diff --git a/test/porousmediumflow/richards/CMakeLists.txt b/test/porousmediumflow/richards/CMakeLists.txt
index 52318c8c0846044f9f8be3725616d8b529e77697..6fe6c6bdf25ce3e530cb19d5993681f98f9ec2be 100644
--- a/test/porousmediumflow/richards/CMakeLists.txt
+++ b/test/porousmediumflow/richards/CMakeLists.txt
@@ -1 +1,2 @@
+add_subdirectory(benchmarks)
add_subdirectory(implicit)
diff --git a/test/porousmediumflow/richards/benchmarks/CMakeLists.txt b/test/porousmediumflow/richards/benchmarks/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5347c31cc3cf10848fe8171c29ac7ca1f3bed307
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/CMakeLists.txt
@@ -0,0 +1,69 @@
+dune_symlink_to_source_files(FILES
+params_evaporation_sand.input
+params_evaporation_loam1.input
+params_evaporation_loam2.input
+params_evaporation_clay.input
+params_infiltration_sand.input
+params_infiltration_loam.input
+params_infiltration_clay.input
+run_and_plot_m21.py
+run_and_plot_m22.py
+)
+
+add_executable(test_richards_benchmark_tpfa EXCLUDE_FROM_ALL main.cc)
+
+dumux_add_test(NAME test_richards_benchmark_infiltration_tpfa
+ TARGET test_richards_benchmark_tpfa
+ LABELS porousmediumflow richards
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzyData
+ --relative 0.05
+ --files ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_loam_0.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_ana_loam_0.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_1.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_loam_1.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_2.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_loam_2.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_3.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_loam_3.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_clay_0.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_ana_clay_0.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_1.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_clay_1.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_2.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_clay_2.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_3.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_clay_3.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_sand_0.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_ana_sand_0.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_1.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_sand_1.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_2.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_sand_2.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_3.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/theta_deltaeta_num_sand_3.dat
+
+ --command "${CMAKE_CURRENT_BINARY_DIR}/run_and_plot_m21.py")
+
+dumux_add_test(NAME test_richards_benchmark_evaporation_tpfa
+ TARGET test_richards_benchmark_tpfa
+ LABELS porousmediumflow richards
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzyData
+ --files ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_analytical_clay.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_analytical_clay.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_analytical_loam1.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_analytical_loam1.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_analytical_loam2.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_analytical_loam2.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_analytical_sand.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_analytical_sand.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_actual_clay.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_actual_clay.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_actual_loam1.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_actual_loam1.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_actual_loam2.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_actual_loam2.dat
+ ${CMAKE_SOURCE_DIR}/test/references/test_richards_benchmark_tpfa_rate_actual_sand.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/rate_actual_sand.dat
+ --command "${CMAKE_CURRENT_BINARY_DIR}/run_and_plot_m22.py")
diff --git a/test/porousmediumflow/richards/benchmarks/analytical.hh b/test/porousmediumflow/richards/benchmarks/analytical.hh
new file mode 100644
index 0000000000000000000000000000000000000000..3579e80dc38c4d222e4a5c4cb7883794a90cb308
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/analytical.hh
@@ -0,0 +1,330 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Helper functions for analytical solutions
+ */
+
+#ifndef DUMUX_RICHARDS_BENCHMARKS_ANALYTICAL_HH
+#define DUMUX_RICHARDS_BENCHMARKS_ANALYTICAL_HH
+
+#include <cmath>
+#include <algorithm>
+
+#include <dumux/io/format.hh>
+#include <dumux/io/gnuplotinterface.hh>
+
+#include <dumux/common/math.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/integrate.hh>
+
+#include <dumux/material/fluidmatrixinteractions/2p/vangenuchten.hh>
+#include <dumux/material/components/simpleh2o.hh>
+
+namespace Dumux {
+
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Analytical solution for infiltration scenario
+ * \note Root-soil benchmark paper Schnepf et al. (case M2.1, Eq. 4) https://doi.org/10.3389/fpls.2020.00316
+ * \note based on Vanderborght 2005 (see Fig. 4abc and Eq. 56-60) https://doi.org/10.2113/4.1.206
+ *
+ * Assumption is that the infiltration front is sufficiently far
+ * away from the boundary. The boundary conditions for the analytical
+ * solution are prescribed at z = ±∞.
+ */
+class AnalyticalSolutionM21
+{
+ using PcKrSwCurve = FluidMatrix::VanGenuchtenNoReg<double>;
+public:
+ AnalyticalSolutionM21()
+ : pcKrSwCurve_("SpatialParams")
+ {
+ gravity_ = 9.81;
+ density_ = Components::SimpleH2O<double>::liquidDensity(0,0);
+ viscosity_ = Components::SimpleH2O<double>::liquidViscosity(0,0);
+ porosity_ = getParam<double>("SpatialParams.Porosity");
+ permeability_ = getParam<double>("SpatialParams.Permeability");
+
+ const auto initialHead = getParam<double>("Problem.InitialHeadInCm", -400.0)*0.01; // cm to m
+ const auto pwInitial = initialHead*gravity_*density_ + 1.0e5;
+ const auto pcInitial = 1.0e5 - pwInitial;
+ const auto swIntial = pcKrSwCurve_.sw(pcInitial);
+
+ // compute θ_i, K_i, θ_sur, K_sur, θ_a
+ waterContentInitial_ = swIntial*porosity_;
+ conductivityInitial_ = conductivity(waterContentInitial_);
+ waterContentSurface_ = getParam<double>("Analytical.WaterContentSurface");
+ conductivitySurface_ = conductivity(waterContentSurface_);
+ waterContentRef_ = 0.5*(waterContentSurface_ + waterContentInitial_);
+
+ std::cout << std::endl << "Computed analytical solution (Vanderborght 2005 4abc, Schnepf 2020 M2.1) with:\n";
+ const auto soilType = getParam<std::string>("SpatialParams.Name");
+ std::cout << "Material: " << soilType << "\n";
+ std::cout << Fmt::format("-> θ_i: {}\n-> θ_sur: {}\n", waterContentInitial_, waterContentSurface_);
+ std::cout << Fmt::format("-> θ_a: {}\n", waterContentRef_);
+ std::cout << Fmt::format("-> K_i: {}\n-> K_sur: {}\n", conductivityInitial_, conductivitySurface_);
+
+ // create a table for fast evaluation of the inverse
+ // for the inverse we need to go from high water content to low water content so
+ // that deltaEta is monotonically increasing which is a requirement for the value key
+ // for the table interpolation
+ waterContents_ = linspace(waterContentSurface_ - 1e-8, waterContentInitial_ + 1e-8, 10000);
+ deltaEtas_.resize(waterContents_.size());
+ std::transform(waterContents_.begin(), waterContents_.end(), deltaEtas_.begin(),
+ [this](auto theta){ return deltaEtaExact(theta); });
+
+ // plot delta eta over water content
+ GnuplotInterface<double> gnuplot(false);
+ gnuplot.setOpenPlotWindow(false);
+ gnuplot.resetPlot();
+ gnuplot.setXlabel("water content");
+ gnuplot.setYlabel("delta eta");
+ gnuplot.addDataSetToPlot(waterContents_, deltaEtas_, "theta_vs_deltaeta_" + soilType + ".dat", "w l t 'analytical'");
+ gnuplot.plot("infiltration_theta_vs_deltaeta");
+
+ // TODO how to choose these? Is there an exact value?
