" type="string" value="porosity"/>
<Parameter name="component name" type="string" value="cell"/>
<Parameter name="mesh entity" type="string" value="cell"/>
<Parameter name="number of dofs" type="int" value="1"/>
<ParameterList name="time function">
<Parameter name="times" type="Array(double)" value="{1.0, 2.0, 3.0}"/>
</ParameterList>
</ParameterList>
</ParameterList>
The field porosity is defined as a cell-based variable and interpolated between three time intervals.
Secondary Variables
All other evaluators are secondary variable evaluators, and these are grouped by physics concept or process type.
Secondary variables, by definition, define functions that evaluate one or more variables as a function of one or more variables. Therefore all secondary evaluators provide at least one “Key,” which is the variable(s) computed, and at least one “Dependency.”
If the evaluator computes one and only one key, that key is provided by the name of the parameter list in the “evalutors” list of State. If more than one Key is computed, then the second must either be guessed by the code (for instance if the provided key is “saturation_liquid”, it is likely that the other key is “saturation_gas”) or provided by the user. If more than one key is computed, all of the keys computed can be specified exactly via the input spec. Keys are provided in one of two parameters:
“my variable key”
[string]Specifically name the variable used as “my variable”“my variable key suffix”
[string]Name a suffix, and the variable is given by DOMAIN-SUFFIX, where the DOMAIN is given by the prefix in the evaluator list’s name. This is particularly useful for collections of enumerated PKs, e.g. columnar PKs, where the DOMAIN might be computed on the fly based on a column ID.
Dependencies use the same approach – each dependency variable name may include a default, and looks for a “key” and “key suffix” as potential options.
As an example, a saturation evaluator may depend on pressure, and may detail all of its names via something like:
<ParameterList name="domain:1-saturation_liquid">
<Parameter name="saturation gas key" type="string" value="domain:1-saturation_gas" />
<Parameter name="pressure key suffix" type="string" value="pressure" />
<!-- OR EQUIVALENTLY -->
<Parameter name="pressure key" type="string" value="domain:1-pressure" />
</ParameterList>
Conserved quantities
Nearly all ATS process kernels are conservation equations, where there is a formal conserved quantity, that, upon convergence, is conserved to tolerance. These are always an “extensive” quantity.
Water content in ATS is always measured on [mol] and therefore
includes a factor of the cell volume. Energy in ATS is always
measured in [MJ]. Unlike nearly all other variables, this is not
SI, and is done so because this makes for fairly evenly balanced
equations between a coupled flow and energy problem.
Richards Equation water content (liquid only)
Richards water content evaluator: the standard form as a function of liquid saturation.
Specified with evaluator type: “richards water content”
field-evaluator-type-richards-water-content-spec
DEPENDENCIES:
“porosity”
“molar density liquid”
“saturation liquid”
“cell volume”
Liquid+Gas water content
Water content for liquid + water vapor.
Specified with evaluator type: “liquid+gas water content”
field-evaluator-type-liquid-gas-water-content-spec
DEPENDENCIES:
“porosity”
“molar density liquid”
“molar density gas”
“saturation liquid”
“saturation gas”
“mol frac gas”
“cell volume”
Liquid+Ice water content
Water content for liquid + water vapor.
Specified with evaluator type: “liquid+ice water content”
field-evaluator-type-liquid-ice-water-content-spec
DEPENDENCIES:
“porosity”
“molar density liquid”
“molar density ice”
“saturation liquid”
“saturation ice”
“cell volume”
Liquid+Ice+Gas water content
Three phase water content: vapor, liquid, and ice.
Specified with evaluator type: “three phase water content”
field-evaluator-type-three-phase-water-content-spec
DEPENDENCIES:
“porosity”
“molar density liquid”
“saturation liquid”
“molar density ice”
“saturation ice”
“molar density gas”
“saturation gas”
“molar fraction gas”
“cell volume”
Surface water content
Snow or canopy water content
Most other water contents can be formed as Multiplicative evaluators. See below for a few examples:
Multiplicative evalutator for snow-water_content:
<ParameterList name="snow-water_content" type="ParameterList">
<Parameter name="field evaluator type" type="string" value="multiplicative evaluator" />
<Parameter name="evaluator dependencies" type="Array(string)" value="{snow-cell_volume, snow-water_equivalent, surface-molar_density_liquid}" />
<Parameter name="units" type="string" value="mol" />
</ParameterList>
Multiplicative evaluator for canopy-water_content:
<ParameterList name="canopy-water_content" type="ParameterList">
<Parameter name="field evaluator type" type="string" value="multiplicative evaluator" />
<Parameter name="evaluator dependencies" type="Array(string)" value="{canopy-cell_volume, canopy-water_equivalent, surface-molar_density_liquid}" />
<Parameter name="units" type="string" value="mol" />
</ParameterList>
Richards energy
Energy content evaluator for a standard Richards equation’s water content.
Energy associated with a soil and pore-water system, in [KJ]
Specified with evaluator type: “richards energy”
Note this equation assumes that porosity is compressible, but is based on the uncompressed rock grain density (not bulk density). This means that porosity is the base, uncompressible value when used with the energy in the grain, but the larger, compressible value when used with the energy in the water.
Note that this ignores energy in the gas phase.
field-evaluator-type-richards-energy-spec
DEPENDENCIES:
“porosity” The porosity, including any compressibility. [-]
“base porosity” The uncompressed porosity (note this may be the same as porosity for incompressible cases) [-]
“molar density liquid” [mol m^-3]
“saturation liquid” [-]
“internal energy liquid” [KJ mol^-1]
“density rock” Units may be either [kg m^-3] or [mol m^-3]
“internal energy rock” Units may be either [KJ kg^-1] or [KJ mol^-1], but must be consistent with the above density.
“cell volume” [m^3]
Liquid+Gas energy
Energy content evaluator for a standard Richards equation, including energy in the gas phase.
Calculates energy, in [KJ], via the equation:
Specified with evaluator type: “liquid+gas energy”
Note this equation assumes that porosity is compressible, but is based on the uncompressed rock grain density (not bulk density). This means that porosity is the base, uncompressible value when used with the energy in the grain, but the larger, compressible value when used with the energy in the water.
field-evaluator-type-liquid-gas-energy-spec
DEPENDENCIES:
“porosity” The porosity, including any compressibility. [-]
“base porosity” The uncompressed porosity (note this may be the same as porosity for incompressible cases) [-]
“molar density liquid” [mol m^-3]
“saturation liquid” [-]
“internal energy liquid” [KJ mol^-1]
“molar density gas” [mol m^-3]
“saturation gas” [-]
“internal energy gas” [KJ mol^-1]
“density rock” Units may be either [kg m^-3] or [mol m^-3]
“internal energy rock” Units may be either [KJ kg^-1] or [KJ mol^-1], but must be consistent with the above density.
“cell volume” [m^3]
Liquid+Ice energy
Energy content evaluator for a two-phase system, including energy in an ice phase.
Calculates energy, in [KJ], via the equation:
Specified with evaluator type: “liquid+ice energy”
Note this equation assumes that porosity is compressible, but is based on the uncompressed rock grain density (not bulk density). This means that porosity is the base, uncompressible value when used with the energy in the grain, but the larger, compressible value when used with the energy in the water.
Note that this ignores energy in the gas phase.
field-evaluator-type-liquid-ice-energy-spec
DEPENDENCIES:
“porosity” The porosity, including any compressibility. [-]
“base porosity” The uncompressed porosity (note this may be the same as porosity for incompressible cases) [-]
“molar density liquid” [mol m^-3]
“saturation liquid” [-]
“internal energy liquid” [KJ mol^-1]
“molar density ice” [mol m^-3]
“saturation ice” [-]
“internal energy ice” [KJ mol^-1]
“density rock” Units may be either [kg m^-3] or [mol m^-3]
“internal energy rock” Units may be either [KJ kg^-1] or [KJ mol^-1], but must be consistent with the above density.
“cell volume” [m^3]
Liquid+Ice+Gas energy
Energy content evaluator for a three-phase, gas, liquid, ice system including the surrounding soil.
Calculates energy, in [KJ], via the equation:
Specified with evaluator type: “three phase energy”
Note this equation assumes that porosity is compressible, but is based on the uncompressed rock grain density (not bulk density). This means that porosity is the base, uncompressible value when used with the energy in the grain, but the larger, compressible value when used with the energy in the water.
field-evaluator-type-three-phase-energy-spec
DEPENDENCIES:
“porosity” The porosity, including any compressibility. [-]
“base porosity” The uncompressed porosity (note this may be the same as porosity for incompressible cases) [-]
“molar density liquid” [mol m^-3]
“saturation liquid” [-]
“internal energy liquid” [KJ mol^-1]
“molar density ice” [mol m^-3]
“saturation ice” [-]
“internal energy ice” [KJ mol^-1]
“molar density gas” [mol m^-3]
“saturation gas” [-]
“internal energy gas” [KJ mol^-1]
“density rock” Units may be either [kg m^-3] or [mol m^-3]
“internal energy rock” Units may be either [KJ kg^-1] or [KJ mol^-1], but must be consistent with the above density.
“cell volume” [m^3]
Surface water+ice energy
Energy content for a surface water, partially frozen system.
The energy associated with ponded water, in [KJ], given by:
Specified with evaluator type: “surface ice energy”
field-evaluator-type-surface-ice-energy-spec
DEPENDENCIES:
“ponded depth” Height of water above the land surface [m]
“unfrozen fraction” The fraction of unfrozen water ranges from 0 to 1. [-]
“molar density liquid” [mol m^-3]
“internal energy liquid” [KJ mol^-1]
“molar density ice” [mol m^-3]
“internal energy ice” [KJ mol^-1]
“cell volume” [m^2]
Subsurface flow evaluators
Assorted evaluators used for subsurface flow processes, including water retention curves, compressible pore space, relative permeability, and their frozen equivalents.
Many of these evaluators show up in nearly all ATS simulations, as subsurface flow of water is the core process underlying all of ATS physics. For real examples, see ats-demos
Capillary pressure
Capillary pressure for gas on a liquid.
pc-liquid-evaluator-spec
KEYS:
“pressure” DOMAIN-pressure
Capillary pressure of liquid on ice
Water Retention Model and Relative Permeability
Evaluates saturation through water retention models.
Water Retention Models (WRMs) determine the saturation as a function of pressure and the relative permeability as a function of saturation. Most commonly used in practice is the van Genuchten model, but others are available default default;
“evaluator type” = “wrm”
wrm-evaluator-spec
“model parameters”
[string]List (by region) of WRM specs. This will copy “WRM parameters” given in “model parameters” under state here to evaluate WRM.
KEYS:
“saturation” determined from evaluator name The name of the liquid saturation – typically this is determined from the evaluator name and need not be set.
“other saturation” determined from evaluator name The name of the other saturation, usually gas – typically this is determined from the evaluator name and need not be set.
“capillary pressure”` DOMAIN-capillary_pressure_gas_liq The name of the capillary pressure.
Example:
<ParameterList name="PKs" type="ParameterList">
...
<ParameterList name="flow" type="ParameterList">
...
<ParameterList name="water retention evaluator" type="ParameterList">
<Parameter name="minimum rel perm cutoff" type="double" value=" 0" />
<Parameter name="use surface rel perm" type="bool" value="true" />
<Parameter name="model parameters" type="string" value="WRM parameters" />
...
</ParameterList>
...
</ParameterList>
...
</ParameterList>
<ParameterList name="state" type="ParameterList">
<ParameterList name="model parameters" type="ParameterList">
<ParameterList name="WRM parameters" type="ParameterList">
<ParameterList name="domain" type="ParameterList">
<Parameter name="region" type="string" value="domain" />
<Parameter name="wrm type" type="string" value="van Genuchten" />
<Parameter name="van Genuchten alpha [Pa^-1]" type="double" value="2e-05" />
<Parameter name="van Genuchten n [-]" type="double" value="1.58" />
<Parameter name="residual saturation [-]" type="double" value="0.2" />
<Parameter name="smoothing interval width [saturation]" type="double" value="0.05" />
<Parameter name="dessicated zone thickness [m]" type="double" value="0.1" />
</ParameterList>
</ParameterList>
</ParameterList>
...
</ParameterList>
A collection of WRMs along with a Mesh Partition.
A WRM partition is a list of (region, WRM) pairs, where the regions partition the mesh.
wrm-partition-typedinline-spec
“region”
[string]Region on which the WRM is valid.“WRM type”
[string]Name of the WRM type.“_WRM_type_ parameters”
[_WRM_type_-spec]See below for the required parameter spec for each type.
Evaluates relative permeability using water retention models.
Uses a list of regions and water retention models on those regions to evaluate relative permeability, typically as a function of liquid saturation.
Most of the parameters are provided to the WRM model, and not the evaluator. Typically these share lists to ensure the same water retention curves, and this one is updated with the parameters of the WRM evaluator. This is handled by flow PKs.
Some additional parameters are available.
“evaluator type” = “relative permeability, van Genuchten”
rel-perm-evaluator-spec
“use density on viscosity in rel perm”
[bool]true“boundary rel perm strategy”
[string]boundary pressure Controls how the rel perm is calculated on boundary faces. Note, this may be overwritten by upwinding later! One of:“boundary pressure” Evaluates kr of pressure on the boundary face, upwinds normally.
“interior pressure” Evaluates kr of the pressure on the interior cell (bad idea).
“harmonic mean” Takes the harmonic mean of kr on the boundary face and kr on the interior cell.
“arithmetic mean” Takes the arithmetic mean of kr on the boundary face and kr on the interior cell.
“one” Sets the boundary kr to 1.
“surface rel perm” Looks for a field on the surface mesh and uses that.
“minimum rel perm cutoff”
[double]0. Provides a lower bound on rel perm.“permeability rescaling”
[double]Typically rho * kr / mu is very big and K_sat is very small. To avoid roundoff propagation issues, rescaling this quantity by offsetting and equal values is encourage. Typically 10^7 or so is good.“model parameters”
[string]WRM parameters[WRM-typedinline-spec-list]List (by region) of WRM specs. This will copy “WRM parameters” given in “model parameters” under state here to evaluate relative permeability. If use “WRM parameters”, both WRM and relative permeability evaluators use the same set of “WRM parameters”, which can be van Genuchten or Brooks-Corey. If use a customed name, e.g., “relative permeability parameters”, and declare “relative permeability parameters” in “model parameters” under state, this allows to use different models for WRM (by default through “WRM parameters”) and relative permeability.
KEYS:
“rel perm”
“saturation_liquid”
“density” (if “use density on viscosity in rel perm” == true)
“viscosity” (if “use density on viscosity in rel perm” == true)
“surface relative permeability” (if “boundary rel perm strategy” == “surface rel perm”)
Example 1: Using the same set of van Genuchten model paramters for WRM and relative permeability
<ParameterList name="PKs" type="ParameterList">
...
<ParameterList name="flow" type="ParameterList">
...
<ParameterList name="water retention evaluator" type="ParameterList">
<Parameter name="model parameters" type="string" value="WRM parameters" />
...
</ParameterList>
...
</ParameterList>
...
</ParameterList>
<ParameterList name="state" type="ParameterList">
<ParameterList name="model parameters" type="ParameterList">
<ParameterList name="WRM parameters" type="ParameterList">
<ParameterList name="domain" type="ParameterList">
<Parameter name="region" type="string" value="domain" />
<Parameter name="wrm type" type="string" value="van Genuchten" />
<Parameter name="van Genuchten alpha [Pa^-1]" type="double" value="2e-05" />
<Parameter name="van Genuchten n [-]" type="double" value="1.58" />
<Parameter name="residual saturation [-]" type="double" value="0.2" />
<Parameter name="smoothing interval width [saturation]" type="double" value="0.05" />
<Parameter name="dessicated zone thickness [m]" type="double" value="0.1" />
</ParameterList>
</ParameterList>
</ParameterList>
<ParameterList name="evaluators" type="ParameterList">
<ParameterList name="relative_permeability" type="ParameterList">
<Parameter name="evaluator type" type="string" value="relative permeability, van Genuchten" />
<Parameter name="model parameters" type="string" value="WRM parameters" />
<Parameter name="use surface rel perm" type="bool" value="true" />
<Parameter name="minimum rel perm cutoff" type="double" value=" 0" />
</ParameterList>
...
</ParameterList>
...
</ParameterList>
Example 2: Using different set of model/paramters for WRM and relative permeability, van Genuchten for WRM and Brooks-Corey for relative permeability. Note that in this case, van Genuchten parameters and Brooks-Corey parameters need to be consistent. Using tool “convert_parameters_vg2bc.py” to convert van Genuchten parameters to Brooks-Corey parameters.
<ParameterList name="PKs" type="ParameterList">
...
<ParameterList name="flow" type="ParameterList">
...
<ParameterList name="water retention evaluator" type="ParameterList">
<Parameter name="model parameters" type="string" value="WRM parameters" />
...
</ParameterList>
...
</ParameterList>
...
</ParameterList>
<ParameterList name="state" type="ParameterList">
<ParameterList name="model parameters" type="ParameterList">
<ParameterList name="WRM parameters" type="ParameterList">
<ParameterList name="domain" type="ParameterList">
<Parameter name="region" type="string" value="domain" />
<Parameter name="wrm type" type="string" value="van Genuchten" />
<Parameter name="van Genuchten alpha [Pa^-1]" type="double" value="2e-05" />
<Parameter name="van Genuchten n [-]" type="double" value="1.58" />
<Parameter name="residual saturation [-]" type="double" value="0.2" />
<Parameter name="smoothing interval width [saturation]" type="double" value="0.05" />
<Parameter name="dessicated zone thickness [m]" type="double" value="0.1" />
</ParameterList>
</ParameterList>
<ParameterList name="relative permeability parameters" type="ParameterList">
<ParameterList name="domain" type="ParameterList">
<Parameter name="region" type="string" value="domain" />
<Parameter name="wrm type" type="string" value="Brooks-Corey" />
<Parameter name="Brooks-Corey lambda [-]" type="double" value="0.49" />
<Parameter name="Brooks-Corey saturted matric suction [Pa]" type="double" value="32439.03" />
<Parameter name="residual saturation [-]" type="double" value="0.2" />
<Parameter name="smoothing interval width [saturation]" type="double" value="0.05" />
</ParameterList>
</ParameterList>
</ParameterList>
<ParameterList name="evaluators" type="ParameterList">
<ParameterList name="relative_permeability" type="ParameterList">
<Parameter name="evaluator type" type="string" value="relative permeability, van Genuchten" />
<Parameter name="model parameters" type="string" value="relative permeability parameters" />
<Parameter name="use surface rel perm" type="bool" value="true" />
<Parameter name="minimum rel perm cutoff" type="double" value=" 0" />
</ParameterList>
...
</ParameterList>
...
</ParameterList>
Van Genuchten Model
WRMVanGenuchten : water retention model using van Genuchten’s parameterization
van Genuchten’s water retention curve.
WRM-van-Genuchten-spec
“region”
[string]Region to which this applies“van Genuchten alpha [Pa^-1]”
[double]van Genuchten’s alpha
ONE OF:
“van Genuchten n [-]”
[double]van Genuchten’s n
OR
“van Genuchten m [-]”
[double]van Genuchten’s m, m = 1 - 1/n
END
“residual saturation [-]”
[double]0.0“smoothing interval width [saturation]”
[double]0.0“Mualem exponent l [-]”
[double]0.5“Krel function name”
[string]Mualem “Mualem” or “Burdine”
Example:
<ParameterList name="moss" type="ParameterList">
<Parameter name="region" type="string" value="moss" />
<Parameter name="WRM type" type="string" value="van Genuchten" />
<Parameter name="van Genuchten alpha [Pa^-1]" type="double" value="0.002" />
<Parameter name="van Genuchten m [-]" type="double" value="0.2" />
<Parameter name="residual saturation [-]" type="double" value="0.0" />
<Parameter name="smoothing interval width [saturation]" type="double" value=".05" />
</ParameterList>
Linear Model
A linear sat-pc curve.
A linear sat-pc curve, plus a constant rel perm, makes the system linear, so nonlinear solver should always converge in one step.
No error-checking, so the user is responsible for ensuring that the pressure is always less than atmospheric and within the acceptable range of the slope.
Note this is mostly for testing.
Water Retention Model for Freeze-Thaw
Original Implicit model
Painter’s original, implicitly defined permafrost model.
wrm-implicit-permafrost-spec
“converged tolerance”
[double]1.e-12 Convergence tolerance of the implicit solve.“max iterations”
[int]100 Maximum allowable iterations of the implicit solve.“solver algorithm [brent]”
[string]brent Only brent is currently supported.
