From 24133b9d34c226add12d2ef2638e20f279065a1f Mon Sep 17 00:00:00 2001
From: Timo Koch <timo.koch@iws.uni-stuttgart.de>
Date: Mon, 9 Jul 2018 18:47:36 +0200
Subject: [PATCH] [test][multidomain][embedded] Add test and references for
 1p2crichards2c 1d3d coupling (soil-root example)

---
 .../1d3d/1p2c_richards2c/CMakeLists.txt       |   12 +
 .../1d3d/1p2c_richards2c/rootproblem.hh       |  347 +
 .../1d3d/1p2c_richards2c/rootspatialparams.hh |  142 +
 .../1d3d/1p2c_richards2c/soilproblem.hh       |  337 +
 .../1d3d/1p2c_richards2c/soilspatialparams.hh |  123 +
 .../1p2c_richards2c/test_1p2c_richards2c.cc   |  487 ++
 .../test_1p2c_richards2c.input                |   51 +
 test/multidomain/embedded/1d3d/CMakeLists.txt |    1 +
 ...dded_1d3d_1p2c_richards2c_1d-reference.vtp | 2359 +++++
 ...dded_1d3d_1p2c_richards2c_3d-reference.vtu | 7767 +++++++++++++++++
 10 files changed, 11626 insertions(+)
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/CMakeLists.txt
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/rootproblem.hh
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/rootspatialparams.hh
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/soilproblem.hh
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/soilspatialparams.hh
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.cc
 create mode 100644 test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.input
 create mode 100644 test/references/test_embedded_1d3d_1p2c_richards2c_1d-reference.vtp
 create mode 100644 test/references/test_embedded_1d3d_1p2c_richards2c_3d-reference.vtu

diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/CMakeLists.txt b/test/multidomain/embedded/1d3d/1p2c_richards2c/CMakeLists.txt
new file mode 100644
index 0000000000..9d4667a2d8
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/CMakeLists.txt
@@ -0,0 +1,12 @@
+dune_add_test(NAME test_embedded_1d3d_1p2c_richards2c
+              SOURCES test_1p2c_richards2c.cc
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND HAVE_UG )"
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_embedded_1d3d_1p2c_richards2c_1d-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_soilroot_1d-00003.vtp
+                                ${CMAKE_SOURCE_DIR}/test/references/test_embedded_1d3d_1p2c_richards2c_3d-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_soilroot_3d-00003.vtu
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_embedded_1d3d_1p2c_richards2c test_1p2c_richards2c.input")
+dune_symlink_to_source_files(FILES "test_1p2c_richards2c.input")
+set(CMAKE_BUILD_TYPE Release)
diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/rootproblem.hh b/test/multidomain/embedded/1d3d/1p2c_richards2c/rootproblem.hh
new file mode 100644
index 0000000000..63a2bb0aec
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/rootproblem.hh
@@ -0,0 +1,347 @@
+// -*- 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 2 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
+ *
+ * \brief A test problem for the one-phase root model:
+ * Sap is flowing through a 1d network root xylem.