+ waterContentRefDepth_ = getParam<double>("Analytical.WaterContentRefDepth");
+ waterContentRefTime_ = getParam<double>("Analytical.WaterContentRefTime");
+ std::cout << Fmt::format("-> η_a: {}\n", eta(waterContentRefDepth_, waterContentRefTime_));
+ }
+
+ // analytical solution for given x and t
+ double waterContent(double x /*in cm*/, double t /*in days*/) const
+ {
+ const auto deltaEta = eta(x, t) - eta(waterContentRefDepth_, waterContentRefTime_);
+ return interpolate<InterpolationPolicy::LinearTable>(deltaEta, deltaEtas_, waterContents_);
+ }
+
+ double deltaEta(double x /*in cm*/, double t /*in days*/) const
+ { return eta(x, t) - eta(waterContentRefDepth_, waterContentRefTime_); }
+
+ double initialWaterContent() const
+ { return waterContentInitial_; }
+
+ double surfaceWaterContent() const
+ { return waterContentSurface_; }
+
+ double refWaterContent() const
+ { return waterContentRef_; }
+
+ auto waterContentAndDeltaEtaPlot() const
+ { return std::tie(waterContents_, deltaEtas_); }
+
+private:
+ // hydraulic conductivity Kf (including relative permeability) in cm/day
+ double conductivity(double waterContent) const
+ {
+ const auto sw = waterContent/porosity_;
+ const auto krw = pcKrSwCurve_.krw(sw);
+ return krw*permeability_*gravity_*density_/viscosity_*100*86400;
+ }
+
+ // D = Kf*dh/dtheta Van Genuchten 1980 Eq. 10 in cm^2/day
+ double diffusivity(double waterContent) const
+ {
+ // pc = -h*gravity_*density_
+ // h = -pc/(gravity_*density_)
+ const auto sw = waterContent/porosity_;
+ const auto dh_dpc = -1.0/(0.01*gravity_*density_);
+ const auto dpc_dsw = pcKrSwCurve_.dpc_dsw(sw);
+ const auto dsw_dtheta = 1.0/porosity_;
+ const auto dh_dtheta = dh_dpc*dpc_dsw*dsw_dtheta;
+ return conductivity(waterContent)*dh_dtheta;
+ }
+
+ // integral travelling wave (Eq. 4 Schnepf 2020)
+ double integral(double waterContent) const
+ {
+ const auto integrand = [this](auto theta){
+ return diffusivity(theta)/(
+ (conductivitySurface_ - conductivityInitial_)*(theta - waterContentInitial_)
+ - (conductivity(theta) - conductivityInitial_)*(waterContentSurface_ - waterContentInitial_)
+ );
+ };
+
+ return integrateScalarFunction(integrand, waterContent, waterContentRef_);
+ }
+
+ // relative transformed coordinate position (Eq. 4 Schnepf 2020)
+ double deltaEtaExact(double waterContent) const
+ {
+ return (waterContentSurface_ - waterContentInitial_)*integral(waterContent);
+ }
+
+ // tranformed coordinate
+ double eta(double x /*in cm*/, double t /*in days*/) const
+ {
+ return std::fabs(x) - (conductivitySurface_ - conductivityInitial_)/(waterContentSurface_ - waterContentInitial_)*t;
+ }
+
+ PcKrSwCurve pcKrSwCurve_;
+ double waterContentSurface_, waterContentInitial_, waterContentRef_;
+ double waterContentRefDepth_, waterContentRefTime_;
+ double conductivitySurface_, conductivityInitial_;
+ double porosity_, permeability_, viscosity_, density_, gravity_;
+
+ std::vector<double> waterContents_;
+ std::vector<double> deltaEtas_;
+};
+
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Analytical solution for evaporation scenario
+ * \note Root-soil benchmark paper Schnepf et al. (case M2.2) https://doi.org/10.3389/fpls.2020.00316
+ * \note based on Vanderborght 2005 (see Fig. 5abcd and Eq. 39-47) https://doi.org/10.2113/4.1.206
+ * \note Derivation in Lockington 1994 https://doi.org/10.1029/93WR03411
+ *
+ * The analytical solution is an approximative solution for an inifite domain
+ * and is neglects graviational effects. Lockington 1994 estimates less than 1% error
+ * against a given exact solution (without gravity) for a simplified pc-sw relationship.
+ */
+class AnalyticalSolutionM22
+{
+ using PcKrSwCurve = FluidMatrix::VanGenuchtenNoReg<double>;
+public:
+ AnalyticalSolutionM22()
+ : pcKrSwCurve_("SpatialParams")
+ {
+ gravity_ = 9.81;
+ density_ = Components::SimpleH2O<double>::liquidDensity(0,0);
+ viscosity_ = Components::SimpleH2O<double>::liquidViscosity(0,0);
+ porosity_ = getParam<double>("SpatialParams.Porosity");
+ permeability_ = getParam<double>("SpatialParams.Permeability");
+
+ const auto initialHead = getParam<double>("Problem.InitialHeadInCm", -40.0)*0.01; // cm to m
+ potentialEvaporationRate_ = getParam<double>("Problem.SurfaceFluxMilliMeterPerDay");
+
+ const auto pwInitial = initialHead*gravity_*density_ + 1.0e5;
+ const auto pcInitial = 1.0e5 - pwInitial;
+ const auto swIntial = pcKrSwCurve_.sw(pcInitial);
+ waterContentInitial_ = swIntial*porosity_;
+
+ const auto pwSurface = -10000*0.01*gravity_*density_ + 1.0e5;
+ const auto pcSurface = 1.0e5 - pwSurface;
+ const auto swSurface = pcKrSwCurve_.sw(pcSurface);
+ waterContentSurface_ = swSurface*porosity_;
+
+ std::cout << std::endl << "Computed analytical solution (Vanderborght 2005 5abcd, Schnepf 2020 M2.2) with:\n";
+ const auto soilType = getParam<std::string>("SpatialParams.Name");
+ std::cout << "Material: " << soilType << "\n";
+ std::cout << Fmt::format("-> θ_i: {}\n-> θ_sur: {}\n", waterContentInitial_, waterContentSurface_);
+
+ // water content from "effective" water content, Vanderborght 2005 Eq. 40
+ const auto theta = [this](auto thetaEff){
+ return thetaEff*(waterContentInitial_ - waterContentSurface_) + waterContentSurface_;
+ };
+
+ const auto dIntegral = integrateScalarFunction(
+ [&,this](auto thetaEff){ return diffusivity(theta(thetaEff)); }, 0.0, 1.0
+ );
+
+ std::cout << Fmt::format("D(0), D(1): {}, {}\n", diffusivity(waterContentSurface_), diffusivity(waterContentInitial_));
+ std::cout << Fmt::format("Kf(0), Kf(1): {}, {}\n", conductivity(waterContentSurface_), conductivity(waterContentInitial_));
+ std::cout << Fmt::format("-> Integral D(Θ): {}\n", dIntegral);
+
+ const auto dThetaIntegral = integrateScalarFunction(
+ [&,this](auto thetaEff){ return thetaEff*diffusivity(theta(thetaEff)); }, 0.0, 1.0
+ );
+
+ std::cout << Fmt::format("0D(0), 0.5D(0.5) 1D(1): {}, {}, {}\n",
+ 0.0*diffusivity(theta(0.0)), 0.5*diffusivity(theta(0.5)), 1.0*diffusivity(theta(1.0)));
+ std::cout << Fmt::format("-> Integral Θ D(Θ): {}\n", dThetaIntegral);
+
+ // Eq. 43 Vanderborght 2005
+ const auto beta = dThetaIntegral*dThetaIntegral/(dIntegral*dIntegral);
+
+ const auto dThetaFactorIntegral = integrateScalarFunction(
+ [&,this](auto thetaEff){
+ const auto weight = (1.0-beta*thetaEff);
+ return weight*weight*diffusivity(theta(thetaEff));
+ }, 0.0, 1.0
+ );
+
+ std::cout << Fmt::format("-> Integral (1.0 - βΘ)² D(θ): {}\n", dThetaFactorIntegral);
+
+ // Eq. 42 Vanderborght 2005
+ const auto alpha = dThetaFactorIntegral/dIntegral;
+
+ // Eq. 41 Vanderborght 2005
+ const auto bracketFactor = 1.0 - alpha/((1.0 - beta)*(1.0 - beta));
+ const auto mu = 3*beta*(1.0 + std::sqrt(1.0 - 14.0/9.0*bracketFactor)) / ( 2*(beta - 1.0)*bracketFactor );
+
+ std::cout << Fmt::format("-> µ: {}, α: {}, β: {}\n", mu, alpha, beta);
+
+ // Eq. 39 Vanderborght 2005
+ desorptivity_ = (waterContentInitial_ - waterContentSurface_)*std::sqrt(4.0/mu*dIntegral);
+
+ std::cout << Fmt::format("-> Desorptivity, Sw(θ_i, θ_sur): {}\n", desorptivity_);
+
+ // Eq. 44 & 45 Vanderborght 2005
+ tPotential_ = desorptivity_*desorptivity_/(2.0*potentialEvaporationRate_*0.1*potentialEvaporationRate_*0.1);
+ tPrime_ = 0.5*tPotential_;
+
+ std::cout << Fmt::format("-> Critical time (t_pot): {} days\n", tPotential_);
+
+ std::cout << std::endl;
+ }
+
+ // Evaporationrate in mm/day (Eq. 46 & 47 Vanderborght 2005)
+ double evaporationRate(double t /*in days*/) const
+ {
+ if (t < tPotential_)
+ return potentialEvaporationRate_;
+ else
+ return 0.5*desorptivity_/std::sqrt(tPrime_ + t - tPotential_)*10;
+ }
+
+private:
+ // hydraulic conductivity Kf (including relative permeability) in cm/day