Freezing point depression model
Freezing point depression, smoothed model
Painter’s permafrost model with freezing point depression, smoothed.
wrm-fpd-smoothed-permafrost-spec
“reference temperature [K]”
[double]273.15 The phase transition point“interfacial tension ice-water [mN m^-1]”
[double]33.1“interfacial tension air-water [mN m^-1]”
[double]72.7“smoothing width [K]”
[double]1. Smoothing out the freeze curve allows this to be slightly easier to solve.“latent heat [J kg^-1]”
[double]3.34e5 Latent heat of fusion“water density [kg m^-3]”
[double]998.87 Density of water. Note this probably should use the calculated value.
Interfrost model
Sutra-ICE model
This model is based on the emperical freezing curve used by Sutra-Ice, documented in papers by Voss & Walvoord.
wrm-sutra-permafrost-model-spec
“temperature transition [K]”
[double]thickness of the transition from frozen to thawed“residual saturation [-]”
[double]Standard residual saturation“freezing point [K]”
[double]273.15
Compressible porosity
Compressible grains are both physically realistic (based on bulk modulus) and a simple way to provide a non-elliptic, diagonal term for helping solvers to converge.
“evaluator type” = “compressible porosity”
compressible-porosity-evaluator-spec
“compressible porosity model parameters”
[compressible-porosity-standard-model-spec-list]
KEYS:
“pressure” DOMAIN-pressure
“base porosity” DOMAIN-base_porosity
Standard model
A simple model for allowing porosity to vary with pressure.
Based on a linear increase, i.e.
where \(H\) is the heaviside function and \(\alpha\) is the provided compressibility. If the inflection point is set to zero, the above function is exact. However, then the porosity function is not smooth (has discontinuous derivatives), so the inflection point smooths this with a quadratic that matches the value and derivative at the inflection point and is 0 with 0 slope at atmospheric pressure.
compressible-porosity-standard-model-spec
“region”
[string]Region on which this is applied.“pore compressibility [Pa^-1]”
[double]\(\alpha\) as described above“pore compressibility inflection point [Pa]”
[double]1000
The inflection point above which the function is linear.
Example:
<ParameterList name="soil" type="ParameterList">
<Parameter name="region" type="string" value="soil" />
<Parameter name="pore compressibility [Pa^-1]" type="double" value="1.e-9" />
<Parameter name="pore compressibility inflection point [Pa]" type="double" value="1000." />
</ParameterList>
Exponential model
The Leinjnse model is an exponential model of porosity as a function of pressure, based on (insert citation!):
where \(\alpha\) is the provided compressibility, and \(\delta\) is the cutoff (inflection point).
If the inflection point is set to zero, the above function is exact. However, then the porosity function is not smooth (has discontinuous derivatives).
compressible-porosity-leijnse-model-spec
“pore compressibility [Pa^-1]”
[double]\(\alpha\) as described above“pore compressibility inflection point [Pa]”
[double]1000 The inflection point above which the function is linear.
NOTE: additionally the user should provide a parameter in the EWC Globalization Delegate to turn Leijnse model ON in the EWC calculations.
<Parameter name="porosity leijnse model" type="bool" value="true"/>
Viscosity of water
Two main viscosity models are commonly used – a constant and one which is temperature-dependent. The viscosity of water is strongly temperature dependent, so it is highly recommended to use that one if the problem is nonisothermal.
Constant
Like any quantity, a viscosity can simply be a constant value, at which point it is not a secondary variable but an independent variable.
<ParameterList name="viscosity_liquid" type="ParameterList">
<Parameter name="field evaluator type" type="string" value="independent variable constant" />
<Parameter name="value" type="double" value="8.9e-4" />
<Parameter name="units" type="string" value="Pa s" />
</ParameterList>
Nonisothermal
A non-isothermal viscosity model intended for use within a range of temperatures from well below freezing to ~100C.
viscosity-evaluator-spec
“viscosity model parameters”
[viscosity-typedinline-spec-list]
KEYS:
“temperature”
A constitutive relation for the viscosity of water as a function of temperature in K, given as an empirical series expansion fit to data.
Used by setting
“viscosity relation type” = “liquid water”
viscosity-water-spec
NONE
Surface flow evaluators
Assorted evaluators used for surface flow, including potential surfaces, Manning’s conductivity, and their frozen equivalents.
Like the subsurface flow evaluators, many of these evaluators show up in nearly all ATS simulations. For real examples, see ats-demos
Ponded Depth or Water Height
Computes ponded depth from surface water pressure.
where \(H\) is the Heaviside function.
“evaluator type” = “ponded depth”
height-evaluator-spec
KEYS:
“mass density”
“pressure”
Ponded Depth, Frozen
Effective, or Smoothed Height
Computes ponded depth from surface water pressure using a smoothed term to make derivative smooth near 0. This is pretty much never used anymore.
“evaluator type” = “effective height”
effective-height-evaluator-spec
“smoothing width [m]”
[double]0.01 the width over which smoothing is applied.
KEYS:
“height” The unsmoothed ponded depth
Unfrozen fraction
An empirical equation for freezing ponded water – this is simply a smooth sinusoidal curve from 0 to 1 over a given transition in temperature.
“evaluator type” = “unfrozen fraction”
unfrozen-fraction-evaluator-spec
“unfrozen fraction model”
[unfrozen-fraction-model-spec]
KEYS:
“temperature”
unfrozen-fraction-model-spec
“transition width [K]”
[double]0.2 Degrees over which to transition from no ice to all ice.“freezing point [K]”
[double]273.15 Center of the transition, at this point unfrozen fraction is 0.5.“minimum unfrozen fraction [-]”
[double]0 Sets a minimum value.
Unfrozen Flowing Depth
Evaluates the unfrozen mobile depth.
In freezing conditions, water is only mobile if it is unfrozen. This evaluator determines how much water is allowed to flow given that it is partially frozen.
Given a ponded depth, an unfrozen fraction, and an optional power-law exponent, which we call the ice retardation exponent.
unfrozen-effective-depth-evaluator-spec
“ice retardation exponent [-]”
[double]1.0 exponent alpha controlling how quickly ice turns off flow.
DEPENDENCIES: - “depth” DOMAIN-depth - “unfrozen fraction” DOMAIN-unfrozen_fraction
SurfacePotential
Evaluates the potential surface upon which overland flow acts.
“evaluator type” =
pres-elev-evaluator-spec
KEYS:
“height” DOMAIN-ponded_depth Names the height variable. [m]
“elevation” DOMAIN-elevation Names the elevation variable. [m]
NOTE: This is a legacy evaluator, and is not in the factory, so need not be in the input spec. However, we include it here because this could easily be abstracted for new potential surfaces, kinematic wave, etc, at which point it would need to be added to the factory and the input spec.
NOTE: This could easily be replaced by a generic Additive Evaluator.
Overland Conductivity, sheet flow
This implements the conductivity of overland flow, which is the nonlinear coefficient in the diffusion wave equation. The term is given by:
Optionally, this may include a density factor, typically a molar density, which converts the flow law to water flux rather than volumetric flux.
Also, this evaluator can be used in snow redistribution, and in that case needs some extra factors (timestep size) to ensure the correct flow law in that case.
“evaluator type” = “overland conductivity”
overland-conductivity-evaluator-spec
“include density”
[bool]true Include the density prefactor, converting the flux from volumetric flux to water flux.- “dt factor [s]”
[double]-1 The artificial timestep size used in calculating snow redistribution, only used in that case.
- “dt factor [s]”
“swe density factor [-]”
[double]10 Ratio of water to snow density.
DEPENDENCIES:
“mobile depth” DOMAIN-mobile_depth Depth of the mobile water; delta in the above equation.
“slope” DOMAIN-slope_magnitude Magnitude of the bed surface driving flow; | nabla z | above.
“coefficient” DOMAIN-manning_coefficient Surface roughness/shape coefficient; n_{mann} above.
“molar density liquid” DOMAIN-molar_density_liquid If “include density” is true, the density.
Overland Conductivity, litter resistance
(missing documentation!)
Thermodynamic evaluators
Internal energy, enthalpy, thermal conductivity, etc used for both surface and subsurface transport of energy.
Internal energy
Computes (specific) internal energy of as a function of temperature.
“evaluator type” = “iem”
iem-evaluator-spec
“IEM parameters”
[IEM-model-typedinline-spec-list]
KEYS:
“temperature”
Linear
Internal energy based on a linear fit.
Linear internal energy model – function of Cv and temperature
“IEM type” = “linear”
IEM-model-linear-spec
“reference temperature [K]”
[double]273.15 The phase transition point, T_ref above
ONE OF
“latent heat [J kg^-1]”
[double]Latent heat of fusion, L_f above“heat capacity [J kg^-1 K^-1]”
[double]C_v above
OR
“latent heat [J mol^-1]”
[double]Latent heat of fusion, L_f above.“heat capacity [J mol^-1 K^-1]”
[double]C_v above
END
Quadratic
Internal energy based on a quadratic fit to data.
Quadratic internal energy model – function of Cv and temperature
“IEM type” = “quadratic”
IEM-model-quadratic-spec
“reference temperature [K]”
[double]273.15 The phase transition point, T_ref above.
ONE OF
“latent heat [J kg^-1]”
[double]Latent heat of fusion, L_f above“heat capacity [J kg^-1 K^-1]”
[double]C_v above“quadratic b [J kg^-1 K^-2]”
[double]b above
OR
“latent heat [J mol^-1]”
[double]Latent heat of fusion, L_f above.“heat capacity [J mol^-1 K^-1]”
[double]C_v above“quadratic b [J mol^-1 K^-2]”
[double]b above
END
Water Vapor
Computes (specific) internal energy of as a function of temperature and molar fraction of water vapor in the gaseous phase.
“evaluator type” = “iem water vapor”
iem-water-vapor-evaluator-spec
“IEM parameters”
[IEM-water-vapor-model-spec]KEYS:
“temperature”
“vapor molar fraction”
Internal energy model for air and water vapor.
iem-water-vapor-model-spec
“latent heat [J mol^-1]”
[double]Latent heat of vaporization“heat capacity [J mol^-1 K^-1]”
[double]C_v
Enthalpy
Computes enthalpy [MJ / mol] of as a function of internal energy, pressure, and density.
“evaluator type” = “enthalpy”
enthalpy-evaluator-spec
“include work term”
[bool]false If false, e = u, ignoring the work term.
KEYS:
“internal energy”
“pressure”
“mass density”
Thermal Conductivity, two phases
Thermal conductivity based on two-phases (air,liquid) composition of the porous media.
“evaluator type” = “two-phase thermal conductivity”
thermal-conductivity-twophase-evaluator-spec
“thermal conductivity parameters”
[thermal-conductivity-twophase-typedinline-spec-list]
KEYS:
“porosity”
“saturation liquid”
Wet-Dry Model
Simple model of two-phase thermal conductivity, based upon:
Interpolation between saturated and dry conductivities via a Kersten number.
Power-law Kersten number.
“thermal conductivity type” = “two-phase wet/dry”
thermal-conductivity-twophase-wetdry-spec
“region”
[string]Region name on which to apply these parameters.“thermal conductivity, wet [W m^-1 K^-1]”
[double]Thermal conductivity of saturated soil“thermal conductivity, dry [W m^-1 K^-1]”
[double]Thermal conductivity of dry soil“unsaturated alpha [-]”
[double]Interpolating exponent“epsilon”
[double]1e-10 Epsilon to keep saturations bounded away from 0.
Example:
<ParameterList name="thermal conductivity model">
<Parameter name="thermal conductivity type" type="string" value="two-phase wet/dry"/>
<Parameter name="thermal conductivity, wet [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="thermal conductivity, dry [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="epsilon" type="double" value="1.e-10"/>
<Parameter name="unsaturated alpha" type="double" value="1.0"/>
</ParameterList>
Units: [W m^-1 K^-1]
Peters-Lidard Model
A two-phase thermal conductivity, based upon:
Interpolation between saturated and dry conductivities via a Kersten number.
Power-law Kersten number.
Emperical fit for dry conductivity from Peters-Lidard et al ‘98.
See Atchley et al GMD 2015 Supplementary Material for equations.
“thermal conductivity type” = “two-phase Peters-Lidard”
thermal-conductivity-twophase-peterslidard-spec
“region”
[string]Region name on which to apply these parameters.“thermal conductivity of soil [W m^-1 K^-1]”
[double]Thermal conductivity of soil grains (not bulk soil)“thermal conductivity of liquid [W m^-1 K^-1]”
[double]Thermal conductivity of liquid (water)“thermal conductivity of gas [W m^-1 K^-1]”
[double]Thermal conductivity of gas (air)“unsaturated alpha [-]”
[double]Interpolating exponent“epsilon”
[double]1e-10 Epsilon to keep saturations bounded away from 0.
Example:
<ParameterList name="Thermal Conductivity Model">
<Parameter name="thermal conductivity type" type="string" value="two-phase Peters-Lidard"/>
<Parameter name="thermal conductivity of soil [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="thermal conductivity of liquid [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="thermal conductivity of gas [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="unsaturated alpha" type="double" value="1.0"/>
<Parameter name="epsilon" type="double" value="1.e-10"/>
</ParameterList>
Units: [W m^-1 K^-1]
Thermal Conductivity, three phases
Thermal conductivity based on a three-phase (air,liquid,ice) composition of the porous media.
“evaluator type” = “three-phase thermal conductivity”
thermal-conductivity-threephase-evaluator-spec
“thermal conductivity parameters”
[thermal-conductivity-threephase-typedinline-spec-list]
KEYS:
“porosity”
“saturation liquid”
“second saturation”
“temperature”
Wet-Dry Model
Three-phase thermal conductivity based on paper by Peters-Lidard.
A three-phase thermal conductivity, based upon:
Interpolation between saturated and dry conductivities via a Kersten number.
Power-law Kersten number.
Empirical relationship for frozen soil based on Peters-Lidard
See Atchley et al GMD 2015 Supplementary Material for equations.
“thermal conductivity type” = “three-phase wet/dry”
thermal-conductivity-threephase-wetdry-spec
“region”
[string]Region name on which to apply these parameters.“thermal conductivity, saturated (unfrozen) [W m^-1 K^-1]”
[double]Thermal conductivity of fully saturated, unfrozen bulk soil.“thermal conductivity, dry [W m^-1 K^-1]”
[double]Thermal conductivity of fully dried bulk soil.“unsaturated alpha unfrozen [-]”
[double]Interpolating exponent“unsaturated alpha frozen [-]”
[double]Interpolating exponent“saturated beta frozen [-]”
[double]1.0 Interpolating exponent“epsilon”
[double]1e-10 Epsilon to keep saturations bounded away from 0.
Peters-Lidard Model
Three-phase thermal conductivity based on paper by Peters-Lidard.
A three-phase thermal conductivity, based upon:
A mixture model using interpolation across various components.
Power-law Kersten number.
See Atchley et al GMD 2015 Supplementary Material for equations.
“thermal conductivity type” = “three-phase Peters-Lidard”
thermal-conductivity-threephase-peterslidard-spec
“region”
[string]Region name on which to apply these parameters.“thermal conductivity of soil [W m^-1 K^-1]”
[double]Thermal conductivity of soil grains (not bulk soil)“thermal conductivity of liquid [W m^-1 K^-1]”
[double]Thermal conductivity of liquid (water)“thermal conductivity of gas [W m^-1 K^-1]”
[double]Thermal conductivity of gas (air)“thermal conductivity of ice [W m^-1 K^-1]”
[double]Thermal conductivity of ice“unsaturated alpha unfrozen [-]”
[double]Interpolating exponent“unsaturated alpha frozen [-]”
[double]Interpolating exponent“epsilon”
[double]1e-10 Epsilon to keep saturations bounded away from 0.
Example:
<ParameterList name="thermal_conductivity">
<Parameter name="thermal conductivity type" type="string" value="three-phase Peters-Lidard"/>
<Parameter name="thermal conductivity of soil [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="thermal conductivity of liquid [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="thermal conductivity of gas [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="thermal conductivity of ice [W m^-1 K^-1]" type="double" value=""/>
<Parameter name="unsaturated alpha unfrozen [-]" type="double" value=""/>
<Parameter name="unsaturated alpha frozen [-]" type="double" value=""/>
<Parameter name="epsilon" type="double" value="1.e-10"/>
</ParameterList>
Volume-averaged Model
A volume-averaged thermal conductivity based on TCs of raw components.
A simple model of three-phase thermal conductivity, based upon volume-averaging of four consitutive components.
“thermal conductivity type” = “three-phase volume averaged”
See Atchley et al GMD 2015 Supplementary Material for equations.
thermal-conductivity-volume-averaged-spec
“region”
[string]Region name on which to apply these parameters.“thermal conductivity of soil [W m^-1 K^-1]”
[double]Thermal conductivity of soil grains“thermal conductivity of liquid [W m^-1 K^-1]”
[double]Thermal conductivity of liquid water.“thermal conductivity of gas [W m^-1 K^-1]”
[double]Thermal conductivity of air.“thermal conductivity of ice [W m^-1 K^-1]”
[double]Thermal conductivity of frozen water.
Sutra-ICE model
Thermal conductivity model with constant values as a function of temperature, requires the sutra model for permafrost WRM to also be used. This only exists to support the INTERFROST comparison.
Usage:
<ParameterList name="Thermal Conductivity Model">
<Parameter name="Thermal Conductivity Type" type="string" value="sutra hacked"/>
<Parameter name="thermal conductivity of frozen" type="double" value=""/>
<Parameter name="thermal conductivity of mushy" type="double" value=""/>
<Parameter name="thermal conductivity of unfrozen" type="double" value=""/>
<Parameter name="residual saturation" type="double" value=""/>
</ParameterList>
Units: [W m^-1 K^-1]
Thermal Conductivity, Surface
Thermal conductivity of surface water that can be either frozen or liquid phase.
“evaluator type” = “surface thermal conductivity”
thermal-conductivity-surface-evaluator-spec
“thermal conductivity parameters”
[thermal-conductivity-surface-spec]
KEYS:
“unfrozen fraction”
“ponded depth”
thermal-conductivity-surface-spec
“thermal conductivity of water [W m^-1 K^-1]”
[double]0.58“thermal conductivity of ice [W m^-1 K^-1]”
[double]2.18“minimum thermal conductivity”
[double]1.e-14
Advected Energy Source
Active Layer Averaged Temperature
Water Table
Computes the depth to a saturated water table.
“evaluator type” = “water table depth”
water-table-depth-spec
KEYS:
“saturation of gas” SUBSURFACE_DOMAIN-saturation-gas
“subsurface cell volume” SUBSURFACE_DOMAIN-cell_volume
“surface cell volume” DOMAIN-cell_volume
Thaw Depth
Computes the depth to a saturated water table.
“evaluator type” = “thaw depth”
thaw-depth-spec
KEYS:
“temperature” SUBSURFACE_DOMAIN-temperature
“subsurface cell volume” SUBSURFACE_DOMAIN-cell_volume
“surface cell volume” DOMAIN-cell_volume
Equations of State
The density of water can be specified in many ways, depending upon phase and problem of interest. Options are available from the simplest (constant value) to functions of just temperature, temperature and pressure, and temperature/pressure/concentration (e.g. salinity).
Note that density includes both molar and mass-based values. Most density evaluators can provide either, or do provide both, the difference being simply a factor of the molecular mass of water.
Finally, nearly all (except the constant value) equations of state use a common set of models which accept all of temperature, pressure, and concentration. Many of these models ignore one or the other, so it should be preferred (but is not necessary) to choose the right model for a given evaluator. Choosing a model that uses fewer of these than the evaluator provides is valid, but it is inefficient. Choosing a model that uses more than the evaluator provides will result in an error.
Constant Value
Like any quantity, a density can simply be a constant value, at which point it is not a secondary variable but an independent variable.
<ParameterList name="surface-molar_density_liquid" type="ParameterList">
<Parameter name="field evaluator type" type="string" value="independent variable constant" />
<Parameter name="value" type="double" value="55000" />
<Parameter name="units" type="string" value="mol m^-3" />
</ParameterList>
Standard Equation of State
EOSEvaluator is the interface between state/data and the model, an EOS.
Models
Constant EOS
Linear EOS
Ideal Gas
EOS of Water
EOS of Ice
EOS of Vapor in Air
EOS of Saltwater
Surface energy balance evaluators
Evaluators used to solve the fluxes to and from the atmosphere and between layers of the surface. Typically in ATS these calculate evapotranspiration.