+ */
+#ifndef DUMUX_ROOT_PROBLEM_HH
+#define DUMUX_ROOT_PROBLEM_HH
+
+#include <dune/foamgrid/foamgrid.hh>
+
+#include <dumux/common/parameters.hh>
+#include <dumux/common/properties.hh>
+#include <dumux/discretization/cellcentered/tpfa/properties.hh>
+
+#include <dumux/porousmediumflow/1pnc/model.hh>
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/material/components/simpleh2o.hh>
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/liquidphase2c.hh>
+
+#include "rootspatialparams.hh"
+
+namespace Dumux {
+// forward declaration
+template <class TypeTag> class RootProblem;
+
+namespace Properties {
+
+NEW_TYPE_TAG(RootTypeTag, INHERITS_FROM(CCTpfaModel, OnePNC));
+
+// Set the grid type
+SET_TYPE_PROP(RootTypeTag, Grid, Dune::FoamGrid<1, 3>);
+
+SET_BOOL_PROP(RootTypeTag, EnableFVGridGeometryCache, true);
+SET_BOOL_PROP(RootTypeTag, EnableGridVolumeVariablesCache, true);
+SET_BOOL_PROP(RootTypeTag, EnableGridFluxVariablesCache, true);
+SET_BOOL_PROP(RootTypeTag, SolutionDependentAdvection, false);
+SET_BOOL_PROP(RootTypeTag, SolutionDependentMolecularDiffusion, false);
+SET_BOOL_PROP(RootTypeTag, SolutionDependentHeatConduction, false);
+
+// Set the problem property
+SET_TYPE_PROP(RootTypeTag, Problem, RootProblem<TypeTag>);
+
+// Set the fluid system
+SET_PROP(RootTypeTag, FluidSystem)
+{
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+    using type = FluidSystems::LiquidPhaseTwoC<Scalar, Components::SimpleH2O<Scalar>,
+                                                       Components::Constant<1, Scalar>>;
+};
+
+// Set the spatial parameters
+SET_TYPE_PROP(RootTypeTag, SpatialParams, RootSpatialParams<typename GET_PROP_TYPE(TypeTag, FVGridGeometry),
+                                                            typename GET_PROP_TYPE(TypeTag, Scalar)>);
+
+SET_BOOL_PROP(RootTypeTag, UseMoles, true);
+
+} // end namespace Properties
+
+/*!
+ * \ingroup OnePTests
+ * \brief Exact solution 1D-3D
+ */
+template <class TypeTag>
+class RootProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+    using PointSource = typename GET_PROP_TYPE(TypeTag, PointSource);
+    using PrimaryVariables = typename GET_PROP_TYPE(TypeTag, PrimaryVariables);
+    using NeumannFluxes = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+    using SourceValues = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+    using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+    using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
+    using GridView = typename FVGridGeometry::GridView;
+    using FVElementGeometry = typename FVGridGeometry::LocalView;
+    using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+    using SubControlVolumeFace = typename FVGridGeometry::SubControlVolumeFace;
+    using GlobalPosition = typename FVGridGeometry::GlobalCoordinate;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
+    using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+
+    using CouplingManager = typename GET_PROP_TYPE(TypeTag, CouplingManager);
+
+public:
+    using FluidSystem = typename GET_PROP_TYPE(TypeTag, FluidSystem);
+    enum Indices {
+        // Grid and world dimension
+        dim = GridView::dimension,
+        dimworld = GridView::dimensionworld,
+
+        pressureIdx = 0,
+        transportCompIdx = 1,
+
+        conti0EqIdx = 0,
+        transportEqIdx = 1,
+
+        liquidPhaseIdx = 0
+    };
+
+    template<class SpatialParams>
+    RootProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+                std::shared_ptr<SpatialParams> spatialParams,
+                std::shared_ptr<CouplingManager> couplingManager)
+    : ParentType(fvGridGeometry, spatialParams)
+    , couplingManager_(couplingManager)
+    {
+        //read parameters from input file
+        name_ = getParam<std::string>("Problem.Name") + "_1d";
+        transpirationRate_ = getParam<Scalar>("BoundaryConditions.TranspirationRate");
+        initPressure_ = getParam<Scalar>("BoundaryConditions.InitialRootPressure");
+    }
+
+    /*!
+     * \brief Return how much the domain is extruded at a given sub-control volume.
+     *
+     * The extrusion factor here makes extrudes the 1d line to a circular tube with
+     * cross-section area pi*r^2.
+     */
+    template<class ElementSolution>
+    Scalar extrusionFactor(const Element &element,
+                           const SubControlVolume &scv,
+                           const ElementSolution& elemSol) const
+    {
+        const auto eIdx = this->fvGridGeometry().elementMapper().index(element);
+        const auto radius = this->spatialParams().radius(eIdx);
+        return M_PI*radius*radius;
+    }
+
+    /*!