+ double conductivity(double waterContent) const
+ {
+ const auto sw = waterContent/porosity_;
+ const auto krw = pcKrSwCurve_.krw(sw);
+ return krw*permeability_*gravity_*density_/viscosity_*100*86400;
+ }
+
+ // D = Kf*dh/dtheta Van Genuchten 1980 Eq. 10 in cm^2/day
+ double diffusivity(double waterContent) const
+ {
+ // pc = -h*gravity_*density_
+ // h = -pc/(gravity_*density_)
+ const auto sw = waterContent/porosity_;
+ const auto dh_dpc = -1.0/(0.01*gravity_*density_);
+ const auto dpc_dsw = pcKrSwCurve_.dpc_dsw(sw);
+ const auto dsw_dtheta = 1.0/porosity_;
+ const auto dh_dtheta = dh_dpc*dpc_dsw*dsw_dtheta;
+ return conductivity(waterContent)*dh_dtheta;
+ }
+
+ PcKrSwCurve pcKrSwCurve_;
+ double waterContentSurface_, waterContentInitial_;
+ double desorptivity_;
+ double tPrime_, tPotential_;
+ double potentialEvaporationRate_;
+ double porosity_, permeability_, viscosity_, density_, gravity_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/porousmediumflow/richards/benchmarks/main.cc b/test/porousmediumflow/richards/benchmarks/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..bca77d5a3029f1c35a987e2932f5c5685d972703
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/main.cc
@@ -0,0 +1,287 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Richards benchmark test
+ *
+ * Infiltration benchmark:
+ * Root-soil benchmark paper Schnepf et al. (case M2.1, Eq. 4) https://doi.org/10.3389/fpls.2020.00316
+ * based on Vanderborght 2005 (see Fig. 4abc and Eq. 56-60) https://doi.org/10.2113/4.1.206
+ *
+ * Evaporation benchmark:
+ * Root-soil benchmark paper Schnepf et al. (case M2.2) https://doi.org/10.3389/fpls.2020.00316
+ * based on Vanderborght 2005 (see Fig. 5abcd and Eq. 39-47) https://doi.org/10.2113/4.1.206
+ */
+
+#include <config.h>
+#include <iostream>
+
+#include <dune/common/parallel/mpihelper.hh>
+
+#include <dumux/common/parameters.hh>
+#include <dumux/common/math.hh>
+
+#include <dumux/linear/linearsolvertraits.hh>
+#include <dumux/linear/amgbackend.hh>
+
+#include <dumux/io/format.hh>
+#include <dumux/io/gnuplotinterface.hh>
+#include <dumux/io/vtkoutputmodule.hh>
+#include <dumux/io/grid/gridmanager_yasp.hh>
+
+#include <dumux/porousmediumflow/richards/newtonsolver.hh>
+#include <dumux/assembly/fvassembler.hh>
+
+#include <test/porousmediumflow/richards/benchmarks/analytical.hh>
+#include <test/porousmediumflow/richards/benchmarks/properties.hh>
+
+int main(int argc, char** argv)
+{
+ using namespace Dumux;
+
+ // initialize MPI, finalize is done automatically on exit
+ const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+ // parse command line arguments and input file
+ Parameters::init(argc, argv);
+
+ // Choose tpfa scheme
+ using TypeTag = Properties::TTag::RichardsBenchmarkCCTpfa;
+
+ // try to create a grid (from the given grid file or the input file)
+ GridManager<GetPropType<TypeTag, Properties::Grid>> gridManager;
+ gridManager.init();
+
+ // we compute on the leaf grid view
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
+ gridGeometry->update();
+
+ // the problem (initial and boundary conditions)
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(gridGeometry);
+
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector x(gridGeometry->numDofs());
+ problem->applyInitialSolution(x);
+ auto xOld = x;
+
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
+ gridVariables->init(x);
+
+ // intialize the vtk output module
+ auto vtkWriter = std::make_shared<VtkOutputModule<GridVariables, SolutionVector>>(*gridVariables, x, problem->name());
+ vtkWriter->addVolumeVariable([](const auto& volVars){ return volVars.saturation(0)*volVars.porosity(); }, "water content");
+ vtkWriter->addVolumeVariable([](const auto& volVars){ return volVars.saturation(0); }, "saturation");
+ vtkWriter->addVolumeVariable([](const auto& volVars){ return volVars.pressure(0); }, "pressure");
+
+ using LinearSolver = AMGBiCGSTABBackend<LinearSolverTraits<GridGeometry>>;
+ auto linearSolver = std::make_shared<LinearSolver>(leafGridView, gridGeometry->dofMapper());
+
+ // using Assembler = FVAssembler<TypeTag, DiffMethod::analytic>; // TODO: something is wrong with analytic derivatives!
+ using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
+
+ const auto dt = getParam<double>("TimeLoop.DtInitial");
+ const auto checkPoints = getParam<std::vector<double>>("TimeLoop.TEnd");
+ const auto tEnd = checkPoints.back();
+
+ // instantiate time loop
+ auto timeLoop = std::make_shared<CheckPointTimeLoop<double>>(0.0, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(getParam<double>("TimeLoop.MaxTimeStepSize"));
+ timeLoop->setCheckPoint(checkPoints);
+ int checkPointCounter = 0;
+
+ auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, xOld);
+ using Newton = RichardsNewtonSolver<Assembler, LinearSolver>;
+ Newton nonLinearSolver(assembler, linearSolver);
+
+ // find out which scenario we are running (evaporation/infiltration)
+ const auto soilType = getParam<std::string>("SpatialParams.Name");
+ const double rate = getParam<double>("Problem.SurfaceFluxMilliMeterPerDay");
+ const BenchmarkScenario scenario = (rate > 0) ? BenchmarkScenario::evaporation : BenchmarkScenario::infiltration;
+
+ // compute analytical solution for given scenario
+ std::unique_ptr<AnalyticalSolutionM21> solutionInfiltration;
+ std::unique_ptr<AnalyticalSolutionM22> solutionEvaporation;
+ if (scenario == BenchmarkScenario::infiltration)
+ solutionInfiltration = std::make_unique<AnalyticalSolutionM21>();
+ else if (scenario == BenchmarkScenario::evaporation)
+ solutionEvaporation = std::make_unique<AnalyticalSolutionM22>();
+
+ ///////////////////////////////////////
+ // for evaporation scenario output
+ ///////////////////////////////////////
+
+ const bool openGnuplotWindow = getParam<bool>("Problem.OpenGnuplotWindow", false);
+ GnuplotInterface<double> gnuplotEvap(openGnuplotWindow);
+ gnuplotEvap.setOpenPlotWindow(openGnuplotWindow);
+ std::vector<double> outTime, outActual, outAnalytic;
+
+ ///////////////////////////////////////
+ ///////////////////////////////////////
+
+ ///////////////////////////////////////
+ // for infiltration scenario output
+ ///////////////////////////////////////
+
+ const auto updateAnalyticalWaterContent = [&](auto& theta)
+ {
+ const auto t = timeLoop->time()/86400.0;
+ for (const auto& element : elements(leafGridView))
+ {
+ const auto eIdx = leafGridView.indexSet().index(element);
+ const auto pos = element.geometry().center()[GridGeometry::GridView::dimensionworld -1];
+ theta[eIdx] = solutionInfiltration->waterContent(pos*100, t);
+ }
+ };
+
+ const auto updateDeltaEtaOutput = [&](auto& deltaEtaNum, auto& thetaNum)
+ {
+ const auto t = timeLoop->time()/86400.0;
+ for (const auto& element : elements(leafGridView))
+ {
+ const auto eIdx = leafGridView.indexSet().index(element);
+ const auto pos = element.geometry().center()[GridGeometry::GridView::dimensionworld -1];
+ deltaEtaNum[eIdx] = solutionInfiltration->deltaEta(pos*100, t);
+
+ auto fvGeometry = localView(*gridGeometry);
+ auto elemVolVars = localView(gridVariables->curGridVolVars());
+ fvGeometry.bindElement(element);
+ elemVolVars.bindElement(element, fvGeometry, x);
+ for (const auto& scv : scvs(fvGeometry))
+ thetaNum[eIdx] = elemVolVars[scv].saturation() * elemVolVars[scv].porosity();
+ }
+ };
+
+ std::vector<double> pos(leafGridView.size(0));
+ for (const auto& element : elements(leafGridView))
+ pos[leafGridView.indexSet().index(element)] = element.geometry().center()[GridGeometry::GridView::dimensionworld -1];
+
+
+ GnuplotInterface<double> gnuplotInfilt(openGnuplotWindow);
+ gnuplotInfilt.setOpenPlotWindow(openGnuplotWindow);