Area Fractions
Frequently, the surface of a grid cell is split across at least two “subgrid components,” for instance snow covered and bare ground. This “subgrid” model allows smooth transitions between fully snow-covered and fully bare ground.
These area fractions often get included as area-weights in calculating full-cell quantities.
Two-component model
A subgrid model for determining the area fraction of snow vs not snow within a grid cell.
Uses a simple linear transition to vary between liquid and bare ground, and another linear transition to vary between snow-covered and not-snow-covered.
Ordering of the area fractions calculated are: [bare ground/water, snow].
“evaluator type” = “area fractions, two components”
area-fractions-twocomponent-evaluator-spec:
- “minimum fractional area [-]”
[double]1.e-5 Mimimum area fraction allowed, less than this is rebalanced as zero.
- “minimum fractional area [-]”
DEPENDENCIES:
“snow depth”
[string]
Three-component model
A subgrid model for determining the area fraction of land, water, and snow within a grid cell.
Uses a simple linear transition to vary between liquid and bare ground, and another linear transition to vary between snow-covered and not-snow-covered.
Ordering of the area fractions calculated are: [bare ground, water, snow].
“evaluator type” = “area fractions, three components”
area-fractions-threecomponent-evaluator-spec:
- “minimum fractional area [-]”
[double]1.e-5 Mimimum area fraction allowed, less than this is rebalanced as zero.
- “minimum fractional area [-]”
DEPENDENCIES:
“snow depth” DOMAIN_SNOW-depth
“ponded depth” DOMAIN-ponded_depth
Three-component model, with microtopography
A subgrid model for determining the area fraction of land, open water, and snow within a grid cell.
Uses the subgrid equation from Jan et al WRR 2018 for volumetric or effective ponded depth to determine the area of water, then heuristically places snow on top of that surface.
“evaluator type” = “area fractions, three components with microtopography”
area-fractions-threecomponent-microtopography-evaluator-spec
“snow transitional height [m]”
[double]0.02 Minimum thickness for specifying the snow gradient.“minimum fractional area [-]”
[double]1.e-5 Mimimum area fraction allowed, less than this is rebalanced as zero.“snow domain name”
[string]DOMAIN_SNOW A default is guessed at by replacing “surface” with “snow” in the this’s domain.
KEYS:
“microtopographic relief” DOMAIN-microtopographic_relief The name of del_max, the max microtopography value.
“excluded volume” DOMAIN-excluded_volume The name of del_excluded, the integral of the microtopography.
“ponded depth” DOMAIN-pressure The name of the surface water ponded depth.
“snow depth” DOMAIN_SNOW-depth The name of the snow depth.
“volumetric snow depth” DOMAIN_SNOW-volumetric_depth The name of the snow depth.
NOTE: this evaluator simplifies the situation by assuming constant density. This make it so that ice and water see the same geometry per unit pressure, which isn’t quite true thanks to density differences. However, we hypothesize that these differences, on the surface (unlike in the subsurface) really don’t matter much. –etc
Potential Evapotranspiration
Models of potential evapotranspiration approximate the difference in vapor pressure between the atmosphere and the soil as a function of available energy, allowing the calculation of the max flux of ET that the atmosphere could accept. This can then be limited based on water availability, etc.
Priestley-Taylor Potential Evapotranspiration
Evaluates potential evapotranpiration (PET) using Priestley & Taylor formulation.
This implementation is based on models provided in the PRMS-IV, Version 4, see pages 90-93, Equations 1-57 to 1-60
Requires the following dependencies:
pet-priestley-taylor-evaluator-spec:
“include limiter”
[bool]false If true, multiply potential ET by a limiter to get an actual ET.“limiter number of dofs”
[int]1 Area fractions are often used as limiters, and these have multiple dofs. This provides how many.“limiter dof”
[int]0 Area fractions are often used as limiters, and these have multiple dofs. This provides which one to use.“include 1 - limiter”
[bool]false If true, multiply potential ET by 1 - a limiter (e.g. a limiter that partitions between two pools) to get actual ET.“1 - limiter number of dofs”
[int]1 Area fractions are often used as limiters, and these have multiple dofs. This provides how many.“1 - limiter dof”
[int]0 Area fractions are often used as limiters, and these have multiple dofs. This provides which one to use.- “sublimate snow”
[bool]false If true, use latent heat of vaporization of snow, not water.
- “sublimate snow”
KEYS:
“air temperature” DOMAIN-air_temperature Air temp, in [K]
- “surface temperature” DOMAIN-temperature Ground or leaf temp, in [K]. Note this may be the
same as air temperature.
“elevation” DOMAIN-elevation Elevation [m]
“net radiation” DOMAIN-net_radiation [W m^-2] Net radiation balance, positive to the ground.
“limiter” [-] See “include limiter” above.
“1 - limiter” [-] See “include 1 - limiter” above.
Downregulation and limiters
Given a potential, the actual ET is often limited by available water (or nutrients or other quantities). These evaluators are used to limit, downregulate, distribute, or otherwise move a potential to an actual ET.
Transpiration Distribution
Distributes and downregulates potential transpiration to the rooting zone.
The transpiration distribution evaluator looks to take a potential evapotranspiration and distribute it across the vertical column based on water availability and rooting depths. It also potentially limits the transpiration to avoid taking water where it is not available (thereby crashing the code).
This model is based off of versions from both CLM 4.5 and PRMS. It requires:
A root distribution profile.
A plant wilting factor (e.g. how water stressed is the plant?)
A potential transpiration, typically calculated from data or a potential difference based on a latent heat calculation.
Note this also requires columnar meshes – meaning that the subsurface mesh must have “build columns from set” provided.
A normalized fraction of water is calculated through multiplying the water factor by the root distribution factor, integrating across the column, and dividing by the integral. This gives a factor which sums to 1 and can be used to distribute the potential ET throughout the soil column.
Then, this potential ET is down-regulated and multiplied by the plant wilting factor. If there is no water locally, it cannot be taken. Note that almost always, if there is no water, this did not contribute (much) to the integral and so is already small. But if the entire root zone is dried out, this might have been a bunch of small numbers which then got normalized to 1, meaning they are all now significant.
Finally, transpiration may be turned off for winter – relative to time zero, parameters “leaf on doy” and “leaf off doy” are used to control when ET is zero. By default these are set to 0 and 366 days, ensuring that transpiration is never turned off and the potential ET must include this factor. This is the right choice for, e.g. ELM output, or eddy covariance flux tower data (where leaf on and off are already included in the potential calculation). It is the wrong choice for, e.g. Priestly-Taylor or Penmann-Montief models, which are happy to predict transpiration all winter long. Good choices for those models depend upon the local climate, but may be something like Julian day 101 for leaf on and Julian day 254 for leaf off (PRMS defaults for US temperate forests).
Note that “leaf on doy” and “leaf off doy” are relative to the simulation’s zero time, not the start time. Typically these are Julian day of the year, but this assumes that the 0 time of the simulation (not the “start time”, but time 0!) is Jan 1. This leaf on/off cycle is modulo the “year duration” (typically 1 noleap). Note if “leaf off doy” < “leaf on time” is ok too – this is the case if simulation time zero is mid-summer. These parameters come from the LandCover type.
transpiration-distribution-evaluator-spec
* “year duration” [double] 1
* “year duration units” [string] noleap
“water limiter function”
[function-spec]optional If provided, limit the total water sink as a function of the integral of the water potential * rooting fraction.
KEYS:
“plant wilting factor” DOMAIN-plant_wilting_factor
“rooting depth fraction” DOMAIN-rooting_depth_fraction
“potential transpiration” DOMAIN_SURF-potential_transpiration
“cell volume” DOMAIN-cell_volume
“surface cell volume” DOMAIN_SURF-cell_volume
Rooting Depth Fraction
Provides a depth-based profile of root density.
Sets the (discrete) root fraction as a function of depth. The rooting density is given by:
This function is such that the integral over depth = [0,inf) is 1. Then, computing this over the vertical corridor is done by integrating this function between the depth of the face above and below for each grid cell, with the bottom-most grid cell integrating to infinity.
Note that the two parameters, \(\alpha\) and \(\beta\) are provided in the Land Cover class as “rooting profile alpha” and “rooting profile beta” respectively.
rooting-depth-fraction-evaluator-spec
“surface domain name”
[string]SURFACE_DOMAIN Sane default provided for most domain names.
KEYS:
“cell volume” DOMAIN-cell_volume
“surface area” SURFACE_DOMAIN-cell_volume
Plant Wilting Point
Plant wilting factor provides a moisture availability-based limiter on transpiration.
Also known as Beta, or the water availability factor, or the plant wilting factor, or the transpiration reduction function.
where p is the capillary pressure or water potential, and closed and open indicate the values at which stomates are fully open or fully closed (the wilting point).
Note this makes use of LandCover objects for water potential of fully open and fully closed stomata.
Note the challenges of using this model with arbitrary van Genuchten WRMs. See Verhoef & Egea, Ag. & Forest Meteorology, 2014 https://doi.org/10.1016/j.agrformet.2014.02.009
plant-wilting-factor-evaluator-spec
KEYS:
“capillary pressure” DOMAIN-capillary_pressure_gas_liq
Soil Resistance
Downregulates evaporation through a dessicated zone via soil resistance. Currently support two soil resistance methods: Sakagucki-Zeng and Sellers. This will call soil resistance evaluator.
Radiation Balance Terms
Often a balance of incoming and outgoing short and longwave radiations are required to determine the energy available to go into latent heat, and therefore potential evapotranspiration.
Note that incoming shortwave radiation is typically a user-provided meterological forcing dataset.
Radiation Balance
Evaluates a net radiation balance for ground and canopy.
Here the net radiation is positive for energy inputs to the layer. Note that ground is based on the two-channel (land + snow) while canopy is assumed to be a simple, single layer.
This evaluator requires that the surface temperature, snow temperature, and canopy temperature are known, or at least being solved for.
Requires the use of LandCover types, for albedo and Beer’s law coefficients.
This is combination of CLM v4.5 Tech Note and Beer’s law for attenuation of radiation absorption. In particular, long-wave is exactly as Figure 4.1c in CLM 4.5 Tech Note. The main difference comes in how absorptivity (which is equal to emissivity, epsilon in that document) is defined. Here we use Beer’s law which is an exponential decay with LAI.
Unlike CLM 4.5, here we do not split shortwave into direct and diffuse light.
Computes:
“surface radiation balance” – Net radiation seen by the bare soil/ponded water, this includes radiation transmitted to the surface through the canopy, longwave emitted by the canopy, and less the longwave emitted by the surface itself. [W m^-2] of actual area – this does NOT include the surface area fraction factor which would be required to compute a total energy flux in W.
“snow radiation balance” – Net radiation seen by the snow. See surface above – all are the same except using snow properties. [W m^-2]
“canopy radiation balance” – this is a compute computation of the net radiation experienced by the canopy. It includes the portion of shortwave and longwave from the atmosphere that are absorbed via Beer’s law, minus the outgoing longwave emitted from the canopy, plus upward longwave radiation emitted by the snow and surface. It also does not include any secondary bounces (e.g. reflected atmosphere->canopy->cloud->back to canopy, or transmitted by the canopy, reflected by snow/surface.
Requires the use of LandCover types, for canopy albedo and Beer’s law coefficients.
“evaluator type” = “radiation balance, surface and canopy”
radiation-balance-evaluator-spec
KEYS: - “surface albedos” SURFACE_DOMAIN-albedos - “surface emissivities” SURFACE_DOMAIN-emissivities - “incoming shortwave radiation” SURFACE_DOMAIN-incoming_shortwave_radiation - “incoming longwave radiation” SURFACE_DOMAIN-incoming_longwave_radiation - “surface temperature” SURFACE_DOMAIN-temperature - “snow temperature” SNOW_DOMAIN-temperature - “canopy temperature” CANOPY_DOMAIN-temperature - “leaf area index” CANOPY_DOMAIN-leaf_area_index - “area fractions” SURFACE_DOMAIN-area_fractions
Note that this is a superset of the physics in the “canopy radiation evaluator,” and is therefore mutually exclusive with that model.
Canopy Radiation Balance
Evaluates the canopy radiation balance, providing canopy net and radiation to the snow/surface.
Computes and sums the downward radiation terms, determining the total radiation sent down to the surface from the canopy and above.
Requires the use of LandCover types, for albedo and emissivity of the canopy itself, along with Beer’s law coefficients.
Computes:
canopy-downward_shortwave_radiation – transmitted shortwave. Note that incoming shortwave is attenuated by Beer’s law, and partially transmitted without attenuation when there are gaps (e.g. LAI < 1) in the canopy.
canopy-downward_longwave_radiation – transmitted longwave (see above, noting that Beer’s law coefficients should be used that absorb most if not all the longwave radiation), along with longwave emitted by the canopy computed using a canopy leaf temperature and a Bolzmann equation.
canopy-downward_net_radiation – this is a partial computation of the net radiation experienced by the canopy. It includes the portion of shortwave and longwave from the atmosphere that are absorbed via Beer’s law, minus the outgoing longwave emitted from the canopy (see downward above). It does NOT include upward longwave radiation emitted by the snow or surface. It also does not include any secondary bounces (e.g. reflected atmosphere->canopy->cloud->back to canopy, or transmitted by the canopy, reflected by snow).
Here the net radiation is positive for energy added to the canopy, while the other two are positive for energy sent to the layer below.
In the canopy-downward_net_radiation, we cannot include the upward terms YET, because these are a function of snow and surface temperature, which in turn depend upon the downward radiation computed here. So we choose to break the loop here, by computing downard terms first, then iterating to compute snow temperature, then compute upward terms. The alternative would be to have a formal snow energy PK that computed snow temperature, at which point we would solve all of these balances to convergence simultaneously.
“evaluator type” = “canopy radiation balance from above”
canopy-radiation-evaluator-spec
KEYS: - “incoming shortwave radiation” SURFACE_DOMAIN-incoming_shortwave_radiation - “incoming longwave radiation” SURFACE_DOMAIN-incoming_longwave_radiation - “canopy temperature” CANOPY_DOMAIN-temperature - “leaf area index” CANOPY_DOMAIN-leaf_area_index
Note that this is a subset of the physics in the “radiation balance evaluator,” and is therefore mutually exclusive with that model.
Surface Albedo
Note that albedo is also a multiple subgrid component model, like surface balance.
Evaluates albedos and emissivities in a two-component subgrid model.
Evaluates the albedo and emissivity as an interpolation on the surface properties and cover. This allows for two components – snow and not snow (water/ice/land). Note this internally calculates albedo of snow based upon snow density.
Components are indexed by: 0 = land/ice/water, 1 = snow.
Requires the use of LandCover types, for ground albedo and emissivity.
albedo-evaluator-spec
“albedo ice [-]”
[double]0.44“albedo water [-]”
[double]0.1168“emissivity ice [-]”
[double]0.98“emissivity water [-]”
[double]0.995“emissivity snow [-]”
[double]0.98KEYS:
“subgrid albedos” DOMAIN-subgrid_albedos
“subgrid emissivities” DOMAIN-subgrid_emissivities
DEPENDENCIES:
“snow density” SNOW_DOMAIN-density
“ponded depth” DOMAIN-ponded_depth
“unfrozen fraction” DOMAIN-unfrozen_fraction
Evaluates albedos and emissivities in a three-component subgrid model.
Evaluates the albedo and emissivity as an interpolation on the surface properties and cover. This allows for three components – water/ice, land, and snow. Note this internally calculates albedo of snow based upon snow density.
Components are: 0 = land, 1 = ice/water, 2 = snow.
Requires the use of LandCover types, for ground albedo and emissivity.
albedo-evaluator-subgrid-spec
“albedo ice [-]”
[double]0.44“albedo water [-]”
[double]0.1168“emissivity ice [-]”
[double]0.98“emissivity water [-]”
[double]0.995“emissivity snow [-]”
[double]0.98
KEYS:
“subgrid albedos” DOMAIN-subgrid_albedos
“subgrid emissivities” DOMAIN-subgrid_emissivities
DEPENDENCIES:
“snow density” SNOW_DOMAIN-density
“unfrozen fraction” DOMAIN-unfrozen_fraction
Incident Shortwave Radiation
Evaluates the radiation incident on a non-flat surface.
Aspect modified shortwave radiation is determined by a factor which is multiplied by the ‘incoming radiation incident on a flat surface’ to determine the ‘incoming radiation incident on a sloping surface of a given aspect’ as a function of slope and aspect, Julian day of the year, and time of day. The latitude and Julian day of the year are used to modify this with both time of day and seasonal changes of the planet.
Note that some careful checking and experimentation has found that, in general, the daily average incoming radiation times the 12-noon aspect modifier correlates reasonably well with the daily average of the product of the hourly incoming radiation and the hourly aspect modifier. It is notably better than the daily average radiation times the daily average aspect modifier.
This implementation is derived from LandLab code, which is released under the MIT license.
incident_shortwave_radiation_evaluator-spec
“incident shortwave radiation parameters”
[incident_shortwave_radiation_model-spec]KEYS: - “slope” DOMAIN-slope_magnitude - “aspect” DOMAIN-aspect - “incoming shortwave radiation” DOMAIN-incoming_shortwave_radiation
Evaluates shortwave as a function of slope/aspect/etc.
incident_shortwave_radiation_model-spec
“latitude [degrees]”
[double]Latitude of the site. A single typical value is fine for most domains, even relatively large ones (e.g. HUC4).“daily averaged”
[bool]true Compute a daily averaged radiation, as opposed to a time-specific, diurnal-cycle-resolving value.“day of year at time 0 [Julian days]”
[int]0 (Jan 1). ATS has no notion of absolute time, so to do things that depend upon planetary dynamics we must know what the day of the year is. Typically this is set by your meteorological data – set this to be equal to the day of year of met data’s time 0.
Longwave Radiation
Evaluates incoming longwave radiation from vapor pressure and air temperature.
longwave_evaluator-spec
DEPENDENCIES:
“air temperature key”
[string]DOMAIN-air_temperature“vapor pressure air key”
[string]DOMAIN-vapor_pressure_air
Full Surface Energy Balance Models
Finally, in addition to the potential-based models above, a few full-physics model are available. These are often based on older, monolithic models.
Bare Soil Surface Energy Balance
Calculates source terms for surface fluxes to and from the atmosphere and a ground surface.
The ground is assumed to consist of two potential area-fraction components – snow and no-snow. In the case of snow on the ground, this solves for a snow temperature, given a skin temperature, that satisfies a energy balance equation. In the case of no-snow, this calculates a conductive heat flux to the ground from the atmosphere.
“evaluator type” = “surface energy balance, two components”
seb-twocomponent-evaluator-spec
“wind speed reference height [m]”
[double]2.0 Reference height at which wind speed is measured.“minimum wind speed [m s^-1]”
[double]1.0 Sets a floor on wind speed for potential wierd data. Models have trouble with no wind.“save diagnostic data”
[bool]false Saves a suite of diagnostic variables to vis.“surface domain name”
[string]DEFAULT Default set by parameterlist name.“subsurface domain name”
[string]DEFAULT Default set relative to surface domain name.“snow domain name”
[string]DEFAULT Default set relative to surface domain name.
KEYS:
“surface water source” DOMAIN-water_source [m s^-1]
“surface energy source” DOMAIN-total_energy_source [MW m^-2]
“subsurface water source” DOMAIN-water_source [mol s^-1]
“subsurface energy source” DOMAIN-total_energy_source [MW m^-3]
“snow mass source - sink” DOMAIN-source_sink [m_SWE s^-1]
“new snow source” DOMAIN-source [m_SWE s^-1]
“albedo” DOMAIN-albedo [-] A single variate diagnostic of the final albedo.
“snowmelt” DOMAIN_SNOW-melt [m_SWE s^-1]
“evaporation” DOMAIN-evaporative_flux [m s^-1]
“snow temperature” DOMAIN_SNOW-temperature [K]
“sensible heat flux” DOMAIN-qE_sensible_heat [W m^-2]
“latent heat of evaporation” DOMAIN-qE_latent_heat [W m^-2]
“latent heat of snowmelt” DOMAIN-qE_snowmelt [W m^-2]
“outgoing longwave radiation” DOMAIN-qE_lw_out [W m^-2]
“conducted energy flux” DOMAIN-qE_conducted [W m^-2]
DEPENDENCIES:
“incoming shortwave radiation” DOMAIN-incoming_shortwave_radiation [W m^-2]
“incoming longwave radiation” DOMAIN-incoming_longwave_radiation [W m^-2]
“air temperature” DOMAIN-air_temperature [K]
“vapor pressure air” DOMAIN-vapor_pressure_air [Pa]
“wind speed” DOMAIN-wind_speed [m s^-1]
“precipitation rain” DOMAIN-precipitation_rain [m s^-1]
“precipitation snow” DOMAIN_SNOW-precipitation [m_SWE s^-1]
“snow depth” DOMAIN_SNOW-depth [m]
“snow density” DOMAIN_SNOW-density [kg m^-3]
“snow death rate” DOMAIN_SNOW-death_rate [m s^-1] Snow “death” refers to the last bit of snowmelt that we want to remove discretely.