+     * \name Problem parameters
+     */
+    // \{
+
+    /*!
+     * \brief The problem name.
+     *
+     * This is used as a prefix for files generated by the simulation.
+     */
+    const std::string& name() const
+    { return name_; }
+
+    /*!
+     * \brief Return the temperature within the domain in [K].
+     */
+    Scalar temperature() const
+    { return 273.15 + 10.0; }
+
+    // \}
+    /*!
+     * \name Boundary conditions
+     */
+    // \{
+
+   /*!
+     * \brief Specifies which kind of boundary condition should be
+     *        used for which equation on a given boundary segment.
+     *
+     * \param globalPos The global position
+     */
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        return values;
+    }
+
+    /*!
+     * \brief Evaluate the boundary conditions for a dirichlet
+     *        control volume.
+     *
+     * \param globalPos The global position
+     *
+     * For this method, the \a values parameter stores primary variables.
+     */
+    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+    { return initialAtPos(globalPos); }
+
+
+    /*!
+     * \brief Evaluate the boundary conditions for a neumann
+     *        boundary segment.
+     *
+     * For this method, the \a priVars parameter stores the mass flux
+     * in normal direction of each component. Negative values mean
+     * influx.
+     */
+    template<class ElementVolumeVariables>
+    NeumannFluxes neumann(const Element& element,
+                          const FVElementGeometry& fvGeometry,
+                          const ElementVolumeVariables& elemVolvars,
+                          const SubControlVolumeFace& scvf) const
+    {
+        NeumannFluxes values(0.0);
+        if (scvf.center()[2] + eps_ > this->fvGridGeometry().bBoxMax()[2])
+        {
+            const auto& volVars = elemVolvars[scvf.insideScvIdx()];
+            const Scalar value = transpirationRate_ * volVars.molarDensity(liquidPhaseIdx)/volVars.density(liquidPhaseIdx);
+
+            values[conti0EqIdx] = value / volVars.extrusionFactor() / scvf.area();
+            // use upwind mole fraction to get outflow condition for the tracer
+            values[transportEqIdx] = values[conti0EqIdx] * volVars.moleFraction(liquidPhaseIdx, transportCompIdx);
+        }
+        return values;
+
+    }
+
+    // \}
+
+    /*!
+     * \name Volume terms
+     */
+    // \{
+
+     /*!
+     * \brief Applies a vector of point sources. The point sources
+     *        are possibly solution dependent.
+     *
+     * \param pointSources A vector of PointSource s that contain
+              source values for all phases and space positions.
+     *
+     * For this method, the \a values method of the point source
+     * has to return the absolute mass rate in kg/s. Positive values mean
+     * that mass is created, negative ones mean that it vanishes.
+     */
+    void addPointSources(std::vector<PointSource>& pointSources) const
+    { pointSources = this->couplingManager().lowDimPointSources(); }
+
+    /*!
+     * \brief Evaluate the point sources (added by addPointSources)
+     *        for all phases within a given sub-control-volume.
+     *
+     * This is the method for the case where the point source is
+     * solution dependent and requires some quantities that
+     * are specific to the fully-implicit method.
+     *
+     * \param pointSource A single point source
+     * \param element The finite element
+     * \param fvGeometry The finite-volume geometry
+     * \param elemVolVars All volume variables for the element
+     * \param scv The sub-control volume within the element
+     *
+     * For this method, the \a values() method of the point sources returns
+     * the absolute rate mass generated or annihilate in kg/s. Positive values mean
+     * that mass is created, negative ones mean that it vanishes.