+ std::vector<double> deltaEtaNum(leafGridView.size(0)), thetaNum(leafGridView.size(0));
+
+ std::vector<double> analyticalWaterContent;
+ if (scenario == BenchmarkScenario::infiltration)
+ {
+ analyticalWaterContent.resize(leafGridView.size(0), solutionInfiltration->initialWaterContent());
+ vtkWriter->addField(analyticalWaterContent, "analytic water content");
+
+ // analytical solution
+ const auto& [theta, deltaEta] = solutionInfiltration->waterContentAndDeltaEtaPlot();
+ gnuplotInfilt.addDataSetToPlot(theta, deltaEta,
+ Fmt::format("theta_deltaeta_ana_{}_{:d}.dat", soilType, checkPointCounter), "w l t 'analytic'"
+ );
+
+ const auto yLimits = getParam<std::vector<double>>("Analytical.PlotLimits");
+ gnuplotInfilt.setYRange(yLimits[0], yLimits[1]);
+ gnuplotInfilt.setXRange(0.0, 0.5);
+ }
+
+ ///////////////////////////////////////
+ ///////////////////////////////////////
+
+ // initial solution
+ vtkWriter->write(0.0);
+
+ // time loop
+ timeLoop->start();
+ while (!timeLoop->finished())
+ {
+ // solve the non-linear system with time step control
+ nonLinearSolver.solve(x, *timeLoop);
+
+ // make the new solution the old solution
+ xOld = x;
+ gridVariables->advanceTimeStep();
+
+ // advance to the time loop to the next step
+ timeLoop->advanceTimeStep();
+
+ ///////////////////////////////////////
+ // output for infiltration scenario
+ ///////////////////////////////////////
+ if (scenario == BenchmarkScenario::infiltration && (timeLoop->finished() || timeLoop->isCheckPoint()))
+ {
+ ++checkPointCounter;
+
+ // write analytical solution to ParaView
+ updateAnalyticalWaterContent(analyticalWaterContent);
+ vtkWriter->write(timeLoop->time());
+
+ updateDeltaEtaOutput(deltaEtaNum, thetaNum);
+
+ const auto posRef = interpolate<InterpolationPolicy::LinearTable>(solutionInfiltration->refWaterContent(), thetaNum, pos);
+ std::cout << Fmt::format("Simulated x_a: {}cm\n", posRef);
+
+ gnuplotInfilt.addDataSetToPlot(thetaNum, deltaEtaNum,
+ Fmt::format("theta_deltaeta_num_{}_{:d}.dat", soilType, checkPointCounter),
+ Fmt::format("w p t 'DuMux {:.1f} days'", timeLoop->time()/86400.0)
+ );
+
+ gnuplotInfilt.plot(Fmt::format("infiltration_{}_{:d}", soilType, checkPointCounter));
+ }
+
+ ///////////////////////////////////////
+ // output for evaporation scenario
+ ///////////////////////////////////////
+ if (scenario == BenchmarkScenario::evaporation)
+ {
+ if (timeLoop->finished())
+ vtkWriter->write(timeLoop->time());
+
+ const double rate = problem->computeActualRate(x, *gridVariables, false);
+ const double analyticRate = solutionEvaporation->evaporationRate(timeLoop->time()/86400.0);
+ std::cout << Fmt::format("Actual rate: {:.5g} (mm/day), analytic rate: {:.5g} (mm/day)\n", rate, analyticRate);
+
+ outTime.push_back(timeLoop->time()/86400.0);
+ outActual.push_back(rate);
+ outAnalytic.push_back(analyticRate);
+
+ gnuplotEvap.resetPlot();
+ gnuplotEvap.setXRange(0, tEnd/86400.0);
+ gnuplotEvap.setXlabel("time in days");
+ gnuplotEvap.setYlabel("evaporation rate in mm/days");
+ gnuplotEvap.addDataSetToPlot(outTime, outActual, Fmt::format("rate_actual_{}.dat", soilType), "w p t 'DuMux'");
+ gnuplotEvap.addDataSetToPlot(outTime, outAnalytic, Fmt::format("rate_analytical_{}.dat", soilType), "w l t 'reference'");
+ gnuplotEvap.plot(Fmt::format("evaporation_{}", soilType));
+ }
+
+ // report statistics of this time step
+ timeLoop->reportTimeStep();
+
+ // set new dt as suggested by the newton solver
+ timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+ }
+
+ timeLoop->finalize(leafGridView.comm());
+
+ nonLinearSolver.report();
+
+ // print dumux end message
+ if (mpiHelper.rank() == 0)
+ Parameters::print();
+
+ return 0;
+}
diff --git a/test/porousmediumflow/richards/benchmarks/params_evaporation_clay.input b/test/porousmediumflow/richards/benchmarks/params_evaporation_clay.input
new file mode 100644
index 0000000000000000000000000000000000000000..4ae520b69428d0ab6ea2616a091d2d677f0ba656
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_evaporation_clay.input
@@ -0,0 +1,37 @@
+[TimeLoop]
+DtInitial = 10 # [s]
+TEnd = 518400 # [s]
+MaxTimeStepSize = 1200 # [s]
+
+[Grid]
+Cells0 = 1000
+Grading0 = -0.99
+Positions0 = -1.0 0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_evaporation_clay
+EnableGravity = false
+InitialHeadInCm = -200.0
+CriticalSurfaceHeadInCm = -10000.0
+SurfaceFluxMilliMeterPerDay = 3.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[Assembly.NumericDifference]
+BaseEpsilon = 1e-7
+
+[SpatialParams]
+Name = clay
+Swr = 0.25
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 1e-6
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenAlpha = 1.01936799e-4
+VanGenuchtenN = 1.1
+VanGenuchtenL = 0.5
+Porosity = 0.40
+Permeability = 1.1798241e-13
diff --git a/test/porousmediumflow/richards/benchmarks/params_evaporation_loam1.input b/test/porousmediumflow/richards/benchmarks/params_evaporation_loam1.input
new file mode 100644
index 0000000000000000000000000000000000000000..fb06224bf48f02a6e998ff5141191e397e374cfa
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_evaporation_loam1.input
@@ -0,0 +1,37 @@
+[TimeLoop]
+DtInitial = 10 # [s]
+TEnd = 864000 # [s]
+MaxTimeStepSize = 7200 # [s]
+
+[Grid]
+Cells0 = 1000
+Grading0 = -0.99
+Positions0 = -1.0 0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_evaporation_loam1
+EnableGravity = false
+InitialHeadInCm = -200.0
+CriticalSurfaceHeadInCm = -10000.0
+SurfaceFluxMilliMeterPerDay = 1.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[Assembly.NumericDifference]
+BaseEpsilon = 1e-7
+
+[SpatialParams]
+Name = loam1
+Swr = 0.18604651162
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 1e-5
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenAlpha = 4.07747197e-4
+VanGenuchtenN = 1.6
+VanGenuchtenL = 0.5
+Porosity = 0.43
+Permeability = 5.8991203e-13
diff --git a/test/porousmediumflow/richards/benchmarks/params_evaporation_loam2.input b/test/porousmediumflow/richards/benchmarks/params_evaporation_loam2.input
new file mode 100644
index 0000000000000000000000000000000000000000..046a1215fb15efa7d3349327a8ede1c546ccf3b8
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_evaporation_loam2.input
@@ -0,0 +1,37 @@
+[TimeLoop]
+DtInitial = 10 # [s]
+TEnd = 172800 # [s]
+MaxTimeStepSize = 7200 # [s]
+
+[Grid]
+Cells0 = 1000
+Grading0 = -0.99
+Positions0 = -1.0 0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_evaporation_loam2
+EnableGravity = false
+InitialHeadInCm = -200.0
+CriticalSurfaceHeadInCm = -10000.0
+SurfaceFluxMilliMeterPerDay = 3.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[Assembly.NumericDifference]
+BaseEpsilon = 1e-7
+
+[SpatialParams]
+Name = loam2
+Swr = 0.18604651162
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 1e-5
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenAlpha = 4.07747197e-4
+VanGenuchtenN = 1.6
+VanGenuchtenL = 0.5
+Porosity = 0.43
+Permeability = 5.8991203e-13
diff --git a/test/porousmediumflow/richards/benchmarks/params_evaporation_sand.input b/test/porousmediumflow/richards/benchmarks/params_evaporation_sand.input
new file mode 100644
index 0000000000000000000000000000000000000000..f1e3d0cbefe512edfcae843510fdee53f737805a
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_evaporation_sand.input
@@ -0,0 +1,37 @@
+[TimeLoop]
+DtInitial = 1 # [s]
+TEnd = 86400 # [s]
+MaxTimeStepSize = 360 # [s]
+
+[Grid]
+Cells0 = 1000
+Grading0 = -0.99
+Positions0 = -1.0 0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_evaporation_sand
+EnableGravity = false
+InitialHeadInCm = -40.0
+CriticalSurfaceHeadInCm = -10000.0