“ponded depth” DOMAIN-ponded_depth [m]
“unfrozen fraction” DOMAIN-unfrozen_fraction [-] 1 –> all surface water, 0 –> all surface ice
“subgrid albedos” DOMAIN-albedos [-] Dimension 2 field of (no-snow, snow) albedos.
“subgrid emissivity” DOMAIN-emissivities [-] Dimension 2 field of (no-snow, snow) emissivities.
“area fractions” DOMAIN-fractional_areas Dimension 2 field of (no-snow, snow) area fractions (sum to 1).
“temperature” DOMAIN-temperature [K] surface skin temperature.
“pressure” DOMAIN-pressure [Pa] surface skin pressure.
“rsoil” DOMAIN-rsoil [s/m] soil resistance of top cells.
“subsurface pressure” DOMAIN_SS-pressure [Pa]
“molar density liquid” DOMAIN-molar_density_liquid [mol m^-3]
“mass density liquid” DOMAIN-mass_density_liquid [kg m^-3]
Calculates source terms for surface fluxes to and from the atmosphere and a ground surface characterized by three components – snow, water-covered ground, and vegetated/bare soil.
The surface energy balance on these area weighted patches are individually calculated then averaged to form the total quantities. All down- and up-scaling of relevant quantities are done through the area weighting, which is calculated by a minimum threshold in snow and a depression depth/geometry-based approach for water. All snow is assumed to first cover water (likely ice), then cover land, as both water and snow prefer low-lying depressions due to gravity- and wind-driven redistributions, respectively.
“evaluator type” = “surface energy balance, two components”
seb-threecomponent-evaluator-spec
“wind speed reference height [m]”
[double]2.0 Reference height at which wind speed is measured.“minimum wind speed [m s^-1]”
[double]1.0 Sets a floor on wind speed for potential wierd data. Models have trouble with no wind.“save diagnostic data”
[bool]false Saves a suite of diagnostic variables to vis.“surface domain name”
[string]DEFAULT Default set by parameterlist name.“subsurface domain name”
[string]DEFAULT Default set relative to surface domain name.“snow domain name”
[string]DEFAULT Default set relative to surface domain name.
KEYS:
“surface water source” DOMAIN-water_source [m s^-1]
“surface energy source” DOMAIN-total_energy_source [MW m^-2]
“subsurface water source” DOMAIN-water_source [mol s^-1]
“subsurface energy source” DOMAIN-total_energy_source [MW m^-3]
“snow mass source - sink” DOMAIN-source_sink [m_SWE s^-1]
“new snow source” DOMAIN-source [m_SWE s^-1]
“albedo” DOMAIN-albedo [-] A single variate diagnostic of the final albedo.
“snowmelt” DOMAIN_SNOW-melt [m_SWE s^-1]
“evaporation” DOMAIN-evaporative_flux [m s^-1]
“snow temperature” DOMAIN_SNOW-temperature [K]
“sensible heat flux” DOMAIN-qE_sensible_heat [W m^-2]
“latent heat of evaporation” DOMAIN-qE_latent_heat [W m^-2]
“latent heat of snowmelt” DOMAIN-qE_snowmelt [W m^-2]
“outgoing longwave radiation” DOMAIN-qE_lw_out [W m^-2]
“conducted energy flux” DOMAIN-qE_conducted [W m^-2]
DEPENDENCIES:
“incoming shortwave radiation” DOMAIN-incoming_shortwave_radiation [W m^-2]
“incoming longwave radiation” DOMAIN-incoming_longwave_radiation [W m^-2]
“air temperature” DOMAIN-air_temperature [K]
“vapor pressure air” DOMAIN-vapor_pressure_air [Pa]
“wind speed” DOMAIN-wind_speed [m s^-1]
“precipitation rain” DOMAIN-precipitation_rain [m s^-1]
“precipitation snow” DOMAIN_SNOW-precipitation [m_SWE s^-1]
“snow depth” DOMAIN_SNOW-depth [m]
“snow density” DOMAIN_SNOW-density [kg m^-3]
“snow death rate” DOMAIN_SNOW-death_rate [m s^-1] Snow “death” refers to the last bit of snowmelt that we want to remove discretely.
“ponded depth” DOMAIN-ponded_depth [m]
“unfrozen fraction” DOMAIN-unfrozen_fraction [-] 1 –> all surface water, 0 –> all surface ice
“subgrid albedos” DOMAIN-albedos [-] Dimension 2 field of (no-snow, snow) albedos.
“subgrid emissivity” DOMAIN-emissivities [-] Dimension 2 field of (no-snow, snow) emissivities.
“area fractions” DOMAIN-fractional_areas Dimension 2 field of (no-snow, snow) area fractions (sum to 1).
“temperature” DOMAIN-temperature [K] surface skin temperature.
“pressure” DOMAIN-pressure [Pa] surface skin pressure.
“rsoil” DOMAIN-rsoil [s/m] soil resistance of top cells.
“subsurface pressure” DOMAIN_SS-pressure [Pa]
“molar density liquid” DOMAIN-molar_density_liquid [mol m^-3]
“mass density liquid” DOMAIN-mass_density_liquid [kg m^-3]
Snow evaluators
Evaluators used for solving snowpack and/or snow redistribution laterally.
SnowSurfacePotential
Computes the potential surface upon which snow redistribution acts.
Snow distribution moves snow precipitation around to ensure that low-lying areas fill up first. This represents a potential field driving movement of snow precip, so defines what we mean by low-lying.
“evaluator type” = “snow skin potential”
snow-skin-potential-evaluator-spec
“dt factor [s]”
[double]A free-parameter factor for providing a time scale for diffusion of snow precipitation into low-lying areas. Typically on the order of 1e4-1e7. This timestep times the wave speed of snow provides an approximate length of how far snow precip can travel. Extremely tunable! [s]
KEYS:
“ponded depth” SURFACE_DOMAIN-ponded_depth [m]
“snow depth” DOMAIN-depth [m]
“precipitation snow” DOMAIN-precipitation [m s^-1]
“elevation” SURFACE_DOMAIN-elevation [m]
Example:
<ParameterList name="snow_skin_potential" type="ParameterList">
<Parameter name="evaluator type" type="string" value="snow skin potential" />
<Parameter name="dt factor [s]" type="double" value="864000.0" />
</ParameterList>
Snow Melt Rate
Evaluates snow melt via USDA - Natural Resources Conservation Service model
From: National Engineering Handbook (NEH) part 630, Chapter 11
Snow melt rate is given by:
where \(R\) is the snow melt rate per degree-day and \(T_{snow}^{expected}\) is the expected snow temperature, which is typically given by \(T_{snow}^{expected} = T_{air} - \Delta\), where \(\Delta\) is the expected air-snow temperature difference [C] (note this is NOT prescribed here – the user must supply the expected snow temperature via an evalutor).
Note that the Heaviside function is used to ensure this is only active when the expected snow temperature is above 0 C.
Then, a linear transition factor is applied to ensure that this goes to zero as the snow SWE goes to zero. That factor is 1 at the snow transition depth, and 0 when snow SWE is 0. This uses LandCover for the snow_ground_transition parameter.
snow-meltrate-evaluator-spec
“snow melt rate [mm day^-1 C^-1]”
[double]2.74 the melt rate per degree-day, above 0 C, e.g. \(R\) above.
KEYS:
“snow water equivalent” DOMAIN-water_equivalent
“expected snow temperature” DOMAIN-expected_temperature
Canopy evaluators
Interception
Partitions water between interception and throughfall, combining throughfall with drainage.
Based on CLM 4.5 and Lawrence et al 2007, interception is given by:
Throughfall is given by:
Drainage is provided as input here, as a total drainage from the canopy. The phase of this drainage is assumed to match the phase of the precipitation. So if it is raining, drainage is rain, while if it is 50/50 rain and snow, drainage is also 50/50 rain and snow. If total precipitation is 0, then drainage is partitioned by air temperature (above 0C –> all rain, otherwise all snow). This evaluator partitions the drainage and sums it with throughfall to compute the total source, in each phase, to the layer below the canopy (snow and/or ground surface).
interception-fraction-evaluator-spec
“interception fraction parameters”
[interception-fraction-model-spec]MY KEYS: - “interception” DOMAIN-interception - “throughfall and drainage rain” DOMAIN-throughfall_drainage_rain - “throughfall and drainage snow” DOMAIN-throughfall_drainage_snow
KEYS: - “area index” DOMAIN-area_index - “precipitation rain” DOMAIN_SURFACE-precipitation_rain - “precipitation snow” DOMAIN_SNOW-precipitation - “drainage” DOMAIN-drainage - “air temperature” DOMAIN_SURFACE-air_temperature
Fraction of incoming water that is intercepted.
Based on CLM 4.5 and Lawrence et al 2007:
The interception fraction is everything here after the precip.
interception-fraction-model-spec
- “leaf area interception fraction [-]”
[double]0.25 The alpha term, this describes the fraction of leaf area that intercepts water.
- “leaf area interception fraction [-]”
Drainage
Drainage rate from the canopy to the lower layers.
A simple model based on relaxation from current water content to a saturated water content.
|
| source
V
/ \
I / \
V |
--Theta-- | T
^ |
| D |
V V
-- -- -- -- -- -- --
This is the model for drainage D.
Drainage is given by:
drainage-evaluator-spec
“drainage timescale [s]”
[double]864 Timescale over which drainage occurs.- “saturated specific water content [m^3 H2O / m^2 leaf area]”
[double]1e-4 The thickness of the wetting surface – determines maximum canopy water storage.
- “saturated specific water content [m^3 H2O / m^2 leaf area]”
KEYS: - “area index” - “water equivalent”
Carbon and Biogeochemistry Models
Carbon Decomposition Rate
Cryo/bioturbation
Pool Decomposition
Pool Transfer
Multiscale Models
Subgrid Aggregation
SubgridAggregateEvaluator restricts a field to the subgrid version of the same field.
subgrid-aggregate-evaluator-spec
“source domain name”
[string]Domain name of the source mesh.
KEYS:
“field” SOURCE_DOMAIN-KEY Default set from this evaluator’s name.
Subgrid disaggregation
SubgridDisaggregateEvaluator restricts a field to the subgrid version of the same field.
Note that this evaluator fills exactly one subdomain in a domain set – there will be N evaluators each filling one subdomain.
subgrid-disaggregate-evaluator-spec
“source domain name”
[string]Domain name of the source mesh.
KEYS:
“field” SOURCE_DOMAIN-KEY Default set from this evaluator’s name.
Geometric evaluators
Evaluators that capture various aspects of the mesh geometry.
SurfaceElevation
Evaluates the elevation (z-coordinate) and slope magnitude of a mesh.
“evaluator type” = “meshed elevation”
Evaluates the z-coordinate and the magnitude of the slope :math:|\nambla_h z|
meshed-elevation-evaluator-spec
“parent domain name”
[string]SUBSURFACE_DOMAIN Domain name of the parent mesh, which is the 3D version of this domain. Attempts to generate an intelligent default by stripping “surface” from this domain.“dynamic mesh”
[bool]false Lets the evaluator know that the elevation changes in time, and adds the “deformation” dependency.
MY KEYS:
“elevation” DOMAIN-elevation Name the elevation variable. [m]
“slope magnitude” DOMAIN-slope_magnitude Name the elevation variable. [-]
KEYS:
“deformation” optional If “dynamic mesh” == True, this is required to tell when the mesh has been deformed.
Elevation of a Column
ElevationEvaluatorColumn: evaluates the elevation (z-coordinate) and slope magnitude of a mesh.
Evaluates elevation, slope, and aspect of the “surface_star” mesh of the Arctic Intermediate Scale Model (ISM).
Evaluates the z-coordinate and the magnitude of the slope :math:|\nambla_h
z| Note that this is evaluator is different from both the standard elevation
evaluator, which would take elevation/slope/aspect from the parent 3D mesh, and
from the standard “single cell” column mesh elevation, which can do the same.
Instead, it is a mix of:
elevation is aggregated from the column meshes’ top faces
slope is calculated using a cell-neighbor differencing scheme. Unlike 3D meshes, in the ISM, we deform columns of cells and so do not have faces. Therefore, we use all neighboring cells to compute an average normal for the cell, and use that to compute slope and aspect.
aspect is set to 0. It could easily be calculated using the same normal as the slope algorithm, but is not done currently.
“evaluator type” = “elevation column”
column-elevation-evaluator-spec
“elevation key”
[string]elevation Name the elevation variable. [m]“slope magnitude key”
[string]slope_magnitude Name the elevation variable. [-]“dynamic mesh”
[bool]false Lets the evaluator know that the elevation changes in time, and adds the “deformation” and “base_porosity” dependencies.“parent domain name”
[string]DOMAIN Domain name of the parent mesh, which is the 3D version of this domain. In the columnar meshes the surface elevation and slope are assigned based on the columns and not the base 3D domain.
Example:
<ParameterList name="surface_star-elevation">
<Parameter name="evaluator type" type="string" value="column elevation"/>
</ParameterList>
Depth Evaluator
Computes depth, positive downward relative to the surface, of mesh cells.
Computes cell depths only.
Note that two algorithms for computing the depth are available:
“cell centroid” uses the cell centroid, as computed by the Mesh, directly.
“mean face centroid” is the default, as the cell centroid can have problems in the case of non-planar faces. Instead, it uses the mean of the above and below face centroids in place of the face centroid, with the implicit assumption that dz is uniform (e.g. this is an extruded mesh).
“evaluator type” = “depth”
depth-evaluator-spec
“algorithm”
[string]mean face centroid Valid is “mean face centroid” and “cell centroid”, see above.
Cell Volume evaluator
Deforming Cell Volume evaluator
Generic evaluators
These evaluators take arguments to allow the user to provide custom functions via the input spec.
Additive
A generic evaluator for summing a collection of fields.
additive-evaluator-spec
* “constant shift” [double] 0 A constant value to add to the sum.
“enforce positivity”
[bool]false If true, max the result with 0.“DEPENDENCY coefficient”
[double]1.0 A multiple for each dependency in the list below.
ONE OF
“dependencies”
[Array(string)]The things to sum.
OR
“evaluator dependency suffixes”
[Array(string)]
END
Multiplicative
A generic evaluator for multiplying a collection of fields.
multiplicative-evaluator-spec
* “coefficient” [double] 1 A constant prefix to the product.
“enforce positivity”
[bool]false If true, max the result with 0.“DEPENDENCY dof”
[double]0 Degree of Freedom for each given dependency to use in the multiplication. NOTE, this should only be provided if the dependency has more than 1 DoF – if it just has one leaving this blank results in better error checking than providing the value 0 manually.
ONE OF
“dependencies”
[Array(string)]The fields to multiply.
OR
“evaluator dependency suffixes”
[Array(string)]
END
Column summation
Sums a subsurface field vertically only a surface field.
Simple vertical sum of all cells below each surface cell. Note that their are options for including volume factors (multiply by subsurface cell volume, sum, divide by surface cell area) and density (useful for the most common use case of summing fluxes onto the surface and converting to m/s instead of mol/m^2/s).
column-sum-evaluator-spec
“include volume factor”
[bool]true In summing, multiply the summand subsurface cell volume, then divide the sum by the surface cell area. Useful for converting volumetric fluxes to total fluxes.“divide by density”
[bool]true Divide the summand by density. Useful for converting molar fluxes to volumetric fluxes (e.g. transpiration).“column domain name”
[string]domain The domain of the subsurface mesh. Note this defaults to a sane thing based on the variable’s domain (typically “surface” or “surface_column:*”) and is rarely set by the user.
KEYS:
“summed” The summand, defaults to the root suffix of the calculated variable.
“cell volume” Defaults to domain’s cell volume.
“surface cell volume” Defaults to surface domain’s cell volume.
“molar density” Defaults to domain’s molar_density_liquid.
Top cell
Arbitrary function
Uses functions to evaluate arbitrary algebraic functions of its dependencies.
For example, one might write a dependency:
VARNAME = 0.2 * DEP1 - DEP2 + 3
“evaluator type” = “secondary variable from function”
secondary-variable-from-function-evaluator-spec
ONE OF
“functions”
[composite-vector-function-spec-list]Note this is used for multiple Degress of Freedom.
OR
“function”
[composite-vector-function-spec]Used for a single degree of freedom.
END
Example:
<ParameterList name="VARNAME">
<Parameter name="field evaluator type" type="string" value="algebraic variable from function"/>
<Parameter name="evaluator dependencies" type="Array{string}" value="{DEP1, DEP2}"/>
<ParameterList name="function">
<ParameterList name="function-linear">
<Parameter name="x0" type="Array(double)" value="{0.0,0.0}" />
<Parameter name="y0" type="double" value="3." />
<Parameter name="gradient" type="Array(double)" value="{0.2, -1}" />
</ParameterList>
</ParameterList>
</ParameterList>
InitialConditions
Initial condition specs are used in three places:
In the “initial conditions” sublist of state, in which the value of atomic constants are provided (not really initial conditions and should be renamed). These atomic values are not controlled by evaluators, and are not included in the DaG.
Within the PK spec which describes the initial condition of primary variables (true initial conditions).
The first may be of multiple types of data, while the latter two are nearly always fields on a mesh (e.g. CompositeVectors). The specific available options for initializing various data in state differ by data type.
constants-scalar-spec
“value”
[double]Value of a scalar constant
constants-dense-vector-spec
“value”
[Array(double)]Value of a dense, local vector.
constants-point-spec
“value”
[Array(double)]Array containing the values of the point.
constants-composite-vector-spec
“constant”
[double]optional Constant value.“value”
[double]optional Constant value, same as “constant” above.“function”
[composite-vector-function-spec-list]optional Initialize from a function, see CompositeVectorFunction“restart file”
[string]optional Path to a checkpoint file from which to read the values.“cells from file”
[string]optional Same as “restart file”, but only reads the cell component.“exodus file initialization”
[exodus-file-initialization-spec]optional See Exodus File Initialization.“initialize from 1D column”
[column-file-initialization-spec]optional See Column File Initialization.
BoundaryConditions
In general, boundary conditions are provided in a hierarchical list by boundary condition type, then functional form. Boundary condition specs are split between two types – those which require a user-provided function (i.e. Dirichlet data, etc) and those which do not (i.e. zero gradient conditions).
A list of conditions might pull in both Dirichlet and Neumann data on different regions, or use different functions on different regions. The following example illustrates how boundary conditions are prescribed across the domain for a typical PK:
Example:
<ParameterList name="boundary conditions">
<ParameterList name="DIRICHLET_TYPE">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="DIRICHLET_FUNCTION_NAME">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="101325.0"/>
</ParameterList>
</ParameterList>
</ParameterList>
<ParameterList name="BC east">
<Parameter name="regions" type="Array(string)" value="{east}"/>
<ParameterList name="DIRICHLET_FUNCTION_NAME">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="102325."/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
<ParameterList name="water flux">
<ParameterList name="BC north">
<Parameter name="regions" type="Array(string)" value="{north}"/>
<ParameterList name="outward water flux">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0."/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
<ParameterList name="zero gradient">
<ParameterList name="BC south">
<Parameter name="regions" type="Array(string)" value="{south}"/>
</ParameterList>
</ParameterList>
</ParameterList>
Different PKs populate this general format with different names, replacing DIRICHLET_TYPE and DIRICHLET_FUNCTION_NAME.
Flow-specific Boundary Conditions
Flow boundary conditions must follow the general format shown in BoundaryConditions. Specific conditions implemented include:
Dirichlet (pressure) boundary conditions
Used for both surface and subsurface flows, this provides pressure data on boundaries (in [Pa]).
Example:
<ParameterList name="boundary conditions">
<ParameterList name="pressure">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="boundary pressure">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="101325.0"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Dirichlet (head) boundary conditions
Used for both surface and subsurface flows, this provides head data (in [m] above the land surface), typically as a function of x & y. In the subsurface case, the z-value is given by hydrostatic relative to that head.
where h is the head function provided.
Example:
<ParameterList name="boundary conditions">
<ParameterList name="head">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="boundary head">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0.01"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Dirichlet (fixed level) boundary conditions
This fixes the water table at a constant elevation. It is a head condition that adapts to the surface elevation, adjusting the head to a datum that is a fixed absolute z coordinate.
where h is the head function provided.
