Infiltration 1D =============== Capabilities Tested ------------------- * partially saturated one-dimensional flow * steady-state flow * pressure and flux boundary conditions * porous medium with discontinuous properties (permeability, van Genuchten parameters) Background ---------- Verification problems from the literature have been identified to test isothermal, single-phase, variably saturated flow. We initially focus on test problems that address the two most widely used k-s-p functions, Mualem-van Genuchten :cite:`scinfil-Mualem_1976` :cite:`scinfil-vanGenuchten_1980` and Brooks-Corey :cite:`scinfil-brooks1964hydraulic`. These include steady-state and transient tests with Dirichlet and Neumann boundary conditions. This documentation is intended to compare the results from Amanzi against the semi-analytical results documented in "A set of Analytical Benchmarks to Test Numerical Models of Flow and Transport in Soils." by J. Vanderborght, et. al. http://vzj.geoscienceworld.org/content/4/1/206.abstract :cite:`scinfil-vanderborght2005set`, see the first line in Table 3 of that paper. We consider three cases of the steady-state flux in a layered soil profile. The presure profiles should match that in the Vanderborght paper. The difference between the cases is as follows: * case #1 is 0.5 m of clay and 1.5 m of sand; * case #2 is 0.5 m of loam and 1.5 m of sand; * case #3 is 1.5 m of loam and 0.5 m of sand. Model ----- Initial condition. Pressure :math:`p` as the function of depths z and time t=0 is 81747 Pa. Boundary conditions. The pressure at z=0m, the left end in the Figures below, is 99630.6336 Pa. The outflow at the opposite end, z=2m, is fixed at 0.5 cm/d = 5.78703704E-8 m/s. The absolute permeability tensor is isotropic but discontinuous. The porosity is constant in all tests, :math:`\phi=0.43`. .. image:: geometry.png :align: center :width: 200px Problem Specification --------------------- The problem is solved in a box domain with hight 2 m. The other box dimenstions are equal to 1 m. Mesh ~~~~ We consider a column mesh with 200 cells in the vertical direction. Case #1: Sand Clay Layers ------------------------- The steady-state solution is shown below. The sand region corresponds to the left part of the pressure profile. The van Genuchten parameters are :math:`\alpha=1.532333\cdot 10^{-3}`, :math:`m=0.6666667`, and residual saturation is :math:`s_r=0.104651`. The absolute permeability is given by the isotropic tensor :math:`K=1.18472\cdot 10^{-11} [m^2]`. The clay region corresponds to the right part of the pressure profile. The van Genuchten parameters are :math:`\alpha=1.02 \cdot 10^{-4}`, :math:`m=0.0909`, and residual saturation is :math:`s_r=0.25`. The absolute permeability is given by the isotropic tensor :math:`K=1.18\cdot 10^{-13} [m^2]`. Results and Comparison ~~~~~~~~~~~~~~~~~~~~~~ We compare with the Amanzi's golden data that were verified against the Vanderborght paper. .. plot:: verification/infiltration/infiltration_1d/amanzi_infiltration_1d-c.py :align: center Case #2 Loam Sand Layers ------------------------ The steady-state solution is shown below. The sand region corresponds to the left part of the pressure profile. The van Genuchten parameters are :math:`\alpha=1.532333\cdot 10^{-3}`, :math:`m=0.6666667`, and residual saturation is :math:`s_r=0.104651`. The absolute permeability is given by the isotropic tensor :math:`K=1.18472E-11 [m^2]`. The loam region corresponds to the right part of the pressure profile. The van Genuchten parameters are :math:`\alpha=4.08622\cdot 10^{-4}`, :math:`m=0.375`, and residual saturation is :math:`s_r=0.186047`. The absolute permeability is given by the isotropic tensor :math:`K=5.9236 \cdot 10^{-13} [m^2]`. Results and Comparison ~~~~~~~~~~~~~~~~~~~~~~ We compare with the Amanzi's golden data that were verified against the Vanderborght paper. .. plot:: verification/infiltration/infiltration_1d/amanzi_infiltration_1d-a.py :align: center Case #3: Sand Loam Layers ------------------------- The steady-state solution is shown below. Now, we swap the sand is loam regions. The van Genuchten parameters are :math:`\alpha=4.08622\cdot 10^{-4}`, :math:`m=0.375`, and residual saturation is :math:`s_r=0.186047`. The absolute permeability is given by the isotropic tensor :math:`K=5.9236 \cdot 10^{-13} [m^2]`. The sand region corresponds to the right part of the pressure profile. The van Genuchten parameters are :math:`\alpha=1.532333\cdot 10^{-3}`, :math:`m=0.6666667`, and residual saturation is :math:`s_r=0.104651`. The absolute permeability is given by the isotropic tensor :math:`K=1.18472 \cdot 10^{-11} [m^2]`. Results and Comparison ~~~~~~~~~~~~~~~~~~~~~~ We compare with the Amanzi's golden data that were verified against the Vanderborght paper. .. plot:: verification/infiltration/infiltration_1d/amanzi_infiltration_1d-b.py :align: center References ---------- .. bibliography:: /bib/ascem.bib :filter: docname in docnames :style: alpha :keyprefix: scinfil- .. _about_sand_clay: About ----- * Directory: testing/verification/flow/richards/steady-state/infiltration_1d * Author: * Maintainer: David Moulton (moulton@lanl.gov) * Input Files: * amanzi_infiltration_clay_sand_1d-u.xml * amanzi_infiltration_loam_sand_1d-u.xml * amanzi_infiltration_sand_loam_1d-u.xml * Spec 2.3, unstructured mesh framework * mesh is generated internally