+SurfaceFluxMilliMeterPerDay = 1.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[Assembly.NumericDifference]
+BaseEpsilon = 1e-7
+
+[SpatialParams]
+Name = sand
+Swr = 0.10465116279
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 1e-5
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenAlpha = 1.52905199e-3
+VanGenuchtenN = 3.0
+VanGenuchtenL = 0.5
+Porosity = 0.43
+Permeability = 1.1798241e-11
diff --git a/test/porousmediumflow/richards/benchmarks/params_infiltration_clay.input b/test/porousmediumflow/richards/benchmarks/params_infiltration_clay.input
new file mode 100644
index 0000000000000000000000000000000000000000..3e7b6d4a63e765b0a5d521ea94ede97e54be1eb0
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_infiltration_clay.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+DtInitial = 1 # [s]
+TEnd = 8640 17280 43200 # [s]
+MaxTimeStepSize = 40 # [s]
+
+[Grid]
+Cells0 = 300
+Grading0 = 1.0
+Positions0 = -2.0 0
+
+[Analytical]
+WaterContentRefDepth = -24.41 # cm determined with 1500 cells
+WaterContentRefTime = 0.1 # days
+WaterContentSurface = 0.40
+PlotLimits = 2.0 -5.0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_infiltration_clay
+EnableGravity = true
+InitialHeadInCm = -400.0
+CriticalSurfaceHeadInCm = 0
+SurfaceFluxMilliMeterPerDay = -1000.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[SpatialParams]
+Name = clay
+Swr = 0.25
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 0.0
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenKrwHighSweThreshold = 0.9999
+VanGenuchtenAlpha = 1.01936799e-4
+VanGenuchtenN = 1.1
+VanGenuchtenL = 0.5
+Porosity = 0.40
+Permeability = 1.1798241e-13
diff --git a/test/porousmediumflow/richards/benchmarks/params_infiltration_loam.input b/test/porousmediumflow/richards/benchmarks/params_infiltration_loam.input
new file mode 100644
index 0000000000000000000000000000000000000000..3d28e6ceb378d180aa3aae21bdc717bfe26ebafe
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_infiltration_loam.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+DtInitial = 1 # [s]
+TEnd = 17280 43200 86400 # [s]
+MaxTimeStepSize = 200 # [s]
+
+[Grid]
+Cells0 = 300
+Grading0 = 1.0
+Positions0 = -2.0 0
+
+[Analytical]
+WaterContentRefDepth = -40.03 # cm determined with 1500 cells
+WaterContentRefTime = 0.2 # days
+WaterContentSurface = 0.43
+PlotLimits = 5.0 -10.0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_infiltration_loam
+EnableGravity = true
+InitialHeadInCm = -400.0
+CriticalSurfaceHeadInCm = 0
+SurfaceFluxMilliMeterPerDay = -1000.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[SpatialParams]
+Name = loam
+Swr = 0.18604651162
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 0.0
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenKrwHighSweThreshold = 1.0
+VanGenuchtenAlpha = 4.07747197e-4
+VanGenuchtenN = 1.6
+VanGenuchtenL = 0.5
+Porosity = 0.43
+Permeability = 5.8991203e-13
diff --git a/test/porousmediumflow/richards/benchmarks/params_infiltration_sand.input b/test/porousmediumflow/richards/benchmarks/params_infiltration_sand.input
new file mode 100644
index 0000000000000000000000000000000000000000..cec5295ce625246921cf8aed2394fe4aefd7a769
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/params_infiltration_sand.input
@@ -0,0 +1,41 @@
+[TimeLoop]
+DtInitial = 1 # [s]
+TEnd = 8640 17280 25920 # [s]
+MaxTimeStepSize = 25 # [s]
+
+[Grid]
+Cells0 = 300
+Grading0 = 1.0
+Positions0 = -2.0 0
+
+[Analytical]
+WaterContentRefDepth = -42.78 # cm determined with 1500 cells
+WaterContentRefTime = 0.1 # days
+WaterContentSurface = 0.2824
+PlotLimits = 5.0 -10.0
+
+[Flux]
+UpwindWeight = 0.5
+
+[Problem]
+Name = test_richards_benchmark_infiltration_sand
+EnableGravity = true
+InitialHeadInCm = -400.0
+CriticalSurfaceHeadInCm = 0
+SurfaceFluxMilliMeterPerDay = -1000.0
+
+[Newton]
+MaxRelativeShift = 1e-6
+
+[SpatialParams]
+Name = sand
+Swr = 0.10465116279
+Snr = 0.0
+VanGenuchtenPcLowSweThreshold = 0.0
+VanGenuchtenPcHighSweThreshold = 1.0
+VanGenuchtenKrwHighSweThreshold = 1.0
+VanGenuchtenAlpha = 1.52905199e-3
+VanGenuchtenN = 3.0
+VanGenuchtenL = 0.5
+Porosity = 0.43
+Permeability = 1.1798241e-11
diff --git a/test/porousmediumflow/richards/benchmarks/problem.hh b/test/porousmediumflow/richards/benchmarks/problem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..473730805914b350d0a05cde3f1e0b414e92f51a
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/problem.hh
@@ -0,0 +1,244 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Richards benchmarks base problem
+ *
+ * Infiltration benchmark:
+ * Root-soil benchmark paper Schnepf et al. (case M2.1, Eq. 4) https://doi.org/10.3389/fpls.2020.00316
+ * based on Vanderborght 2005 (see Fig. 4abc and Eq. 56-60) https://doi.org/10.2113/4.1.206
+ *
+ * Evaporation benchmark:
+ * Root-soil benchmark paper Schnepf et al. (case M2.2) https://doi.org/10.3389/fpls.2020.00316
+ * based on Vanderborght 2005 (see Fig. 5abcd and Eq. 39-47) https://doi.org/10.2113/4.1.206
+ */
+
+#ifndef DUMUX_RICHARDS_BECHMARK_PROBLEM_HH
+#define DUMUX_RICHARDS_BECHMARK_PROBLEM_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/boundarytypes.hh>
+
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/material/components/simpleh2o.hh>
+
+namespace Dumux {
+
+enum class BenchmarkScenario {
+ evaporation, infiltration
+};
+
+/*!
+ * \ingroup RichardsTests
+ * \brief Richards benchmarks base problem
+ */
+template <class TypeTag>
+class RichardsBenchmarkProblem : public PorousMediumFlowProblem<TypeTag>
+{
+ using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+ using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
+
+ using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using FVElementGeometry = typename GridGeometry::LocalView;
+ using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
+ using GridView = typename GridGeometry::GridView;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename GridView::template Codim<0>::Geometry::GlobalCoordinate;
+
+ static constexpr int dimWorld = GridView::dimensionworld;
+
+public:
+ RichardsBenchmarkProblem(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ {
+ name_ = getParam<std::string>("Problem.Name");
+ const auto density = Components::SimpleH2O<double>::liquidDensity(0,0);
+ const auto initialHead = getParam<Scalar>("Problem.InitialHeadInCm")*0.01;
+ const auto criticalHead = getParam<Scalar>("Problem.CriticalSurfaceHeadInCm")*0.01;
+ initialPressure_ = 1.0e5 + initialHead*9.81*density;
+ criticalSurfacePressure_ = 1.0e5 + criticalHead*9.81*density;
+ const auto& fm = this->spatialParams().fluidMatrixInteractionAtPos(0.0);
+ const auto criticalSaturation = fm.sw(1.0e5 - criticalSurfacePressure_);
+ criticalSurfaceKrw_ = fm.krw(criticalSaturation);
+ enableGravity_ = getParam<bool>("Problem.EnableGravity", true);
+
+ const auto potentialRate = getParam<Scalar>("Problem.SurfaceFluxMilliMeterPerDay");
+ potentialRate_ = density*potentialRate/(1000*86400.0); // mm/day -> kg/s/m^2
+ useKrwAverage_ = getParam<bool>("Problem.UseKrwAverage", false);
+ bottomDirichlet_ = getParam<bool>("Problem.BottomDirichlet", false);
+ scenario_ = (potentialRate > 0) ? BenchmarkScenario::evaporation : BenchmarkScenario::infiltration;
+ surfaceArea_ = (scenario_ == BenchmarkScenario::evaporation) ? 0.1*0.1 : 0.05*0.05;
+ }
+
+ // output name
+ const std::string& name() const
+ { return name_; }
+
+ // reference temperature (unused but required)
+ Scalar temperature() const
+ { return 273.15 + 10; };
+
+ // reference pressure
+ Scalar nonwettingReferencePressure() const
+ { return 1.0e5; };
+
+ // column cross-section area
+ Scalar extrusionFactorAtPos(const GlobalPosition &globalPos) const
+ { return surfaceArea_; }
+
+ /*!