Example:
<ParameterList name="boundary conditions">
<ParameterList name="fixed level">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="fixed level">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0.0"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Neumann (water flux) boundary conditions
Used for both surface and subsurface flows, this provides water flux data (in [mol m^-2 s^-1], for the subsurface, or [mol m^-1 s^-1] for the surface, in the outward normal direction) on boundaries.
Example:
<ParameterList name="boundary conditions">
<ParameterList name="water flux">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="outward water flux">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="-1.e-3"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Neumann (fix level flux) boundary conditions
Used for surface only, this provides fixed level ([m]) velocity data (in [m s^-1], in the outward normal direction on boundaries.
Example:
<ParameterList name="boundary conditions">
<ParameterList name="fixed level flux">
<ParameterList name="river level south">
<Parameter name="regions" type="Array(string)" value="{river south}"/>
<ParameterList name="fixed level">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0.5"/>
</ParameterList>
</ParameterList>
<ParameterList name="velocity">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="2.5"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Seepage face boundary conditions
A variety of seepage face boundary conditions are permitted for both surface and subsurface flow PKs. Typically seepage conditions are of the form:
if \(q \cdot \hat{n} < 0\), then \(q = 0\)
if \(p > p0\), then \(p = p0\)
This ensures that flow is only out of the domain, but that the max pressure on the boundary is specified by \(p0\).
Example: pressure (for surface or subsurface)
<ParameterList name="boundary conditions">
<ParameterList name="seepage face pressure">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="boundary pressure">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="101325."/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Example: head (for surface)
<ParameterList name="boundary conditions">
<ParameterList name="seepage face head">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="boundary head">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0.0"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Additionally, an infiltration flux may be prescribed, which describes the max flux. This is for surface faces on which a typical precipitation rate might be prescribed, to be enforced until the water table rises to the surface, at which point the precip is turned off and water seeps into runoff. This capability is experimental and has not been well tested.
if \(q \cdot \hat{n} < q_0\), then \(q = q_0\)
if \(p > p_{atm}\), then \(p = p_{atm}\)
Note the condition also accepts a parameter:
“explicit time index”
[bool]false If true, the _type_ of the BC is evaluated at the old time, keeping it fixed while the nonlinear solve iterates.
Example: seepage with infiltration
<ParameterList name="boundary conditions">
<ParameterList name="seepage face with infiltration">
<ParameterList name="BC west">
<Parameter name="explicit time index" type="bool" value="true"/>
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="outward water flux">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="-1.e-5"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Note it would be straightforward to add both p0 and q0 in the same condition; this has simply not had a use case yet.
Zero head gradient boundary conditions
Used for surface flows, this is an “outlet” boundary condition which looks to enforce the condition that
for head \(h\) and outward normal \(\hat{n}\). Note that this is an “outlet” boundary, in the sense that it should really not be used on a boundary in which
This makes it a useful boundary condition for benchmark and 2D problems, where the elevation gradient is clear, but not so useful for DEM-based meshes.
Example:
<ParameterList name="boundary conditions">
<ParameterList name="zero gradient">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
</ParameterList>
</ParameterList>
</ParameterList>
Critical depth boundary conditions
Also for surface flows, this is an “outlet” boundary condition which looks to set an outward flux to take away runoff. This condition is given by:
Example:
<ParameterList name="boundary conditions">
<ParameterList name="critical depth">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
</ParameterList>
</ParameterList>
</ParameterList>
Dynamic boundary condutions
The type of boundary conditions maybe changed in time depending on the switch function of TIME.
<ParameterList name="dynamic">
<Parameter name="regions" type="Array(string)" value="{surface west}"/>
<ParameterList name="switch function">
<ParameterList name="function-tabular">
<Parameter name="file" type="string" value="../data/floodplain2.h5" />
<Parameter name="x header" type="string" value="Time" />
<Parameter name="y header" type="string" value="Switch" />
<Parameter name="form" type="Array(string)" value="{constant}"/>
</ParameterList>
</ParameterList>
<ParameterList name="bcs">
<Parameter name="bc types" type="Array(string)" value="{head, water flux}"/>
<Parameter name="bc functions" type="Array(string)" value="{boundary head, outward water flux}"/>
<ParameterList name="water flux">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{surface west}"/>
<ParameterList name="outward water flux">
<ParameterList name="function-tabular">
<Parameter name="file" type="string" value="../data/floodplain2.h5" />
<Parameter name="x header" type="string" value="Time" />
<Parameter name="y header" type="string" value="Flux" />
<Parameter name="form" type="Array(string)" value="{linear}"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
<ParameterList name="head">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{surface west}"/>
<ParameterList name="boundary head">
<ParameterList name="function-tabular">
<Parameter name="file" type="string" value="../data/floodplain2.h5" />
<Parameter name="x header" type="string" value="Time" />
<Parameter name="y header" type="string" value="Head" />
<Parameter name="form" type="Array(string)" value="{linear}"/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Transport-specific Boundary Conditions
Energy-specific Boundary Conditions
Energy boundary conditions must follow the general format shown in BoundaryConditions. Energy-specific conditions implemented include:
Dirichlet (temperature) boundary conditions
Provide temperature data in units of [K].
Example:
<ParameterList name="boundary conditions">
<ParameterList name="temperature">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="boundary temperature">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="276.15."/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Neumann (diffusive energy flux) boundary conditions
Note that for an energy equation, there are two mechanisms by which energy can be fluxed into the domain: through diffusion and through advection. This boundary condition sets the diffusive flux of energy, and allows the advective flux to be whatever it may be. Frequently this is used in combination with boundaries where water is expected to be advected out of the domain, and we wish to allow the energy of that water to be advected away with it, but wish to independently specify diffusive fluxes. This can also be used in cases where the mass flux is prescribed to be zero (e.g. bottom boundaries, where this might be the geothermal gradient).
Units are in [MW m^-2], noting the deviation from SI units!
Example:
<ParameterList name="boundary conditions">
<ParameterList name="diffusive flux">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="outward diffusive flux">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0."/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Note that another commonly implemented boundary condition is one where the diffusive flux is prescribed, and also the temperature of incoming water is prescribed. This is not currently implemented, but would be straightforward to do so if requested.
Neumann (total energy flux) boundary conditions
This boundary condition sets the total flux of energy, from both advection and diffusion. This is not used all that often in real applications, but is common for benchmarks or other testing.
Units are in [MW m^-2], noting the deviation from SI units!
Example:
<ParameterList name="boundary conditions">
<ParameterList name="enthalpy flux">
<ParameterList name="BC west">
<Parameter name="regions" type="Array(string)" value="{west}"/>
<ParameterList name="outward enthalpy flux">
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="0."/>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Time integrators, solvers, and other mathematical specs
Common specs for all solvers and time integrators, used in PKs.
There are three commonly used broad classes of time integration strategies.
“Update” methods are the simplest – they use no formal mathematical definition of a differential equation, but instead implicitly use a process by which variables at the new time are directly calculated. Typically there is an implied ODE or PDE here, but it is not stated as such and time integration routines are not used. Examples of these are common in biogeochemistry and vegetation models.
“Explicit” time methods are the next simplest. These include a variety of options from forward Euler to higher order Runge-Kutta schemes. These only require evaluating forward models where we have existing of the dependencies. If they work, these are great thanks to their deterministic nature and lack of expensive, memory-bandwith limited solvers. But they only work on some types of problems. Examples of of these include transport, where we use high order time integration schemes to preserve fronts.
“Implicit” and semi-implicit methods instead require the evaluation of a residual equation – the solution is guessed at, and the residual is calculated, which measures how far the equation is from being satisfied. This measure is then inverted, finding a correction to the guess which hopefully reduces the residual. As the residual goes to zero, the error, a measure of the difference between the guess and the true solution, also goes to zero. To do this inversion, we lean on Newton and Newton-like methods, which attempt to somehow linearize, or approximately linearize, the residual function near the guess in order to calculate an update. In this case, the time integration scheme requires both a nonlinear solver (to drive the residual to zero) and a linear solver or approximate solver (to calculate the correction).
TimeIntegrator
Currently there are two classes of time integration schemes used in ATS: explicit (including a range of single and multi-stage) methods and BDF1, or Backward Euler.
Explicit Time Integration
Explicit time integration methods in a generalized form.
This class implements several explicit Runge Kutta methods:
forward Euler (1st order) –> “forward_euler”
Heun-Euler method (2nd order) –> “heun_euler”
Midpoint method (2nd order) –> “midpoint”
Ralston method (2nd order) –> “ralston”
TVD RK method (3rd order) –> “tvd_3rd_order”
Kutta method (3rd order) –> “kutta_3rd_order”
Runge Kutta (4th order) –> “runge_kutta_4th_order”
User defined (whatever) –> user_defined, use special constructor to create
Note that user-defined is only for developers currently, and cannot be created from an input file.
The RK tableau is made up of the three private objects a, b, and c below. they are arranged as follows:
Note that c[0] should always equal zero, and that the entries in the matrix a that are not listed in this tableau are not used
The implemented general Runge Kutta scheme of order s based on this tableau arrangement is
explicit-ti-rk-spec
“verbose object”
[verbose-object-spec]A Verbose Object“RK method”
[string]forward euler One of: “forward Euler”, “heun euler”, “midpoint”, “ralston”, “tvd 3rd order”, “kutta 3rd order”, “runge kutta 4th order”
Backward Euler
Solves globally implicit systems using backward Euler
Backward Euler is the simplest of the implicit methods. It solves time integration schemes by evaluating all time derivatives at the new time. This makes it unconditionally stable, though potentially not very accurate. This unconditional stability tends to make it the workhorse of the types of stiff, nonlinear parabolic equations such as Richards equation and the diffusion wave approximation.
In this method, we look to solve:
via the time discretization scheme:
bdf1-ti-spec
“verbose object”
[verbose-object-spec]A Verbose Object“residual debugger”
[residual-debugger-spec]A Residual Debugger object.“max preconditioner lag iterations”
[int]0 specifies frequency of preconditioner recalculation.“freeze preconditioner”
[bool]false enforces preconditioner to be updated only once per non-linear solver. When set to true, the above parameter is ignored.“extrapolate initial guess”
[bool]true identifies forward time extrapolation of the initial guess.“nonlinear iteration initial guess extrapolation order”
[int]1 defines extrapolation algorithm. Zero value implies no extrapolation.“restart tolerance relaxation factor”
[double]1 Changes the nonlinear tolerance on restart. The time integrator is usually restarted when a boundary condition changes drastically. It may be beneficial to loosen the nonlinear tolerance on the first several time steps after the time integrator restart. The default value is 1, while a reasonable value may be as large as 1000.“restart tolerance relaxation factor damping”
[double]1 Controls how fast the loosened nonlinear tolerance will revert back to the one specified in “nonlinear tolerance”. If the nonlinear tolerance is “tol”, the relaxation factor is “factor”, and the damping is “d”, and the time step count is “n” then the actual nonlinear tolerance is “tol * max(1.0, factor * d ** n)”. Reasonable values are between 0 and 1.
INCLUDES
- [solver-typed-spec] Uses a Solver.
- [timestep-controller-typed-spec] Uses a Timestep Controller
Note this also accepts an object that provides the BDF1 Solver Interface.
<ParameterList name="time integrator">
<Parameter name="time integration method" type="string" value="BDF1"/>
<ParameterList name="BDF1">
<Parameter name="max preconditioner lag iterations" type="int" value="5"/>
<Parameter name="freeze preconditioner" type="bool" value="false"/>
<Parameter name="extrapolate initial guess" type="bool" value="true"/>
<Parameter name="nonlinear iteration initial guess extrapolation order" type="int" value="1"/>
<Parameter name="restart tolerance relaxation factor" type="double" value="1.0"/>
<Parameter name="restart tolerance relaxation factor damping" type="double" value="1.0"/>
<Parameter name="timestep controller type" type="string" value="standard"/>
<ParameterList name="timestep controller standard parameters">
...
</ParameterList>
<Parameter name="solver type" type="string" value="nka"/>
<ParameterList name="nka parameters">
...
</ParameterList>
</ParameterList>
</ParameterList>
BDF1 Solver Interface
Timestep Controller
Factory for creating TimestepController objects
A TimestepController object sets what size timestep to take. This can be a variety of things, from fixed timestep size, to adaptive based upon error control, to adapter based upon simple nonlinear iteration counts.
Available types include:
Timestep Controller Fixed (type “fixed”), a constant timestep
Timestep Controller Standard (type ‘standard”), an adaptive timestep based upon nonlinear iterations
Timestep Controller Smarter (type ‘smarter”), an adaptive timestep based upon nonlinear iterations with more control
Timestep Controller Adaptive (type “adaptive”), an adaptive timestep based upon error control.
Timestep Controller From File (type “from file”), uses a timestep history loaded from an HDF5 file. (Usually only used for regression testing.)
timestep-controller-typed-spec
“timestep controller type”
[string]Set the type. One of: “fixed”, “standard”, “smarter”, “adaptive”, or “from file”“timestep controller X parameters”
[list]List of parameters for a timestep controller of type X.
Timestep Controller Fixed
Timestep controller providing constant timestep size.
TimestepControllerFixed is a simple timestep control mechanism which sets
a constant timestep size. Note that the actual timestep size is given by the
minimum of PK’s initial timestep sizes.
No parameters are required.
Timestep Controller Standard
Simple timestep control based upon previous iteration count.
This is a simple timestep control mechanism which sets the next timestep based upon the previous timestep and how many nonlinear iterations the previous timestep took to converge.
The timestep for step \(k+1\), \(\Delta t_{k+1}\), is given by:
if \(N_k > N^{max}\) then \(\Delta t_{k+1} = f_{reduction} * \Delta t_{k}\)
if \(N_k < N^{min}\) then \(\Delta t_{k+1} = f_{increase} * \Delta t_{k}\)
otherwise \(\Delta t_{k+1} = \Delta t_{k}\)
where \(\Delta t_{k}\) is the previous timestep and \(N_k\) is the number of nonlinear iterations required to solve step \(k\):.
timestep-controller-standard-spec
“max iterations”
[int]\(N^{max}\), decrease the timestep if the previous step took more than this.“min iterations”
[int]\(N^{min}\), increase the timestep if the previous step took less than this.“time step reduction factor”
[double]\(f_{reduction}\), reduce the previous timestep by this multiple.“time step increase factor”
[double]\(f_{increase}\), increase the previous timestep by this multiple.“max time step”
[double]The max timestep size allowed.“min time step”
[double]The min timestep size allowed. If the step has failed and the new step is below this cutoff, the simulation fails.
<ParameterList name="BDF1"> <!-- parent list -->
<Parameter name="timestep controller type" type="string" value="standard"/>
<ParameterList name="timestep controller standard parameters">
<Parameter name="min iterations" type="int" value="10"/>
<Parameter name="max iterations" type="int" value="15"/>
<Parameter name="time step increase factor" type="double" value="1.2"/>
<Parameter name="time step reduction factor" type="double" value="0.5"/>
<Parameter name="max time step" type="double" value="1e+9"/>
<Parameter name="min time step" type="double" value="0.0"/>
</ParameterList>
</ParameterList>
In this example, the time step is increased by factor 1.2 when the nonlinear solver converges in 10 or less iterations. The time step is not changed when the number of nonlinear iterations is between 11 and 15. The time step will be cut twice if the number of nonlinear iterations exceeds 15.
Timestep Controller Smarter
Slightly smarter timestep controller based upon a history of previous timesteps.
This is based on Timestep Controller Standard, but also tries to be a bit smarter to avoid repeated increase/decrease loops where the step size decreases, converges in few iterations, increases, but then fails again. It also tries to grow the step geometrically to more quickly recover from tricky nonlinearities.
timestep-controller-smarter-spec
“max iterations”
[int]\(N^{max}\), decrease the timestep if the previous step took more than this.“min iterations”
[int]\(N^{min}\), increase the timestep if the previous step took less than this.“time step reduction factor”
[double]\(f_{reduction}\), reduce the previous timestep by this multiple.“time step increase factor”
[double]\(f_{increase}\), increase the previous timestep by this multiple. Note that this can be modified geometrically in the case of repeated successful steps.“max time step increase factor”
[double]10. The max \(f_{increase}\) will ever get.“growth wait after fail”
[int]Wait at least this many timesteps before attempting to grow the timestep after a failed timestep.“count before increasing increase factor”
[int]Require this many successive increasions before multiplying \(f_{increase}\) by itself.
Timestep Controller Adaptive
Adaptive timestep control based upon previous iteration count.
This is under development and is based on a posteriori error estimates.
Timestep Controller From File
Timestep controller which loads a timestep history from file.
This loads a timestep history from a file, then advances the step size with those values. This is mostly used for testing purposes, where we need to force the same timestep history as previous runs to do regression testing. Otherwise even machine roundoff can eventually alter number of iterations enough to alter the timestep history, resulting in solutions which are enough different to cause doubt over their correctness.
timestep-controller-from-file-spec
“file name”
[string]Path to hdf5 file containing timestep information.“timestep header”
[string]Name of the dataset containing the history of timestep sizes.
Nonlinear Solver
A factory for creating nonlinear solvers.
Nonlinear solvers are used within implicit time integration schemes to drive the residual to zero and thereby solve for the primary variable at the new time.
solver-typed-spec
“solver type”
[string]Type of the solver. One of:“Newton” See Solver: Newton and Inexact Newton
“JFNK” See Solver: Jacobian-Free Newton Krylov
“line search” See Solver: Newton with Line Search
“continuation” See Solver: Nonlinear Continuation
“nka” See Solver: Nonlinear Krylov Acceleration
“aa” See Solver: Anderson Acceleration
“nka line search” See Solver: NKA with Line Search”
“nka_ls_ats” See Solver: NKA with Line Search, ATS
“nka_bt_ats” See Solver: NKA with backtracking, ATS
“nox” See Solver: NOX
“_solver_type_ parameters”
[_solver_type_-spec]A sublist containing parameters specific to the type.
Warning
“JFNK”, “line search”, and “continuation” methods have not been beaten on as much as other methods. “nka_ls_ats” is somewhat deprecated and probably shouldn’t be used. Prefer “nka” for simple problems, “nka_bt_ats” for freeze-thaw problems or other problems with strong nonlinearities, and “Newton” when you have a good Jacobian. While “nox” hasn’t been used extensively, it may be quite useful.
Solver: Newton and Inexact Newton
Straightforward Newton/Inexact Newton solver.
The classical Newton method works well for cases where Jacobian is available and corresponds to a stable (e.g. upwind) discretization. The inexact Newton methods work for cases where the discrete Jacobian is either not available, or not stable, or computationally expensive. The discrete Jacobian is replaced by a stable approximation of the continuum Jacobian. The choice between exact and inexact is not made by the Solver, but instead by the PK. Both use the ApplyPreconditioner() method – if this applies the true Jacobian, then the method is Newton. If it applies an appoximation, it is inexact Newton.
solver-newton-spec
“nonlinear tolerance”
[double]1.e-6 defines the required error tolerance. The error is calculated by a PK.“monitor”
[string]monitor update specifies control of the nonlinear residual. The available options are “monitor update” and “monitor residual”.“limit iterations”
[int]50 defines the maximum allowed number of iterations.“diverged tolerance”
[double]1.e10 defines the error level indicating divergence of the solver. The error is calculated by a PK.“max du growth factor”
[double]1.e5 allows the solver to identify divergence pattern on earlier iterations. If the maximum norm of the solution increment changes drastically on two consecutive iterations, the solver is terminated.“max error growth factor”
[double]1.e5 defines another way to identify divergence pattern on earlier iterations. If the PK-specific error changes drastically on two consecutive iterations, the solver is terminated.“max divergent iterations”
[int]3 defines another way to identify divergence pattern on earlier iterations. If the maximum norm of the solution increment grows on too many consecutive iterations, the solver is terminated.“make one iteration”
[bool]false require at least one iteration to be performed before declaring success. This options makes any effect only when “monitor residual” is choose.“modify correction”
[bool]true allows a PK to modify the solution increment. One example is a physics-based clipping of extreme solution values.“stagnation iteration check”
[int]8 determines the number of iterations before the stagnation check is turned on. The stagnation happens when the current l2-error exceeds the initial l2-error.
Solver: Jacobian-Free Newton Krylov
Decorator for using a Solver with JFNK as the preconditioner.
Jacobian-Free Newton Krylov uses a finite difference scheme to approximate the action of the Jacobian matrix, then uses a Krylov method (which only needs the action of the Jacobian and not the Jacobian itself) to calculate the action of the inverse of the Jacobian, thereby providing a Newton-like update. As the linear Krylov scheme converges to the inverse action, the nonlinear solution converges to the same solution as a true Newton method.