+ * \brief Specifies which kind of boundary condition should be
+ * used for which equation on a given boundary segment.
+ */
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+ {
+ BoundaryTypes bcTypes;
+ if (onLowerBoundary(globalPos) && !bottomDirichlet_)
+ bcTypes.setAllNeumann();
+ else if (onLowerBoundary(globalPos) && bottomDirichlet_)
+ bcTypes.setAllDirichlet();
+ else if (onUpperBoundary(globalPos))
+ bcTypes.setAllNeumann();
+ else
+ DUNE_THROW(Dune::InvalidStateException, "Wrong boundary?");
+ return bcTypes;
+ }
+
+ /*!
+ * \brief Evaluates the boundary conditions for a Dirichlet boundary segment.
+ */
+ PrimaryVariables dirichletAtPos(const GlobalPosition &globalPos) const
+ { return initialAtPos(globalPos); }
+
+ /*!
+ * \brief Evaluates the initial values for a control volume
+ */
+ PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+ {
+ PrimaryVariables values(0.0);
+ values[Indices::pressureIdx] = initialPressure_;
+ values.setState(Indices::bothPhases);
+ return values;
+ }
+
+ /*!
+ * \brief Evaluates the boundary conditions for a Neumann boundary segment.
+ * Negative values mean influx.
+ */
+ template<class ElementVolumeVariables, class ElementFluxVariablesCache>
+ NumEqVector neumann(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const ElementVolumeVariables& elemVolVars,
+ const ElementFluxVariablesCache& elemFluxVarsCache,
+ const SubControlVolumeFace& scvf) const
+ {
+ NumEqVector values(0.0);
+ const auto& globalPos = scvf.ipGlobal();
+ if (onUpperBoundary(globalPos))
+ {
+ const auto& volVars = elemVolVars[scvf.insideScvIdx()];
+
+ const auto dist = (fvGeometry.scv(scvf.insideScvIdx()).center() - globalPos).two_norm();
+ const auto cellPressure = volVars.pressure(0);
+ const auto density = volVars.density(0);
+ const auto viscosity = volVars.viscosity(0);
+ const auto relPerm = volVars.relativePermeability(0);
+ const auto K = volVars.permeability();
+ const auto gravity = enableGravity_ ? 9.81 : 0.0;
+ const auto avgRelPerm = 0.5*(relPerm + criticalSurfaceKrw_);
+
+ // kg/m^3 * m^2 * Pa / m / Pa / s = kg/s/m^2
+ auto criticalRate = density*K/viscosity*((cellPressure - criticalSurfacePressure_)/dist - density*gravity);
+ if (!std::signbit(criticalRate))
+ criticalRate *= useKrwAverage_ ? avgRelPerm : relPerm;
+
+ if (scenario_ == BenchmarkScenario::evaporation)
+ values[Indices::conti0EqIdx] = std::min(potentialRate_, criticalRate);
+ else
+ values[Indices::conti0EqIdx] = std::max(potentialRate_, criticalRate);
+ }
+
+ // free drainage (gravitational flux) for infiltration scenario
+ else if (onLowerBoundary(globalPos) && (scenario_ == BenchmarkScenario::infiltration))
+ {
+ const auto& volVars = elemVolVars[scvf.insideScvIdx()];
+ const auto gravity = enableGravity_ ? 9.81 : 0.0;
+ const auto density = volVars.density(0);
+ const auto viscosity = volVars.viscosity(0);
+ const auto relPerm = volVars.relativePermeability(0);
+ const auto K = volVars.permeability();
+
+ values[Indices::conti0EqIdx] = density*K*relPerm/viscosity*(density*gravity);
+ }
+
+ return values;
+ }
+
+ bool onLowerBoundary(const GlobalPosition &globalPos) const
+ { return globalPos[dimWorld-1] < this->gridGeometry().bBoxMin()[dimWorld-1] + eps_; }
+
+ bool onUpperBoundary(const GlobalPosition &globalPos) const
+ { return globalPos[dimWorld-1] > this->gridGeometry().bBoxMax()[dimWorld-1] - eps_; }
+
+ //! compute the actual evaporation/infiltration rate
+ template<class SolutionVector, class GridVariables>
+ Scalar computeActualRate(const SolutionVector& sol, const GridVariables& gridVars, bool verbose = true) const
+ {
+ Scalar rate = 0.0;
+
+ auto fvGeometry = localView(this->gridGeometry());
+ auto elemVolVars = localView(gridVars.curGridVolVars());
+ for (const auto& element : elements(this->gridGeometry().gridView()))
+ {
+ fvGeometry.bindElement(element);
+ elemVolVars.bindElement(element, fvGeometry, sol);
+ for (const auto& scvf : scvfs(fvGeometry))
+ if (scvf.boundary())
+ rate += this->neumann(element, fvGeometry, elemVolVars, 0.0, scvf)[0];
+ }
+
+ if (verbose)
+ std::cout << Fmt::format("Actual rate: {:.5g} (mm/day)\n", rate*86400*1000/1000);
+
+ return rate*86400*1000/1000;
+ }
+
+private:
+ Scalar initialPressure_, criticalSurfacePressure_, potentialRate_;
+ Scalar criticalSurfaceKrw_;
+ static constexpr Scalar eps_ = 1.5e-7;
+ std::string name_;
+ bool enableGravity_;
+ bool bottomDirichlet_;
+ bool useKrwAverage_;
+ BenchmarkScenario scenario_;
+ Scalar surfaceArea_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/porousmediumflow/richards/benchmarks/properties.hh b/test/porousmediumflow/richards/benchmarks/properties.hh
new file mode 100644
index 0000000000000000000000000000000000000000..324729690d2bccf83322c6fb1bd7a666151b3d2e
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/properties.hh
@@ -0,0 +1,66 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Common properties for the Richards benchmarks
+ */
+#ifndef DUMUX_RICHARDS_BENCHMARKS_PROPERTIES_HH
+#define DUMUX_RICHARDS_BENCHMARKS_PROPERTIES_HH
+
+#include <dune/grid/yaspgrid.hh>
+
+#include <dumux/common/properties.hh>
+
+#include <dumux/discretization/cctpfa.hh>
+
+#include <dumux/porousmediumflow/richards/model.hh>
+
+#include "spatialparams.hh"
+#include "problem.hh"
+
+namespace Dumux::Properties {
+
+// Create new type tags
+namespace TTag {
+struct RichardsBenchmark { using InheritsFrom = std::tuple<Richards>; };
+struct RichardsBenchmarkCCTpfa { using InheritsFrom = std::tuple<RichardsBenchmark, CCTpfaModel>; };
+} // end namespace TTag
+
+template<class TypeTag>
+struct Grid<TypeTag, TTag::RichardsBenchmark>
+{ using type = Dune::YaspGrid<1, Dune::TensorProductCoordinates<double, 1>>; };
+
+// Set the physical problem to be solved
+template<class TypeTag>
+struct Problem<TypeTag, TTag::RichardsBenchmark>
+{ using type = RichardsBenchmarkProblem<TypeTag>; };
+
+// Set the spatial parameters
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::RichardsBenchmark>
+{
+ using type = RichardsBenchmarkSpatialParams<
+ GetPropType<TypeTag, Properties::GridGeometry>, GetPropType<TypeTag, Properties::Scalar>
+ >;
+};
+
+} // end namespace Dumux::Properties
+
+#endif
diff --git a/test/porousmediumflow/richards/benchmarks/run_and_plot_m21.py b/test/porousmediumflow/richards/benchmarks/run_and_plot_m21.py
new file mode 100755
index 0000000000000000000000000000000000000000..338e6fdff881487636d8ab0bbd5b6e36d1ff8a29
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/run_and_plot_m21.py
@@ -0,0 +1,59 @@
+#!/usr/bin/env python3
+
+import sys
+import numpy as np
+import subprocess
+
+# Run benchmark M2.1 infiltration scenarios
+subprocess.run(["./test_richards_benchmark_tpfa", "params_infiltration_sand.input"])
+subprocess.run(["./test_richards_benchmark_tpfa", "params_infiltration_loam.input"])
+subprocess.run(["./test_richards_benchmark_tpfa", "params_infiltration_clay.input"])
+
+try:
+ import matplotlib.pyplot as plt
+except ImportError:
+ print("Matplotlib not found so no result plots will be created.")
+ sys.exit(0)
+
+# Create Fig. 4def (right column) of Vanderborght 2005
+fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(5, 10), dpi=72)
+
+# set labels
+axes[0].set_title(r"$\theta$")
+for ax in axes:
+ ax.set_ylabel(r"$\Delta\eta$ (cm)")
+
+# set limits
+axes[0].set_ylim([5.0, -10.0])
+axes[0].set_xlim([0.0, 0.5])
+axes[1].set_ylim([5.0, -10.0])
+axes[1].set_xlim([0.0, 0.5])
+axes[2].set_ylim([2.0, -5.0])
+axes[2].set_xlim([0.0, 0.5])
+
+# first plot
+for i, (t, marker) in enumerate(zip([0.1, 0.2, 0.3], ["x", "D", "o"])):
+ theta, eta = np.genfromtxt("theta_deltaeta_num_sand_{}.dat".format(i+1)).T
+ axes[0].plot(theta, eta, linestyle='none', fillstyle='none', marker=marker, label="{:.1f} days".format(t))
+theta, eta = np.genfromtxt("theta_deltaeta_ana_sand_0.dat").T
+axes[0].plot(theta, eta, "k", label="Benchmark")
+axes[0].legend()
+
+# second plot
+for i, (t, marker) in enumerate(zip([0.2, 0.5, 1.0], ["x", "D", "o"])):
+ theta, eta = np.genfromtxt("theta_deltaeta_num_loam_{}.dat".format(i+1)).T
+ axes[1].plot(theta, eta, linestyle='none', fillstyle='none', marker=marker, label="{:.1f} days".format(t))
+theta, eta = np.genfromtxt("theta_deltaeta_ana_loam_0.dat").T
+axes[1].plot(theta, eta, "k", label="Benchmark")
+axes[1].legend()
+
+# third plot
+for i, (t, marker) in enumerate(zip([0.1, 0.2, 0.5], ["x", "D", "o"])):
+ theta, eta = np.genfromtxt("theta_deltaeta_num_clay_{}.dat".format(i+1)).T
+ axes[2].plot(theta, eta, linestyle='none', fillstyle='none', marker=marker, label="{:.1f} days".format(t))
+theta, eta = np.genfromtxt("theta_deltaeta_ana_clay_0.dat").T
+axes[2].plot(theta, eta, "k", label="Benchmark")
+axes[2].legend()
+
+fig.tight_layout()
+plt.savefig("benchmark_infiltration.png")
diff --git a/test/porousmediumflow/richards/benchmarks/run_and_plot_m22.py b/test/porousmediumflow/richards/benchmarks/run_and_plot_m22.py
new file mode 100755
index 0000000000000000000000000000000000000000..7c3f8b5f29345d442ebbe5e0a66fa45b1f121538
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/run_and_plot_m22.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+
+import sys
+import numpy as np
+import subprocess
+
+# Run benchmark M2.2 evaporation scenarios
+subprocess.run(["./test_richards_benchmark_tpfa", "params_evaporation_sand.input"])
+subprocess.run(["./test_richards_benchmark_tpfa", "params_evaporation_loam1.input"])
+subprocess.run(["./test_richards_benchmark_tpfa", "params_evaporation_loam2.input"])
+subprocess.run(["./test_richards_benchmark_tpfa", "params_evaporation_clay.input"])
+
+# Create equally spaced plots to improve test robustness.
+# In the case of slightly different time steps this makes sure
+# we always compare the same number of data points
+for refDataFile in ["rate_analytical_sand.dat", "rate_analytical_loam1.dat", "rate_analytical_loam2.dat", "rate_analytical_clay.dat"]:
+ tRef, rateRef = np.genfromtxt(refDataFile).T
+ # sample output data at equally spaced times using linear interpolation
+ tEquallySpaced = np.linspace(np.min(tRef), np.max(tRef), 50, endpoint=True)
+
+ sampledAnaRate = np.interp(tEquallySpaced, tRef, rateRef)
+ sanitizedOutput = np.vstack((tEquallySpaced, sampledAnaRate)).T
+ np.savetxt(refDataFile, sanitizedOutput)
+
+ numericDataFile = refDataFile.replace("analytical", "actual")
+ t, rate = np.genfromtxt(numericDataFile).T
+ sampledRate = np.interp(tEquallySpaced, t, rate)
+ sanitizedOutput = np.vstack((tEquallySpaced, sampledRate)).T
+ np.savetxt(numericDataFile, sanitizedOutput)
+
+try:
+ import matplotlib.pyplot as plt
+except ImportError:
+ print("Matplotlib not found so no result plots will be created.")
+ sys.exit(0)
+
+# Create Fig. 5abcd of Vanderborght 2005
+fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(8, 8))
+
+axes[0,0].set_ylabel(r"$E_\mathrm{act}$ in (cm day${}^{-1})$")
+axes[1,0].set_ylabel(r"$E_\mathrm{act}$ in (cm day${}^{-1})$")
+axes[1,0].set_xlabel(r"t (days)")
+axes[1,1].set_xlabel(r"t (days)")
+
+axes[0,0].set_ylim([0.0, 0.1])
+axes[1,0].set_ylim([0.0, 0.3])
+
+plots = {"sand": (0,0), "loam1": (0,1), "loam2": (1,0), "clay": (1,1)}
+for soil, index in plots.items():
+ t, e = np.genfromtxt("rate_actual_{}.dat".format(soil)).T
+ t, e = t, e*0.1
+ axes[index].plot(t, e, "k", label="DuMux")
+ t, e = np.genfromtxt("rate_analytical_{}.dat".format(soil)).T
+ t, e = t, e*0.1
+ axes[index].plot(t, e, marker="x", linestyle='none', label="Benchmark")
+ axes[index].legend()
+
+plt.savefig("benchmark_evaporation.png")
diff --git a/test/porousmediumflow/richards/benchmarks/spatialparams.hh b/test/porousmediumflow/richards/benchmarks/spatialparams.hh
new file mode 100644
index 0000000000000000000000000000000000000000..5b1681373b4577de87feeb3abfa3ad34c99bb934
--- /dev/null
+++ b/test/porousmediumflow/richards/benchmarks/spatialparams.hh
@@ -0,0 +1,85 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup RichardsTests
+ * \brief Spatial parameters for the Richards benchmarks
+ */
+
+#ifndef DUMUX_RICHARDS_BENCHMARKS_SPATIAL_PARAMETERS_HH
+#define DUMUX_RICHARDS_BENCHMARKS_SPATIAL_PARAMETERS_HH
+
+#include <dumux/common/parameters.hh>
+
+#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/vangenuchten.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup RichardsTests
+ * \brief Spatial parameters for the Richards benchmarks
+ */
+template<class GridGeometry, class Scalar>
+class RichardsBenchmarkSpatialParams
+: public FVSpatialParams<GridGeometry, Scalar, RichardsBenchmarkSpatialParams<GridGeometry, Scalar>>
+{
+ using ThisType = RichardsBenchmarkSpatialParams<GridGeometry, Scalar>;
+ using ParentType = FVSpatialParams<GridGeometry, Scalar, ThisType>;
+ using GridView = typename GridGeometry::GridView;
+ using GlobalPosition = typename GridView::template Codim<0>::Geometry::GlobalCoordinate;
+ using PcKrSwCurve = FluidMatrix::VanGenuchtenDefault<Scalar>;
+
+public:
+ // export permeability type
+ using PermeabilityType = Scalar;
+
+ RichardsBenchmarkSpatialParams(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ , pcKrSwCurve_("SpatialParams")
+ , permeability_(getParam<Scalar>("SpatialParams.Permeability"))
+ , porosity_(getParam<Scalar>("SpatialParams.Porosity"))
+ {}
+
+ /*!