This implementation simply replaces a SolverFnBase’s ApplyPreconditioner() with a new ApplyPreconditioner() which uses the Krylov method with the action of the forward operator to (hopefully) improve, relative to the supplied approximate inverse, the estimate of the inverse.
solver-jfnk-spec
“nonlinear solver”
[solver-typed-spec]The outer nonlinear solver to use.“inverse”
[inverse-typed-spec]The Krylov method to use.“JF matrix parameters”
[jf-matrix-spec]See jf-matrix-spec
<Parameter name="solver type" type="string" value="JFNK"/>
<ParameterList name="JFNK parameters">
<Parameter name="typical solution value" type="double" value="1.0"/>
<ParameterList name="JF matrix parameters">
<Parameter name="finite difference epsilon" type="double" value="1.0e-8"/>
<Parameter name="method for epsilon" type="string" value="Knoll-Keyes L2"/>
</ParameterList>
<ParameterList name="nonlinear solver">
<Parameter name="nonlinear tolerance" type="double" value="1.0e-05"/>
<Parameter name="diverged tolerance" type="double" value="1.0e+10"/>
<Parameter name="limit iterations" type="int" value="20"/>
<Parameter name="max divergent iterations" type="int" value="3"/>
</ParameterList>
<ParameterList name="linear operator">
<Parameter name="iterative method" type="string" value="gmres"/>
<ParameterList name="gmres parameters">
...
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
The Jacobian-Free Matrix operator, which is used to estimate the action of the Jacobian.
A variety of methods are available for choosing the epsilon used to approximate the action of the Jacobian. They are documented in Knoll & Keyes 2004 paper.
..todo:: Document these
jf-matrix-spec
“typical solution value”
[double]100 Used in relative action approximations. OPTION NOT IMPLEMENTED“finite difference epsilon”
[double]1.e-8 defines the base finite difference epsilon.“method for epsilon”
[string]defines a method for calculating finite difference epsilon. Available option is “Knoll-Keyes”, “Knoll-Keyes L2”, “Brown-Saad”. See Knoll
Solver: Newton with Line Search
Line search on the provided correction as a solver.
Line Search accepts a correction from the Jacobian, then uses a process to attempt to minimize or at least ensure a reduction in the residual while searching in that direction, but not necessarily with the same magnitude, as the provided correction. The scalar multiple of the search direction is given by \(\alpha\).
This globalization recognizes that a true inverse Jacobian is a local measurement of the steepest descent direction, and so while the direction is guaranteed to be the direction which best reduces the residual, it may not provide the correct magnitude.
The algorithm is a reimplementation based on PETSc SNES type BT, which in turn is from Numerical Methods for Unconstrained Optimization and Nonlinear Equations by Dennis & Schnabel, pg 325.
Note, this always monitors the residual.
solver-line-search-spec
“nonlinear tolerance”
[double]1.e-6 defines the required error tolerance. The error is calculated by a PK.“limit iterations”
[int]50 defines the maximum allowed number of iterations.“diverged tolerance”
[double]1.e10 defines the error level indicating divergence of the solver. The error is calculated by a PK. Set to a negative value to ignore this check.“max error growth factor”
[double]1.e5 defines another way to identify divergence pattern on earlier iterations. If the PK-specific error changes drastically on two consecutive iterations, the solver is terminated.“modify correction”
[bool]false allows a PK to modify the solution increment. One example is a physics-based clipping of extreme solution values.“accuracy of line search minimum [bits]”
[int]10“min valid alpha”
[double]0“max valid alpha”
[double]10.“max line search iterations”
[int]10
Solver: Nonlinear Continuation
A very simple nonlinear continuation method.
Continuation methods are useful when the nonlinearity can be controlled by a single simple parameter. In this method, the nonlinear problem is solved with a less-nonlinear value of the parameter, and the solution of that is used as the initial guess to solve a harder problem. As each successive problem is solved, the continuation parameter is changed closer and closer to the true value.
Few if any PKs support this method currently – it requires the PK to provide more interface about how to update the continuation parameter.
solver-continuation-spec
“nonlinear tolerance”
[double]1.e-6 defines the required error tolerance. The error is calculated by a PK.“number of continuation steps”
[int]5 How many steps to take from initial parameter to final parameter.“inner solver”
[solver-typed-spec]A Solver, used at each step.
Solver: Nonlinear Krylov Acceleration
Nonlinear Krylov Acceleration as a nonlinear solver.
Uses the Nonlinear Krylov acceleration method of Carlson and Miller to do effectively a multivariant secant method, accelerating the solution of a nonlinear solve. This method can be significantly faster than Newton, especially with an approximate Jacobian.
Calef et al. “Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem.” JCP 238 (2013): 188-209.
N. N. Carlson, K. Miller, Design and application of a gradient-weighted moving finite element code II: In two dimensions, SIAM J. Sci. Comput. 19 (3) (1998) 766–798.
solver-nka-spec
“nonlinear tolerance”
[double]1.e-6 Defines the required error tolerance. The error is calculated by a PK.“monitor”
[string]monitor update Specifies control of the nonlinear residual. The available options are “monitor update”, “monitor residual”, “monitor preconditioned residual”, “monitor l2 residual”, and “monitor preconditioned l2 residual”.“limit iterations”
[int]20 Defines the maximum allowed number of iterations.“diverged tolerance”
[double]1.e10 Defines the error level indicating divergence of the solver. The error is calculated by a PK. Set to a negative value to ignore this check.“diverged l2 tolerance”
[double]1.e10 Defines another way to identify divergence of the solver. If the relative l2 (little l) norm of the solution increment is above this value, the solver is terminated. Set to a negative value to ignore this check.“diverged pc tolerance”
[double]1e10 Defines another way to identify divergence of the solver. If the relative maximum norm of the solution increment (with respect to the initial increment) is above this value, the solver is terminated. Set to a negative value to ignore this check.“diverged residual tolerance”
[double]1e10 Defines another way to identify divergence of the solver. If the relative l2 norm of the residual (with respect to the initial residual) is above this value, the solver is terminated. Set to a negative value to ignore this check.“max du growth factor”
[double]1e5 Allows the solver to identify divergence pattern on earlier iterations. If the maximum norm of the solution increment changes drastically on two consecutive iterations, the solver is terminated.“max error growth factor”
[double]1e5 Defines another way to identify divergence pattern on earlier iterations. If the PK-specific error changes drastically on two consecutive iterations, the solver is terminated.“max divergent iterations”
[int]3 Defines another way to identify divergence pattern on earlier iterations. If the maximum norm of the solution increment grows on too many consecutive iterations, the solver is terminated.“make one iteration”
[bool]false require at least one iteration to be performed before declaring success. This options makes any effect only when “monitor residual” is choose.“modify correction”
[bool]false Allows a PK to modify the solution increment. One example is a physics-based clipping of extreme solution values.“lag iterations”
[int]0 Delays the NKA acceleration, but updates the Krylov space.“max nka vectors”
[int]10 Defines the maximum number of consecutive vectors used for a local space.“nka vector tolerance”
[double]0.05 Defines the minimum allowed orthogonality between vectors in the local space. If a new vector does not satisfy this requirement, the space is modified.
Solver: Anderson Acceleration
Anderson acceleration as a nonlinear solver.
This is a variation of the GMRES solver for nonlinear problems.
solver-aa-spec
“nonlinear tolerance”
[double]1.e-6 Defines the required error tolerance. The error is calculated by a PK.“limit iterations”
[int]20 Defines the maximum allowed number of iterations.“diverged tolerance”
[double]1.e10 Defines the error level indicating divergence of the solver. The error is calculated by a PK. Set to a negative value to ignore this check.“diverged l2 tolerance”
[double]1.e10 Defines another way to identify divergence of the solver. If the relative L2 norm of the solution increment is above this value, the solver is terminated. Set to a negative value to ignore this check.“max du growth factor”
[double]1e5 Allows the solver to identify divergence pattern on earlier iterations. If the maximum norm of the solution increment changes drastically on two consecutive iterations, the solver is terminated.“max divergent iterations”
[int]3 Defines another way to identify divergence pattern on earlier iterations. If the maximum norm of the solution increment grows on too many consecutive iterations, the solver is terminated.“max aa vectors”
[int]10 Defines the maximum number of consecutive vectors used for a local space.“modify correction”
[bool]false Allows a PK to modify the solution increment. One example is a physics-based clipping of extreme solution values.“relaxation parameter”
[double]1 Damping factor for increment.
Solver: NKA with Line Search
NKA nonlinear solver with a line-search based on a Brendt minimization algorithm.
Does NKA, then checks if that correction has reduced the residual by at least a tolerance. If not, this uses a Brendt minimization algorithm to try and find an \(\alpha\) that minimizes the reduction in the residual.
Note, this always monitors the residual.
Solver: NKA with Line Search, ATS
Solver: NKA with backtracking, ATS
Nonlinear solve using NKA with a heuristic based backtracking.
Whereas line search uses a formal minimization method, backtracking simply uses a heuristic multiplier on \(\alpha\) to find a correction that sufficiently reduces the residual. This can be significantly faster than the full minimization problem, and finding the true minimum may not be as important as simply doing better and going on to the next nonlinear iteration.
This is the workhorse for hard ATS problems, as it is usually rather efficient, even in problems where the linear solve results in a correction that is way too large (e.g. for steep nonlinearities such as phase change).
Note this always monitors the residual, and the correction is always modified.
solver-nka-bt-ats-spec
“nonlinear tolerance”
[double]1.e-6 Defines the required error tolerance. The error is calculated by a PK.“limit iterations”
[int]20 Defines the maximum allowed number of iterations.“diverged tolerance”
[double]1.e10 Defines the error level indicating divergence of the solver. The error is calculated by a PK. Set to a negative value to ignore this check.“nka lag iterations”
[int]0 Delays the NKA acceleration, but updates the Krylov space.“max nka vectors”
[int]10 Defines the maximum number of consecutive vectors used for a local space.“nka vector tolerance”
[double]0.05 Defines the minimum allowed orthogonality between vectors in the local space. If a new vector does not satisfy this requirement, the space is modified.“backtrack tolerance”
[double]0. Require a reduction of at least this much in the residual norm before accepting a correction.“backtrack factor”
[double]0.5 Multiply the correction by this factor each backtracking step. Note, should be in (0, 1)“backtrack monitor”
[string]monitor either What norm is checked to determine whether backtracking has improved the residual or not? One of “monitor enorm”, “monitor L2 residual”, or ‘monitor either”“backtrack max steps”
[int]10 Controls how many multiples of the backtrack factor are applied before declaring failure.“backtrack max total steps”
[int]1e6 Controls how many total backtrack steps may be taken before declaring failure.“backtrack lag iterations”
[int]0 Delay requiring a reduction in residual for this many nonlinear iterations.“backtrack last iteration”
[int]1e6 Stop requiring a reductiontion in residual after this many nonlinear iterations.“backtrack fail on bad search direction”
[bool]false If backtracking for the full number of “backtrack max steps” is taken, and the residual norm has still not be reduced suffiently, this determines the behavior. If true, the solver declares failure. If false, it takes the bad step anyway and hopes to recover in later iterates.
IF
“Anderson mixing”
[bool]false If true, use Anderson mixing instead of NKA.
THEN
“relaxation parameter”
[double]0.7 The relaxation parameter for Anderson mixing.
END
Solver: NOX
Calls Nox nonlinear solvers/JFNK.
The interface to Trilinos NOX solver is as follows:
<Parameter name="solver type" type="string" value="nox"/>
<ParameterList name="nox parameters">
<Parameter name="typical solution value" type="double" value="1.0"/>
<ParameterList name="JF matrix parameters">
<Parameter name="finite difference epsilon" type="double" value="1.0e-8"/>
<Parameter name="method for epsilon" type="string" value="Knoll-Keyes L2"/>
</ParameterList>
<ParameterList name="nonlinear solver">
<Parameter name="solver type" type="string" value="Newton"/>
<ParameterList name="Newton parameters">
...
</ParameterList>
</ParameterList>
<ParameterList name="linear operator">
<Parameter name="iterative method" type="string" value="gmres"/>
<ParameterList name="gmres parameters">
...
</ParameterList>
</ParameterList>
</ParameterList>
</ParameterList>
Linear Solvers
Base class for providing ApplyInverse() methods on operators.
Matrix provides existing Operators with an inverse. Note this may be iterative or non-iterative, assembled or non-assembled, approximate or exact to machine precision.
inverse-typed-spec
“iterative method”
[string]optional“direct method”
[string]optional“preconditioning method”
[string]optional
DOCUMENT ME!
Linear Solver: PCG
Preconditioned conjugate gradient method for a linear solver.
iterative-method-pcg-spec
“error tolerance”
[double]1.e-6 Tolerance on which to declare success.“maximum number of iterations”
[int]100 Maximum iterations before declaring failure.“overflow tolerance”
[double]3.e50 Error above this value results in failure.“convergence criterial”
[Array(string)]{relative rhs} A list of criteria, any of which can be applied. Valid include:“relative rhs” : measure error relative to the norm of the RHS vector
“relative residual” : measure error relative to the norm of the residual
“absolute residual” : measure error directly, norm of error
“make one iteration” : require at least one iteration to be performed before declaring success
<ParameterList name="_PCG with HYPRE AMG"> <!-- parent list -->
<ParameterList name="pcg parameters">
<Parameter name="error tolerance" type="double" value="1e-12"/>
<Parameter name="maximum number of iterations" type="int" value="400"/>
<Parameter name="convergence criteria" type="Array(string)" value="{relative residual,make one iteration}"/>
<Parameter name="overflow tolerance" type="double" value="3.0e+50"/>
<ParameterList name="verbose object">
<Parameter name="verbosity level" type="string" value="high"/>
</ParameterList>
</ParameterList>
</ParameterList>
Linear Solver: GMRES
Generalized minimum residual method for a linear solver.
Based on the methods of Yu. Kuznetsov, 1968; Y.Saad, 1986. Deflated version of GMRES is due to R.Morgan, GMRES with deflated restarting, 2002 SISC; S.Rollin, W.Fichtner, Improving accuracy of GMRES with deflated restarting, 2007 SISC.
iterative-method-gmres-spec
“error tolerance”
[double]1.e-6 Tolerance on which to declare success.“maximum number of iterations”
[int]100 Maximum iterations before declaring failure.“overflow tolerance”
[double]3.e50 Error above this value results in failure.“convergence criterial”
[Array(string)]{relative rhs} A list of criteria, any of which can be applied. Valid include:“relative rhs” : measure error relative to the norm of the RHS vector
“relative residual” : measure error relative to the norm of the residual
“absolute residual” : measure error directly, norm of error
“make one iteration” : require at least one iteration to be performed before declaring success
“size of Krylov space”
[int]10 Size of the Krylov space used to span the residual.“controller training start”
[int]0 Start iteration for determining convergence rates. (Add more please!)“controller training end”
[int]3 Start iteration for determining convergence rates. (Add more please!)“preconditioning strategy”
[string]left Valid are “left” and “right”-type preconditioning (see Saad 1986)“maximum size of deflation space”
[int]0 Size of the deflation space, see Rollin et al.
<ParameterList name="_GMRES with HYPRE AMG"> <!-- parent list -->
<ParameterList name="gmres parameters">
<Parameter name="error tolerance" type="double" value="1e-12"/>
<Parameter name="maximum number of iterations" type="int" value="400"/>
<Parameter name="convergence criteria" type="Array(string)" value="{relative residual}"/>
<Parameter name="size of Krylov space" type="int" value="10"/>
<Parameter name="overflow tolerance" type="double" value="3.0e+50"/>
<Parameter name="maximum size of deflation space" type="int" value="0"/>
<Parameter name="preconditioning strategy`" type="string" value="left"/>
<Parameter name="release Krylov vectors" type="bool" value="false"/>
<ParameterList name="verbose object">
<Parameter name="verbosity level" type="string" value="high"/>
</ParameterList>
</ParameterList>
<!-- Alternative implementation
<ParameterList name="belos gmres parameters">
<Parameter name="error tolerance" type="double" value="1e-12"/>
<Parameter name="maximum number of iterations" type="int" value="400"/>
<Parameter name="convergence criteria" type="Array(string)" value="{relative residual}"/>
<Parameter name="size of Krylov space" type="int" value="10"/>
<Parameter name="overflow tolerance" type="double" value="3.0e+50"/>
</ParameterList-->
</ParameterList>
Linear Solver: NKA
Uses NKA method as a linear solver.
This is effectively equivalent to GMRES with a rolling restart, where vectors fall off the end of the space.
iterative-method-nka-spec
“error tolerance”
[double]1.e-6 Tolerance on which to declare success.“maximum number of iterations”
[int]100 Maximum iterations before declaring failure.“overflow tolerance”
[double]3.e50 Error above this value results in failure.“convergence criterial”
[Array(string)]{relative rhs} A list of criteria, any of which can be applied. Valid include:“relative rhs” : measure error relative to the norm of the RHS vector
“relative residual” : measure error relative to the norm of the residual
“absolute residual” : measure error directly, norm of error
“make one iteration” : require at least one iteration to be performed before declaring success
“max nka vectors”
[int]10 Size of the NKA space used to span the residual, conceptually equivalent to the size of the Krylov space.“nka vector tolerance”
[double]0.05 Vectors whose dot product are within this tolerance are considered parallel, and therefore the old vector is thrown out.
<ParameterList name="_NKA"> <!-- parent list -->
<ParameterList name="nka parameters">
<Parameter name="error tolerance" type="double" value="1e-12"/>
<Parameter name="maximum number of iterations" type="int" value="400"/>
<Parameter name="convergence criteria" type="Array(string)" value="{relative residual}"/>
<Parameter name="overflow tolerance" type="double" value="3.0e+50"/>
<Parameter name="max nka vectors" type="int" value="10"/>
<Parameter name="nka vector tolerance" type="double" value="0.05"/>
<ParameterList name="verbose object">
<Parameter name="verbosity level" type="string" value="high"/>
</ParameterList>
</ParameterList>
</ParameterList>
Linear Solver: Amesos
Direct solvers via Trilinos.
Amesos library of Trilinos package provides interfaces to a few direct solvers. List “amesos parameters” contains parameters that understood by this library. These parameters may violate the camel-case convention employed by this spec. Additional parameters are:
“solver name” [string] declares name of one of the supported direct solvers. Available options are “klu”, “superludist”, “basker”, etc, see Amesos and Amesos2 manuals for details. The default value is serial solver “klu”.
“amesos version” [int] specifies version of Amesos. Available options are 1 and 2. The default value is 1.
<ParameterList name="_AMESOS KLU"> <!-- parent list -->
<Parameter name="direct method" type="string" value="amesos"/>
<ParameterList name="amesos parameters">
<Parameter name="solver name" type="string" value="klu"/>
<Parameter name="amesos version" type="int" value="1"/>
</ParameterList>
</ParameterList>
Linear Solver: Amesos
Direct solvers via Trilinos.
Warning
undocumented
Linear Solver: Belos (GMRES)
Trilinos/Belos implementations of iterative methods.
Includes GMRES and other Belos methods.
Warning
undocumented
Preconditioners
A base class for assembled preconditioners.
This sublist contains entries for various preconditioners required by a simulation. At the moment, we support Trilinos multilevel preconditioner, Hypre BoomerAMG preconditioner, ILU preconditioner, Hypre’s ILU preconditioner, and identity preconditioner.
“preconditioning method” [string] defines preconditioner algorithm.
“xxx parameters” [list] provides parameters for the preconditioner specified by parameter “preconditioning method”.
<ParameterList> <!-- parent list -->
<ParameterList name="preconditioners">
<ParameterList name="_TRILINOS ML">
<Parameter name="preconditioning method" type="string" value="ml"/>
<ParameterList name="ml parameters">
...
</ParameterList>
</ParameterList>
<ParameterList name="_HYPRE AMG">
<Parameter name="preconditioning method" type="string" value="boomer amg"/>
<ParameterList name="boomer amg parameters">
...
</ParameterList>
</ParameterList>
<ParameterList name="_BLOCK ILU">
<Parameter name="preconditioning method" type="string" value="block ilu"/>
<ParameterList name="block ilu parameters">
...
</ParameterList>
</ParameterList>
<ParameterList name="_DIAGONAL">
<Parameter name="preconditioning method" type="string" value="diagonal"/>
</ParameterList>
</ParameterList>
Identity
Identity as a preconditioner.
Simply copies the input vector to the output – uses the Identity matrix as a preconditioner.
This is provided when using the “preconditioning method”=`”identity`” in the Preconditioner spec.
No parameters are required.
Diagonal
Diagonal preconditioner.
Simply applys the pointwise inverse of the diagonal of the matrix as an extremely cheap matrix.
This is provided when using the “preconditioning method”=`”diagonal`” in the Preconditioner spec.
No parameters are required.
Block ILU
Ifpack suite of preconditioners, including block ILU.
The Ifpack (Incomplete Factorization Package) from Trilinos provides additive-Schwarz-based incomplete factorization methods, including ILU and many others.
The method is provided in the parent list, e.g. “preconditioning method” = “ifpack: METHOD” when calling the Preconditioner factory.
Valid methods include:
“point relaxation” : Additive Schwarz + relaxation
“block relaxation” : Additive Schwarz + block relaxation
“Amesos” : Additive Schwarz with Amesos on block
“IC” : Additive Schwarz + Incomplete Cholesky (symmetry required)
“ICT” : Additive Schwarz + tolerance based Incomplete Cholesky (symmetry required)
“ILU” : Additive Schwarz + Incomplete LU
“ILUT” : Additive Schwarz + tolerance based Incomplete LU
“block ilu” : is the same as “ILU”, as this is the legacy Amanzi name.
Note that all of these can be used without Additive Schwarz by appending “stand-alone”.
The full list of relevant parameters is somewhat method-dependent, and is documented extensively in the Trilinos Documentation.
Here we document a subset of the most frequently used parameters – advanced users should read the Ifpack User Guide above to see all options.
preconditioner-ifpack-ilu-spec:
“schwarz: combine mode”
[string]Add Note that “Zero” may perform better for nonsymmetric cases.“overlap”
[int]0 overlap of the Additive Schwarz“fact: relax value”
[double]0.0 If nonzero, dropped values are added to the diagonal (times this factor).“fact: absolute threshold”
[double]0.0 Defines the value to add to each diagonal element (times the sign of the actual diagonal element).“fact: relative threshold”
[double]1.0 Multiplies the diagonal by this value before checking the threshold.“fact: level-of-fill”
[int]0
preconditioner-ifpack-relaxation-spec:
“schwarz: combine mode”
[string]Add Note that “Zero” may perform better for nonsymmetric cases.“overlap”
[int]0 overlap of the Additive Schwarz“relaxation: type”
[string]Jacobi“relaxation: sweeps”
[int]1“relaxation: damping factor”
[double]1.0
preconditioner-amesos-relaxation-spec:
“schwarz: combine mode”
[string]Add Note that “Zero” may perform better for nonsymmetric cases.“overlap”
[int]0 overlap of the Additive Schwarz“amesos: solver type”
[string]Amesos_Klu
Example:
<ParameterList name="block ilu parameters">
<Parameter name="fact: relax value" type="double" value="1.0"/>
<Parameter name="fact: absolute threshold" type="double" value="0.0"/>
<Parameter name="fact: relative threshold" type="double" value="1.0"/>
<Parameter name="fact: level-of-fill" type="int" value="0"/>
<Parameter name="overlap" type="int" value="0"/>
<Parameter name="schwarz: combine mode" type="string" value="Add"/>
</ParameterList>
</ParameterList>
Boomer AMG and Euclid
Hypre based preconditioners include Algebraic MultiGrid and global ILU
Boomer AMG is a HYPRE product consisting of a variety of Algebraic Multigrid methods. It is accessed through Ifpack.
This is provided when using the “preconditioning method”=`”boomer amg`” or “preconditioning method” = “hypre: boomer amg” in the Preconditioner spec.
preconditioner-boomer-amg-spec:
“tolerance”
[double]0. If is not zero, the preconditioner is dynamic and approximate the inverse matrix with the prescribed tolerance (in the energy norm ???).“smoother sweeps”
[int]3 defines the number of smoothing loops. Default is 3.“cycle applications”
[int]5 defines the number of V-cycles.“strong threshold”
[double]0.5 defines the number of V-cycles. Default is 5.“relaxation type”
[int]6 defines the smoother to be used. Default is 6 which specifies a symmetric hybrid Gauss-Seidel / Jacobi hybrid method. TODO: add others!“coarsen type”
[int]0 defines the coarsening strategy to be used. Default is 0 which specifies a Falgout method. TODO: add others!“max multigrid levels”
[int]optionally defined the maximum number of multigrid levels.“use block indices”
[bool]false If true, uses the “systems of PDEs” code with blocks given by the SuperMap, or one per DoF per entity type.“number of functions”
[int]1 Any value > 1 tells Boomer AMG to use the “systems of PDEs” code with strided block type. Note that, to use this approach, unknowns must be ordered with DoF fastest varying (i.e. not the native Epetra_MultiVector order). By default, it uses the “unknown” approach in which each equation is coarsened and interpolated independently.“nodal strength of connection norm”
[int]tells AMG to coarsen such that each variable has the same coarse grid - sometimes this is more “physical” for a particular problem. The value chosen here for nodal determines how strength of connection is determined between the coupled system. I suggest setting nodal = 1, which uses a Frobenius norm. This does NOT tell AMG to use nodal relaxation. Default is 0.“verbosity”
[int]0 prints a summary of run time settings and timing information to stdout. “1” prints coarsening info, “2” prints smoothing info, and “3’” prints both.
Example:
<ParameterList name="boomer amg parameters">
<Parameter name="tolerance" type="double" value="0.0"/>
<Parameter name="smoother sweeps" type="int" value="3"/>
<Parameter name="cycle applications" type="int" value="5"/>
<Parameter name="strong threshold" type="double" value="0.5"/>
<Parameter name="coarsen type" type="int" value="0"/>
<Parameter name="relaxation type" type="int" value="3"/>
<Parameter name="verbosity" type="int" value="0"/>
<Parameter name="number of functions" type="int" value="1"/>
</ParameterList>
ILU is a Parallel Incomplete LU, provided as part of the HYPRE project through the Ifpack interface.
This is provided when using the “preconditioning method”=`”ILU`” or =`”hypre: ILU`” in the Preconditioner spec.
preconditioner-ILU-spec:
“ilu(k) fill level”
[int]1 The factorization level.“ilut drop tolerance”
[double]0 Defines a drop tolerance relative to the largest absolute value of any entry in the row being factored.“verbosity”
[int]0 Prints a summary of runtime settings and timing information to stdout.
ML (Trilinos AMG)
Trilinos ML smoothed aggregation multigrid.
This is provided when using the “preconditioning method”=`”ml`” in the Preconditioner spec.
Warning
no input spec defined
See also: https://trilinos.github.io/pdfs/mlguide5.pdf
Example:
<ParameterList name="ml parameters">
<Parameter name="ML output" type="int" value="0"/>
<Parameter name="aggregation: damping factor" type="double" value="1.33"/>
<Parameter name="aggregation: nodes per aggregate" type="int" value="3"/>
<Parameter name="aggregation: threshold" type="double" value="0.0"/>
<Parameter name="aggregation: type" type="string" value="Uncoupled"/>
<Parameter name="coarse: type" type="string" value="Amesos-KLU"/>
<Parameter name="coarse: max size" type="int" value="128"/>
<Parameter name="coarse: damping factor" type="double" value="1.0"/>
<Parameter name="cycle applications" type="int" value="2"/>
<Parameter name="eigen-analysis: iterations" type="int" value="10"/>
<Parameter name="eigen-analysis: type" type="string" value="cg"/>
<Parameter name="max levels" type="int" value="40"/>
<Parameter name="prec type" type="string" value="MGW"/>
<Parameter name="smoother: damping factor" type="double" value="1.0"/>
<Parameter name="smoother: pre or post" type="string" value="both"/>
<Parameter name="smoother: sweeps" type="int" value="2"/>
<Parameter name="smoother: type" type="string" value="Gauss-Seidel"/>
</ParameterList>
Other Common Specs
IOEvent
IOEvent: base time/timestep control determing when in time to do something.
The IOEvent is used for multiple objects that need to indicate simulation times or cycles on which to do something.
io-event-spec
“cycles start period stop”
[Array(int)]optional The first entry is the start cycle, the second is the cycle period, and the third is the stop cycle or -1, in which case there is no stop cycle. A visualization dump is written at such cycles that satisfy cycle = start + n*period, for n=0,1,2,… and cycle < stop if stop != -1.0.“cycles start period stop 0”
[Array(int)]optional If multiple cycles start period stop parameters are needed, then use these parameters. If one with 0 is found, then one with 1 is looked for, etc, until the Nth one is not found.“cycles”
[Array(int)]optional An array of discrete cycles that at which a visualization dump is written.“times start period stop”
[Array(double)]optional The first entry is the start time, the second is the time period, and the third is the stop time or -1, in which case there is no stop time. A visualization dump is written at such times that satisfy time = start + n*period, for n=0,1,2,… and time < stop if stop != -1.0.“times start period stop units”
[string]s Units corresponding to this spec. One of “s”, “min”, “h”, “d”, “yr”, or “noleap”“times start period stop 0”
[Array(double)]optional If multiple start period stop parameters are needed, then use this these parameters with N=0,1,2. If one with 0 is found, then one with 1 is looked for, etc, until the Nth one is not found.“times start period stop 0 units”
[string]s Units corresponding to this spec. One of “s”, “min”, “h”, “d”, “yr”, or “noleap” See above for continued integer listings.“times”
[Array(double)]optional An array of discrete times that at which a visualization dump shall be written.“times units”
[string]s Units corresponding to this spec. One of “s”, “d”, “yr”, or “yr 365”
Verbose Object
This allows control of log-file verbosity for a wide variety of objects and physics.
verbose-object-spec
“verbosity level”
[string]GLOBAL_VERBOSITY, “low”, “medium”, “high”, “extreme” The default is set by the global verbosity spec, (fix me!) Typically, “low” prints out minimal information, “medium” prints out errors and overall high level information, “high” prints out basic debugging, and “extreme” prints out local debugging information.“write on rank”
[int]0 VerboseObjects only write on a single rank – by deafult the 0th rank. However, sometimes it is useful for debugging to write from another rank due to a need for cleaner output or writing a specific cell/entity information.“output filename”
[string]optional Redirect this output to a specific file rather than writing to screen. Note this will be done by-the-instance, so this may not catch as much as one might think.
Example:
<ParameterList name="verbose object">
<Parameter name="verbosity level" type="string" value="medium"/>
<Parameter name="name" type="string" value="my header"/>
<Parameter name="hide line prefix" type="bool" value="false"/>
<Parameter name="write on rank" type="int" value="0"/>
</ParameterList>
Debugger
A mesh and vector structure aware utility for printing info.
This is a utility that makes it easier for the user to control output written to the screen. It allows the user to provide element IDs, and then provides functionality for a PK to write mesh geometry information and vector values of those elements to screen based upon verbosity levels.
Note, most information is only written if the owning object’s verbosity level from the “Verbose Object” spec is set to “high” or higher.
debugger-spec
“debug cells”
[Array(int)]For each global ID of a cell provided here, controls writing of vectors inside of the using PK.“debug faces”
[Array(int)]For each global ID of a face provided here, writes all adjoining cell information as if each cell was included in “debug cells”.
Residual Debugger
Debugging object for writing vectors to file within an iterative process for use with vis tools.
residual-debugger-spec
“file name base”
[string]amanzi_dbg Prefix for output filenames.
INCLUDES:
[io-event-spec]An IOEvent spec
Functions
A base class for all functions of space and time.
Analytic, algabraic functions of space and time are used for a variety of purposes, including boundary conditions, initial conditions, and independent variables.
For initial conditions, functions are prescribed of space only, i.e.
For boundary conditions and independent variables, functions are also a function of time:
It is straightforward to add new functions as needed.
Constant Function
FunctionConstant: Implements the Function interface using a constant value.
Constant function is defined as \(f(x) = a\), for all \(x\).
“value”
[double]The constant to be applied.
Example:
<ParameterList name="function-constant">
<Parameter name="value" type="double" value="1.0"/>
</ParameterList>
Tabular Function
FunctionTabular: Piecewise-defined function.
A piecewise function of one variable.
A tabular function is tabulated on a series of intervals; given values \({{x_i}}, {{y_i}},, i=0, ... n-1\) and functional forms \({{f_j}},, j=0, ... n-2\) a tabular function \(f(x)\) is defined as:
The functional forms \({f_j}\) may be constant, which uses the left endpoint, i.e.
\(f_i(x) = y_i\),
linear, i.e.
\(f_i(x) = ( y_i * (x - x_i) + y_{{i+1}} * (x_{{i+1}} - x) ) / (x_{{i+1}} - x_i)\)
or arbitrary, in which the \(f_j\) must be provided.
The \(x_i\) and \(y_i\) may be provided in one of two ways – explicitly in the input spec or from an HDF5 file. The length of these must be equal, and the \(x_i\) must be monotonically increasing. Forms, as defined on intervals, must be of length equal to the length of the \(x_i\) less one.
Explicitly specifying the data:
function-tabular-spec
“x values”
[Array(double)]the \(x_i\)“y values”
[Array(double)]the \(y_i\)“forms”
[Array(string)]optional Form of the interpolant, either “constant”, “linear”, or “USER_DEFINED” Default is linear for each * interval. Note the length of this array should be one per interval, or one less than len of x and y values.“USER_DEFINED”
[function-spec]optional user-provided functional forms on the interval“x coordinate”
[string]t, “x”, “y”, “z” defines which coordinate direction the \(x_i\) are formed, defaulting to time.
The below example defines a function that is zero on interval \((-\infty,\,0]\), linear on interval \((0,\,1]\), constant (f(x)=1) on interval \((1,\,2]\), square root of t on interval \((2,\,3]\), and constant (f(x)=2) on interval \((3,\,\infty]\).
Example:
<ParameterList name="function-tabular">
<Parameter name="x values" type="Array(double)" value="{0.0, 1.0, 2.0, 3.0}"/>
<Parameter name="x coordinate" type="string" value="t"/>
<Parameter name="y values" type="Array(double)" value="{0.0, 1.0, 2.0, 2.0}"/>
<Parameter name="forms" type="Array(string)" value="{linear, constant, USER_FUNC}"/>
<ParameterList name="USER_FUNC">
<ParameterList name="function-standard-math">
<Parameter name="operator" type="string" value="sqrt"/>
</ParameterList>
</ParameterList>
</ParameterList>
Loading table from file. (Note that “USER_DEFINED” is not an option here, but could be made so if requested).
function-tabular-fromfile-spec
“file”
[string]filename of the HDF5 data“x header”
[string]name of the dataset for the \(x_i\) in the file“y header”
[string]name of the dataset for the \(y_i\) in the file“forms”
[string]optional, Form of the interpolant, either “constant” or “linear”
The example below would perform linear-interpolation on the intervals provided by data within the hdf5 file “my_data.h5”.
Example:
<ParameterList name="function-tabular">
<Parameter name="file" type="string" value="my_data.h5"/>
<Parameter name="x coordinate" type="string" value="t"/>
<Parameter name="x header" type="string" value="/time"/>
<Parameter name="y header" type="string" value="/data"/>
</ParameterList>
Smooth step Function
FunctionSmoothStep: a smoothed discontinuity.
A smooth \(C^2\) function f(x) on interval \([x_0,\,x_1]\) is defined such that f(x) = y_0 for x < x0, f(x) = y_1 for x > x_1, and monotonically increasing for \(x \in [x_0, x_1]\) through cubic interpolation.
function-smooth-step-spec
“x0”
[double]First fitting point“y0”
[double]First fitting value“x1”
[double]Second fitting point“y1”
[double]Second fitting value
Example:
<ParameterList name="function-smooth-step">
<Parameter name="x0" type="double" value="0.0"/>
<Parameter name="y0" type="double" value="0.0"/>
<Parameter name="x1" type="double" value="1.0"/>
<Parameter name="y1" type="double" value="2.0"/>
</ParameterList>
Polynomial Function
FunctionPolynomial: a polynomial
A generic polynomial function is given by the following expression:
where \(c_j\) are coefficients of monomials, \(p_j\) are integer exponents, and \(x_0\) is the reference point.
function-polynomial-spec
“coefficients”
[Array(double)]c_j polynomial coefficients“exponents”
[Array(int)]p_j polynomail exponents“reference point”
[double]x0 to which polynomial argument is normalized.
Example:
<ParameterList name="function-polynomial">
<Parameter name="coefficients" type="Array(double)" value="{1.0, 1.0}"/>
<Parameter name="exponents" type="Array(int)" value="{2, 4}"/>
<Parameter name="reference point" type="double" value="0.0"/>
</ParameterList>
Multi-variable linear Function
FunctionLinear: a multivariate linear function.
A multi-variable linear function is formally defined by
with the constant term “math:y_0 and gradient \(g_0,\, g_1\,..., g_{{n-1}}\). If the reference point \(x_0\) is specified, it must have the same number of values as the gradient. Otherwise, it defaults to zero. Note that one of the parameters in a multi-valued linear function can be time.
function-linear-spec
“y0”
[double]y_0 in f = y0 + g * (x - x0)“gradient”
[Array(double)]g in f = y0 + g * (x - x0)“x0”
[Array(double)]x0 in f = y0 + g * (x - x0)
Conditions:
len(x0) == len(gradient)
Example:
<ParameterList name="function-linear">
<Parameter name="y0" type="double" value="1.0"/>
<Parameter name="gradient" type="Array(double)" value="{1.0, 2.0, 3.0}"/>
<Parameter name="x0" type="Array(double)" value="{2.0, 3.0, 1.0}"/>
</ParameterList>
Separable Function
FunctionSeparable: f(x,y) = f1(x)*f2(y)
A separable function is defined as the product of other functions such as
where \(f_1\) is defined by the “function1” sublist, and \(f_2\) by the “function2” sublist.
function-separable-spec
“function1”
[function-spec]\(f_1\) in \(f(x) = f_1(x0) * f_2(x1...)\)“function2”
[function-spec]\(f_2\) in \(f(x) = f_1(x0) * f_2(x1...)\)
<ParameterList name="function-separable">
<ParameterList name="function1">
function-specification
</ParameterList>
<ParameterList name="function2">
function-specification
</ParameterList>
</ParameterList>
Additive Function
FunctionAdditive: f(x,y) = f1(x,y) + f2(x,y)
An additive function simply adds two other function results together.
where \(f_1\) is defined by the “function1” sublist, and \(f_2\) by the “function2” sublist.
function-additive-spec
“function1”
[function-spec]\(f_1\) in \(f(x) = f_1(x) + f_2(x)\)“function2”
[function-spec]\(f_2\) in \(f(x) = f_1(x) + f_2(x)\)
Example:
<ParameterList name="function-additive">
<ParameterList name="function1">
function-specification
</ParameterList>
<ParameterList name="function2">
function-specification
</ParameterList>
</ParameterList>
Multiplicative Function
FunctionMultiplicative: f(x,y) = f1(x,y) * f2(x,y)
A multiplicative function simply multiplies two other function results together.
where \(f_1\) is defined by the “function1” sublist, and \(f_2\) by the “function2” sublist.
function-multiplicative-spec
“function1”
[function-spec]\(f_1\) in \(f(x) = f_1(x) * f_2(x)\)“function2”
[function-spec]\(f_2\) in \(f(x) = f_1(x) * f_2(x)\)
Example:
<ParameterList name="function-multiplicative">
<ParameterList name="function1">
function-specification
</ParameterList>
<ParameterList name="function2">
function-specification
</ParameterList>
</ParameterList>
Composition Function
FunctionComposition: f(x,y) = f1(x,y) * f2(x,y)
Function composition simply applies one function to the result of another.
where \(f_1\) is defined by the “function1” sublist, and \(f_2\) by the “function2” sublist.
function-composition-spec
“function1”
[function-spec]\(f_1\) in \(f(x) = f_1(f_2(x))\)“function2”
[function-spec]\(f_2\) in \(f(x) = f_1(f_2(x))\)
<ParameterList name="function-composition">
<ParameterList name="function1">
function-specification
</ParameterList>
<ParameterList name="function2">
function-specification
</ParameterList>
</ParameterList>
Piecewise Bilinear Function
FunctionBilinear: a piecewise bilinear function.
A piecewise bilinear function extends the linear form of the tabular function to two variables.
Define \(i(x) = i : x_i < x <= x_{{i+1}}\) and similarly \(j(y) = j : y_j < y <= y_{{j+1}}\) for monotonically increasing \(x_i\) and \(y_j\).