+ * \brief Returns the intrinsic permeability tensor [m^2] at a given location
+ */
+ PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
+ { return permeability_; }
+
+ /*!
+ * \brief Returns the porosity [-] at a given location
+ */
+ Scalar porosityAtPos(const GlobalPosition& globalPos) const
+ { return porosity_; }
+
+ /*!
+ * \brief Returns the fluid-matrix interaction law for the sub-control volume
+ */
+ auto fluidMatrixInteractionAtPos(const GlobalPosition& globalPos) const
+ { return makeFluidMatrixInteraction(pcKrSwCurve_); }
+
+private:
+ const PcKrSwCurve pcKrSwCurve_;
+ const Scalar permeability_, porosity_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/references/test_richards_benchmark_tpfa_rate_actual_clay.dat b/test/references/test_richards_benchmark_tpfa_rate_actual_clay.dat
new file mode 100644
index 0000000000000000000000000000000000000000..8a134fa862a1d6edff81340bd006021ec3c4ff23
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_rate_actual_clay.dat
@@ -0,0 +1,50 @@
+1.157410000000000020e-04 3.000000000000000000e+00
+1.225623585306122448e-01 3.000000000000000000e+00
+2.450089760612244871e-01 3.000000000000000000e+00
+3.674555935918367156e-01 3.000000000000000000e+00
+4.899022111224489717e-01 3.000000000000000000e+00
+6.123488286530611724e-01 3.000000000000000000e+00
+7.347954461836734286e-01 3.000000000000000000e+00
+8.572420637142856847e-01 2.356547345873095889e+00
+9.796886812448979409e-01 2.009320758820943187e+00
+1.102135298775509975e+00 1.813572569630184761e+00
+1.224581916306122231e+00 1.674257710275444344e+00
+1.347028533836734487e+00 1.566283578193238490e+00
+1.469475151367346744e+00 1.478537553819808670e+00
+1.591921768897959000e+00 1.405009279854189774e+00
+1.714368386428571256e+00 1.342038502374267361e+00
+1.836815003959183512e+00 1.287205304322299293e+00
+1.959261621489795768e+00 1.238836683591719279e+00
+2.081708239020408246e+00 1.195719185054402001e+00
+2.204154856551020281e+00 1.156936192438849043e+00
+2.326601474081632759e+00 1.121785504213962170e+00
+2.449048091612244793e+00 1.089717977096938739e+00
+2.571494709142857271e+00 1.060307494591189670e+00
+2.693941326673469305e+00 1.033201638573059356e+00
+2.816387944204081784e+00 1.008105194632021195e+00
+2.938834561734693818e+00 9.847791777775084521e-01
+3.061281179265306296e+00 9.630198236853880767e-01
+3.183727796795918330e+00 9.426579647906333514e-01
+3.306174414326530808e+00 9.235508530607631217e-01
+3.428621031857142842e+00 9.055723904843258065e-01
+3.551067649387755321e+00 8.886140918390854626e-01
+3.673514266918367355e+00 8.725820234764813943e-01
+3.795960884448979833e+00 8.573946521632799245e-01
+3.918407501979591867e+00 8.429789740355959626e-01
+4.040854119510203901e+00 8.292733565488841219e-01
+4.163300737040816379e+00 8.162193004681020936e-01
+4.285747354571428858e+00 8.037664485738968967e-01
+4.408193972102040448e+00 7.918695582987409498e-01
+4.530640589632652926e+00 7.804893870751060669e-01
+4.653087207163265404e+00 7.695880387120920263e-01
+4.775533824693877882e+00 7.591345019352786494e-01
+4.897980442224489472e+00 7.490973992825950001e-01
+5.020427059755101951e+00 7.394496605387167465e-01
+5.142873677285714429e+00 7.301672105861153339e-01
+5.265320294816326907e+00 7.212267210992168165e-01
+5.387766912346938497e+00 7.126083635941140582e-01
+5.510213529877550975e+00 7.042931380708070677e-01
+5.632660147408163454e+00 6.962637162037216276e-01
+5.755106764938775932e+00 6.885030113987010703e-01
+5.877553382469387522e+00 6.809972017462628813e-01
+6.000000000000000000e+00 6.737319999999999975e-01
diff --git a/test/references/test_richards_benchmark_tpfa_rate_actual_loam1.dat b/test/references/test_richards_benchmark_tpfa_rate_actual_loam1.dat
new file mode 100644
index 0000000000000000000000000000000000000000..433146b3b834510d0745afdb479cd900b4a2058d
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_rate_actual_loam1.dat
@@ -0,0 +1,50 @@
+1.157410000000000020e-04 1.000000000000000000e+00
+2.041950115918367281e-01 1.000000000000000000e+00
+4.082742821836734537e-01 1.000000000000000000e+00
+6.123535527755101793e-01 1.000000000000000000e+00
+8.164328233673469049e-01 1.000000000000000000e+00
+1.020512093959183408e+00 1.000000000000000000e+00
+1.224591364551020245e+00 1.000000000000000000e+00
+1.428670635142857082e+00 7.778737875101386923e-01
+1.632749905734693696e+00 6.728506609907902725e-01
+1.836829176326530311e+00 6.082763028448093801e-01
+2.040908446918367147e+00 5.621196125119106712e-01
+2.244987717510204206e+00 5.257719936418311368e-01
+2.449066988102040821e+00 4.962841255973509114e-01
+2.653146258693877435e+00 4.714697127218852035e-01
+2.857225529285714494e+00 4.502224935268295813e-01
+3.061304799877551108e+00 4.317214223025953035e-01
+3.265384070469387723e+00 4.153780819726516360e-01
+3.469463341061224337e+00 4.008384118433797050e-01
+3.673542611653060952e+00 3.877243180427907832e-01
+3.877621882244898011e+00 3.758831851860980344e-01
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diff --git a/test/references/test_richards_benchmark_tpfa_rate_analytical_sand.dat b/test/references/test_richards_benchmark_tpfa_rate_analytical_sand.dat
new file mode 100644
index 0000000000000000000000000000000000000000..5957e9314772928aba323a6f323600fb7457b77f
--- /dev/null
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_clay_0.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_clay_0.dat
new file mode 100644
index 0000000000000000000000000000000000000000..067521a24d27279160727f81de1d25c07018608c
--- /dev/null
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_loam_0.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_loam_0.dat
new file mode 100644
index 0000000000000000000000000000000000000000..82ef0c469d0646f0f20a5e0798ae2e4f27facd2d
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_loam_0.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_sand_0.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_sand_0.dat
new file mode 100644
index 0000000000000000000000000000000000000000..f6f88a38184a10dd7949bbc452332017d54edb61
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_ana_sand_0.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_1.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_1.dat
new file mode 100644
index 0000000000000000000000000000000000000000..7487a2668c56aaa257a944d46424ad5293ab875a
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_1.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_2.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_2.dat
new file mode 100644
index 0000000000000000000000000000000000000000..2a10886c8fb6ec7550faaab8dcae1bbc71eb39e4
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_2.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_3.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_3.dat
new file mode 100644
index 0000000000000000000000000000000000000000..f3be7af2d67fc798390513f99f78c7eadb75411b
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_clay_3.dat
@@ -0,0 +1,300 @@
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_1.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_1.dat
new file mode 100644
index 0000000000000000000000000000000000000000..1ec0901768937b0e6f4daffff0f0fdd01cf1ec74
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_1.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_2.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_2.dat
new file mode 100644
index 0000000000000000000000000000000000000000..fb3a41643ba8f1fbb734d82631c808ea0f83669b
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_2.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_3.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_3.dat
new file mode 100644
index 0000000000000000000000000000000000000000..8ccec55f5f78ab04aade7f1228edc3679c9020cf
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_loam_3.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_1.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_1.dat
new file mode 100644
index 0000000000000000000000000000000000000000..3e17721d9ed70be231efc4cd9de51dc0a454fc3b
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_1.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_2.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_2.dat
new file mode 100644
index 0000000000000000000000000000000000000000..4c96d351bad2ff4d8cd27592bb526a405928300a
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_2.dat
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diff --git a/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_3.dat b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_3.dat
new file mode 100644
index 0000000000000000000000000000000000000000..94cc5cb91d3801ab2d96b1463bdddb434bae6ccf
--- /dev/null
+++ b/test/references/test_richards_benchmark_tpfa_theta_deltaeta_num_sand_3.dat
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