Given a two-dimensional array \(u_{i,j}\), \(f\) is then defined by bilinear interpolation on \(u_{i(x),j(y)}, u_{i(x)+1,j(y)}, u_{i(x),j(y)+1}, u_{i(x)+1,j(y)+1}\), if \((x,y)\) is in \([x_0,x_n] \times [y_0,y_m]\), linear interpolation if one of \(x,y\) are out of those bounds, and constant at the corner value if both are out of bounds.
function-bilinear-spec
“file”
[string]HDF5 filename of the data“row header”
[string]name of the row dataset, the \(x_i\)“row coordinate”
[string]one of “t”,`”x`”,`”y`”,`”z`”“column header”
[string]name of the column dataset, the \(y_i\)“column coordinate”
[string]one of “t”,`”x`”,`”y`”,`”z`”“value header”
[string]name of the values dataset, the \(u_{{i,j}}\)
Example:
<ParameterList name="function-bilinear">
<Parameter name="file" type="string" value="pressure.h5"/>
<Parameter name="row header" type="string" value="/time"/>
<Parameter name="row coordinate" type="string" value="t"/>
<Parameter name="column header" type="string" value="/x"/>
<Parameter name="column coordinate" type="string" value="x"/>
<Parameter name="value header" type="string" value="/pressure"/>
</ParameterList>
Distance Function
FunctionDistance: distance from a reference point.
A distance function calculates distance from reference point \(x_0\) using by the following expression:
Note that the first parameter in \(x\) can be time.
function-distance-spec
“x0”
[Array(double)]Point from which distance is measured.“metric”
[Array(double)]Linear scaling metric, typically all 1s.
Here is an example of a distance function using isotropic metric:
Example:
<ParameterList name="function-distance">
<Parameter name="x0" type="Array(double)" value="{1.0, 3.0, 0.0}"/>
<Parameter name="metric" type="Array(double)" value="{1.0, 1.0, 1.0}"/>
</ParameterList>
Monomial Function
FunctionMonomial: a multivariate monomial function.
A multi-variable monomial function is given by the following expression:
with the constant factor \(c\), the reference point \(x_0\), and integer exponents \(p_j\). Note that the first parameter in \(x\) can be time.
function-monomial-spec
“c”
[double]c in \(f = c \prod_{j=0}^{n} (x_j - x_{0,j})^{p_j}\)“x0”
[Array(double)]x0 in \(f = c \prod_{j=0}^{n} (x_j - x_{0,j})^{p_j}\)“exponents”
[Array(int)]p in \(f = c \prod_{j=0}^{n} (x_j - x_{0,j})^{p_j}\)
Conditions:
len(x0) == len(exponents)
Here is an example of monomial of degree 6 in three variables:
<ParameterList name="function-monomial">
<Parameter name="c" type="double" value="1.0"/>
<Parameter name="x0" type="Array(double)" value="{1.0, 3.0, 0.0}"/>
<Parameter name="exponents" type="Array(int)" value="{2, 3, 1}"/>
</ParameterList>
Standard Math Function
Provides access to many common mathematical functions.
These functions allow to set up non-trivial time-dependent boundary conditions which increases a set of analytic solutions that can be used in convergence analysis tests.
or
Note that these operate only on the first coordinate, which is often time. Function composition can be used to apply these to other coordinates (or better yet a dimension could/should be added upon request).
function-standard-math-spec
“operator”
[string]specifies the name of a standard mathematical function. Available options are:trigonometric operators: “cos”, “sin”, “tan”, “acos”, “asin”, “atan”
hyperbolic trig operators: “cosh”, “sinh”, “tanh”
power/log operators: “pow”, “exp”, “log”, “log10”, “sqrt”,
integral operators: “ceil”, “floor”, “mod”,
“abs”, “fabs”, “positive” (0 for negative values), “negative” (0 for positive values), “heaviside”, “sign”
“amplitude”
[double]specifies a multiplication factor a in formula a f(x). The multiplication factor is ignored by function mod. Default value is 1.“parameter”
[double]1.0 specifies additional parameter p for math functions with two arguments. These functions are “a pow(x[0], p)” and “a mod(x[0], p)”. Alternative, scales the argument before application, for use in changing the period of trig functions.“shift”
[double]specifies a shift of the function argument. Default is 0.
Example:
<ParameterList name="function-standard-math">
<Parameter name="operator" type="string" value="sqrt"/>
<Parameter name="amplitude" type="double" value="1e-7"/>
<Parameter name="shift" type="double" value="0.1"/>
</ParameterList>
This example defines function 1e-7 sqrt(t-0.1).
Operator
Operator represents a linear map, and typically encapsulates a discretization.
Operators are discrete forms of linearized PDEs operators. They form a layer between physical process kernels and solvers and include accumulation, diffusion, advection, elasticity, reaction, and source operators. The residual associated with an operator \(L_h\) helps to understand the employed sign convention:
Operator represents a map from linear space X to linear space Y. Typically, this map is a linear map, and encapsulates much of the discretization involved in moving from continuous to discrete equations. The spaces X and Y are described by CompositeVectors (CV). A few maps X->Y are supported.
An operator provides an interface for applying both the forward and inverse linear map (assuming the map is invertible).
Typically the Operator is never seen by the user; instead the user provides
input information for helper classes based on the continuous mathematical
operator and the desired discretization. These helpers build the needed
Operator, which may include information from multiple helpers (i.e. in the
case of Jacobian Operators for a PDE).
However, one option may be provided by the user, which is related to dealing with nearly singular operators:
“diagonal shift”
[double]0.0 Adds a scalar shift to the diagonal of theOperator, which can be useful if theOperatoris singular or near-singular.
A PK decides how to bundle operators in a collection of operators. For example, an advection-diffusion problem may benefit from using a single operator that combines two operators representing diffusion and advection process. Collection of operators must be used for implicit solvers and for building preconditioners. In such a case, the collections acts as a single operator.
Operators use a few tools that are generic in nature and can be used independently by PKs. The list includes reconstruction and limiting algorithms.
Schema
The operators use notion of schema to describe operator’s abstract structure. Old operators use a simple schema which is simply the list of geometric objects where scalar degrees of freedom are defined. New operators use a list to define location, type, and number of degrees of freedom. In addition, the base of local stencil is either face or cell. A rectangular operator needs two schemas do describe its domain (called “schema domain”) and its range (called “schema range”). A square operator may use either two identical schema lists or a single list called “schema”.
<ParameterList name="pks operator name"> <!-- parent list-->
<ParameterList name="schema domain">
<Parameter name="base" type="string" value="cell"/>
<Parameter name="location" type="Array(string)" value="{node, face}"/>
<Parameter name="type" type="Array(string)" value="{scalar, normal component}"/>
<Parameter name="number" type="Array(int)" value="{2, 1}"/>
</ParameterList>
<ParameterList name="schema domain">
<Parameter name="base" type="string" value="cell"/>
<Parameter name="location" type="Array(string)" value="{node, face}"/>
<Parameter name="type" type="Array(string)" value="{scalar, normal component}"/>
<Parameter name="number" type="Array(int)" value="{2, 1}"/>
</ParameterList>
</ParameterList>
This example describes a square operator with two degrees of freedom per mesh node and one degree of freedom per mesh face. The face-based degree of freedom is the normal component of a vector field. Such set of degrees of freedom is used in the Bernardi-Raugel element for discretizing Stokes equations. Parameter “base” indicates that local matrices are associated with mesh cells.
PDE_Accumulation
PDE_Accumulation assembles the discrete form of \(\frac{\partial A}{\partial t}\).
This class is usually used as part of a preconditioner, providing the linearization:
for a grid element \(\Omega_E\).
pde-accumulation-spec
“entity kind”
[string]optional Typically set by the PK“number of vectors”
[int]optional Typically set by the PK
PDE_Diffusion
PDE_Diffusion forms local Op s and global Operator s for elliptic equations:
with a variety of discretizations. Note also, for reasons that are one part historical and potentially not that valid, this also supports and implementation with an advective source, i.e.:
for gravitational terms in Richards equations.
The input spec for a diffusion operator consists of:
“discretization primary”
[string]See below for supported options.“fv: default” the standard two-point flux finite volume discretization
“nlfv: default” the nonlinear finite volume method of ???
MFD methods, including:
“mfd: default”
“mfd: monotone for hex”
“mfd: optimized for monotonicity”
“mfd: two-point flux approximation”
“mfd: optimized for sparsity”
“mfd: support operator”
Note that the most commonly used are “fv: default” for simple test problems (this method is not particularly accurate for distorted meshes), “mfd: optimized for sparsity” for most real problems on unstructured meshes, and “mfd: optimized for monotonicity” for orthogonal meshes with diagonal tensor/scalar coefficients.
“gravity”
[bool]false specifies if the gravitational flow term is included“Newton correction”
[string]specifies a model for non-physical terms that must be added to the matrix. These terms represent Jacobian and are needed for the preconditioner. Available options are “true Jacobian” and “approximate Jacobian”. The FV scheme accepts only the first options. The other schemes accept only the second option.“scaled constraint equation”
[bool]false rescales flux continuity equations on mesh faces. These equations are formed without the nonlinear coefficient. This option allows us to treat the case of zero nonlinear coefficient, which otherwise generates zero rows in the operator, which is then singular. At moment this feature does not work with non-zero gravity term.“constraint equation scaling cutoff”
[double]specifies the cutoff value for applying rescaling strategy described above.
Diffusion generates local Ops and global Operators for an elliptic operator.
Diffusion is the most frequently used operator. It employs the old schema.
“pks operator name” [list] a PK specific name for the diffusion operator.
“discretization primary” [string] specifies an advanced discretization method that has useful properties under some a priori conditions on the mesh and/or permeability tensor. The available options are “mfd: optimized for sparsity”, “mfd: optimized for monotonicity”, “mfd: default”, “mfd: support operator”, “mfd: two-point flux approximation”, “fv: default”, and “nlfv: default”. The first option is recommended for general meshes. The second option is recommended for orthogonal meshes and diagonal absolute permeability tensor.
“discretization secondary” [string] specifies the most robust discretization method that is used when the primary selection fails to satisfy all a priori conditions. Default value is equal to that for the primary discretization.
“diffusion tensor” [string] specifies additional properties of the diffusion tensor. It allows us to solve problems with non-symmetric but positive definite tensors. Available options are symmetric (default) and nonsymmetric.
“nonlinear coefficient” [string] specifies a method for treating nonlinear diffusion coefficient, if any. Available options are “none”, “upwind: face”, “divk: cell-face” (default), “divk: face”, “standard: cell”, and “divk: cell-face-twin”. Symmetry preserving methods are the divk-family of methods and the classical cell-centered method (“standard: cell”). The first part of the name indicates the base scheme. The second part (after the semi-column) indicates required components of the composite vector that must be provided by a physical PK. Default is “none”.
“schema” [Array(string)] defines the operator stencil. It is a collection of geometric objects. It equals to “{cell}” for finite volume schemes. It is typically “{face, cell}” for mimetic discretizations.
“preconditioner schema” [Array(string)] defines the preconditioner stencil. It is needed only when the default assembling procedure is not desirable. If skipped, the “schema” is used instead.
“gravity” [bool] specifies if flow is driven also by the gravity.
“gravity term discretization” [string] selects a model for discretizing the gravity term. Available options are “hydraulic head” [default] and “finite volume”. The first option starts with equation for the shifted solution, i.e. the hydraulic head, and derives gravity discretization by the reserve shifting. The second option is based on the divergence formula.
“gravity magnitude” [double] defined magnitude of the gravity vector.
“Newton correction” [string] specifies a model for correction (non-physical) terms that must be added to the preconditioner. These terms approximate some Jacobian terms. Available options are “true Jacobian” and “approximate Jacobian”. The FV scheme accepts only the first options. The othre schemes accept only the second option.
“scaled constraint equation” [bool] rescales flux continuity equations on mesh faces. These equations are divided by the nonlinear coefficient. This option allows us to treat the case of zero nonlinear coefficient. At moment this feature does not work with non-zero gravity term. Default is false.
“constraint equation scaling cutoff”” [double] specifies the cutoff value for applying rescaling strategy described above.
“consistent faces” [list] may contain a “preconditioner” and “linear operator” list (see sections Preconditioners and LinearSolvers respectively). If these lists are provided, and the “discretization primary” is of type “mfd: *”, then the diffusion method UpdateConsistentFaces() can be used. This method, given a set of cell values, determines the faces constraints that satisfy the constraint equation in MFD by assembling and inverting the face-only system. This is not currently used by any Amanzi PKs.
“fracture” [Array(string)] provides list of regions that defines a fracture network. This parameter is used only by the coupled flow PK.
Example:
<ParameterList name="pks operator name">
<Parameter name="discretization primary" type="string" value="mfd: optimized for monotonicity"/>
<Parameter name="discretization secondary" type="string" value="mfd: two-point flux approximation"/>
<Parameter name="schema" type="Array(string)" value="{face, cell}"/>
<Parameter name="preconditioner schema" type="Array(string)" value="{face}"/>
<Parameter name="gravity" type="bool" value="true"/>
<Parameter name="gravity term discretization" type="string" value="hydraulic head"/>
<Parameter name="gravity magnitude" type="double" value="9.81"/>
<Parameter name="nonlinear coefficient" type="string" value="upwind: face"/>
<Parameter name="Newton correction" type="string" value="true Jacobian"/>
<ParameterList name="consistent faces">
<ParameterList name="linear solver">
...
</ParameterList>
<ParameterList name="preconditioner">
...
</ParameterList>
</ParameterList>
</ParameterList>
This example creates a p-lambda system, i.e. the pressure is discretized in mesh cells and on mesh faces. The preconditioner is defined on faces only, i.e. cell-based unknowns are eliminated explicitly and the preconditioner is applied to the Schur complement.
Additional options available only for the MFD family of discretizations include:
“nonlinear coefficient”
[string]specifies a method for treating nonlinear diffusion coefficient, if any. Available options are “none”, “upwind: face”, “divk: cell-face” (default), “divk: face”, “standard: cell”, “divk: cell-face-twin” and “divk: cell-grad-face-twin”. Symmetry preserving methods are the divk-family of methods and the classical cell-centered method (“standard: cell”). The first part of the name indicates the base scheme. The second part (after the semi-column) indicates required components of the composite vector that must be provided by a physical PK.“discretization secondary”
[string]specifies the most robust discretization method that is used when the primary selection fails to satisfy all a priori conditions. This is typically “mfd: default”, and is used only when an MFD “discretization primary” is used.“schema”
[Array(string)]defines the operator stencil. It is a collection of geometric objects. Typically this is set by the implementation and is not provided.“preconditioner schema”
[Array(string)]{face,cell} Defines the preconditioner stencil. It is needed only when the default assembling procedure is not desirable. If skipped, the “schema” is used instead. In addition to the default, {face} may be used, which forms the Schur complement.“consistent faces”
[list]may contain a “preconditioner” and “linear operator” list (see sections Preconditioners and LinearSolvers respectively). If these lists are provided, and the “discretization primary” is of type “mfd: *”, then the diffusion method UpdateConsistentFaces() can be used. This method, given a set of cell values, determines the faces constraints that satisfy the constraint equation in MFD by assembling and inverting the face-only system. This is not currently used by any Amanzi PKs.“diffusion tensor”
[string]allows us to solve problems with symmetric and non-symmetric (but positive definite) tensors. Available options are symmetric (default) and nonsymmetric.“use manifold flux”
[bool]false Computes the flux using algorithms and data structures for manifolds or fracture networks.
Additional options for MFD with the gravity term include:
“gravity term discretization”
[string]selects a model for discretizing the gravity term. Available options are “hydraulic head” (default) and “finite volume”. The first option starts with equation for the shifted solution, i.e. the hydraulic head, and derives gravity discretization by the reserve shifting. The second option is based on the divergence formula.
PDE_Advection
A high-order advection operator may have different domain and range and therefore requires two schemas. The structure of the new schema is described in the previous section. A high-order advection operator has two terms in a weak formulation, corresponding to volume and surface integrals. These two terms are discretixed using two operators with matrix of types advection and flux, respectively.
“pks operator name” [list] a PK specific name for the advection operator.
“method” [string] defines a discretization method. The available option is “dg modal”.
“method order” [int] defines method order. For example, the classical low-order finite volume scheme is equivalent to DG of order 0.
“matrix type” [string] defines matrix type. The supported options are “advection” and “flux”.
“dg basis” [string] defines bases for DG schemes. The available options are “regularized” (recommended), “normalized”, “orthonormalized”, and “natural” (not recommended).
“gradient operator on test function” [bool] defines place of the gradient operator. For integration by parts schemes, the gradient is transfered to a test function. This option is needed for discretizing volumetric integrals.
“jump operator on test function” [bool] defines place of the jump operator. For integration by parts schemes, the jump operator is applied to a test function. This option is needed for discretizing surface fluxes.
“flux formula” [string] defines type of the flux. The available options are “Rusanov” (default), “upwind”, “downwind”, and “NavierStokes”.
“schema domain” [list] defines a discretization schema for the operator domain.
“schema range” [list] defines a discretization schema for the operator range.
<ParameterList name="pks operator name">
<Parameter name="method" type="string" value="dg modal"/>
<Parameter name="method order" type="int" value="2"/>
<Parameter name="flux formula" type="string" value="Rusanov"/>
<Parameter name="matrix type" type="string" value="flux"/>
<Parameter name="jump operator on test function" type="bool" value="true"/>
<ParameterList name="schema domain">
<Parameter name="base" type="string" value="cell"/>
<Parameter name="location" type="Array(string)" value="{node, face}"/>
<Parameter name="type" type="Array(string)" value="{scalar, normal component}"/>
<Parameter name="number" type="Array(int)" value="{2, 1}"/>
</ParameterList>
<ParameterList name="schema range">
<Parameter name="base" type="string" value="cell"/>
<Parameter name="location" type="Array(string)" value="{cell}"/>
<Parameter name="type" type="Array(string)" value="{scalar}"/>
<Parameter name="number" type="Array(int)" value="{1}"/>
</ParameterList>
</ParameterList>
In this example, we construct an operator for volumetric integrals in a weak formulation of advection problem.
The only low-order advection operator in Amanzi is the upwind operator. It employes the old schema.
<ParameterList name="pks operator name">
<Parameter name="base" type="string" value="face"/>
<Parameter name="schema" type="Array(string)" value="{cell}"/>
<Parameter name="method order" type="int" value="0"/>
<Parameter name="matrix type" type="string" value="advection"/>
</ParameterList>
PDE_AdvectionUpwind assembles the discrete form of:
which advects quantity \(C\) with fluxes \(q\).
This is a simple, first-order donor-upwind scheme, and is recommended for use in diffusion-dominated advection-diffusion equations.
Field Initializers
Fields, also known by their underlying datatype, the CompositeVector, can be initialized in a variety of ways. These are used in a variety of places as generic capability.
Function Initialization
Mesh Functions, evaluate a function on a mesh and stick the result in a vector.
CompositeVectorFunctions are ways of evaluating a piecewise function on a mesh and sticking the result into a CompositeVector.
This is used in a variety of ways – Initial Conditions, Boundary Conditions, and Independent Variable Evaluators.
Typically any containing object of this spec is a list of these specs. The list is indexed by Region, and the regions (logically) should partition the domain (or boundary of the domain in the case of BCs).
Each entry in that list is a:
composite-vector-function-spec
ONE OF
“region”
[string]Region on which this function is evaluated.
OR
“regions”
[Array(string)]List of regions on which this function is evaluated.
END
ONE OF
“component”
[string]Mesh component to evaluate this on. This is one of “cell”, “face”, “node”, “edge”, or “boundary_face”. The last two may require additional conditions, such as a proper mesh initialization. The mask “*” could be used in place of the component name.
OR
“components”
[Array(string)]Mesh components to evaluate this on. This is some collection of “cell”, “face”, “node”, “edge”, and/or “boundary_face”. The last two may require additional conditions, such as a proper mesh initialization. The array with the single entry “*” could be used to initialize all existing components.
END
“function”
[function-typedinline-spec]The spec to provide the actual algebraic function.
Column File Initialization
Interpolate a depth-based, 1D column of data onto a mesh. Values are prescribed only to cells. Expected is an HDF5 file in the format:
Depth coordinates z:
- /z[:] = (z_0, z_1, … , z_n)
z_0 = 0.0 z_n >= max depth of mesh z_i > z_(i-1)
Function values u:
/f[:] = (f_0(z_0), f_1(z_1), …, f_n(z_n))
column-initialization-spec
“file”
[string]HDF5 filename“z header”
[string]name of the z-coordinate data: z above. Depth coordinates (positive downward from the surface), [m]“f header”
[string]name of the function data: f above.