+     */
+    template<class ElementVolumeVariables>
+    void pointSource(PointSource& source,
+                     const Element &element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const SubControlVolume &scv) const
+    {
+        SourceValues sourceValues;
+
+        // compute source at every integration point
+        const auto priVars3D = this->couplingManager().bulkPriVars(source.id());
+        const auto priVars1D = this->couplingManager().lowDimPriVars(source.id());
+        const Scalar pressure3D = priVars3D[pressureIdx];
+        const Scalar pressure1D = priVars1D[pressureIdx];
+
+        const auto lowDimElementIdx = this->couplingManager().pointSourceData(source.id()).lowDimElementIdx();
+        const Scalar Kr = this->spatialParams().Kr(lowDimElementIdx);
+        const Scalar rootRadius = this->spatialParams().radius(lowDimElementIdx);
+
+        // sink defined as radial flow Jr * density [m^2 s-1]* [kg m-3]
+        const auto molarDensityH20 = 1000 / 0.018;
+        sourceValues[conti0EqIdx] = 2 * M_PI * rootRadius * Kr * (pressure3D - pressure1D) * molarDensityH20;
+
+        const Scalar x3D = priVars3D[transportCompIdx];
+        const Scalar x1D = priVars1D[transportCompIdx];
+
+        //! advective transport over root wall
+        // compute correct upwind concentration
+        if (sourceValues[conti0EqIdx] > 0)
+            sourceValues[transportEqIdx] = sourceValues[conti0EqIdx]*x3D;
+        else
+            sourceValues[transportEqIdx] = sourceValues[conti0EqIdx]*x1D;
+
+        //! diffusive transport over root wall
+        const auto molarDensityD20 = 1000 / 0.020;
+        sourceValues[transportEqIdx] += 2 * M_PI * rootRadius * 1.0e-8 * (x3D - x1D) * molarDensityD20;
+
+        sourceValues *= source.quadratureWeight()*source.integrationElement();
+        source = sourceValues;
+    }
+
+    /*!
+     * \brief Evaluate the initial value for a control volume.
+     *
+     * For this method, the \a priVars parameter stores primary
+     * variables.
+     */
+    PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+    { return PrimaryVariables({initPressure_, 0.0}); }
+
+    // \}
+
+    /*!
+     * \brief Adds additional VTK output data to the VTKWriter. Function is called by the output module on every write.
+     */
+    template<class VtkOutputModule>
+    void addVtkOutputFields(VtkOutputModule& vtk) const
+    {
+        vtk.addField(this->spatialParams().getRadii(), "radius");
+    }
+
+    //! Set the coupling manager
+    void setCouplingManager(std::shared_ptr<CouplingManager> cm)
+    { couplingManager_ = cm; }
+
+    //! Get the coupling manager
+    const CouplingManager& couplingManager() const
+    { return *couplingManager_; }
+
+private:
+    Scalar transpirationRate_, initPressure_;
+
+    static constexpr Scalar eps_ = 1.5e-7;
+    std::string name_;
+
+    std::shared_ptr<CouplingManager> couplingManager_;
+};
+
+} //end namespace Dumux
+
+#endif
diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/rootspatialparams.hh b/test/multidomain/embedded/1d3d/1p2c_richards2c/rootspatialparams.hh
new file mode 100644
index 0000000000..d4abacbc34
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/rootspatialparams.hh
@@ -0,0 +1,142 @@
+// -*- 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 2 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 OneTests
+ * \brief The spatial parameters class for root xylem flow
+ */
+#ifndef DUMUX_ROOT_SPATIALPARAMS_HH
+#define DUMUX_ROOT_SPATIALPARAMS_HH
+
+#include <dumux/common/parameters.hh>
+#include <dumux/io/grid/griddata.hh>
+#include <dumux/material/components/simpleh2o.hh>
+#include <dumux/material/spatialparams/fv1p.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup OneTests
+ * \brief Definition of the spatial parameters for the root xylem flow
+ */
+template<class FVGridGeometry, class Scalar>
+class RootSpatialParams
+: public FVSpatialParamsOneP<FVGridGeometry, Scalar, RootSpatialParams<FVGridGeometry, Scalar>>
+{
+    using ThisType = RootSpatialParams<FVGridGeometry, Scalar>;
+    using ParentType = FVSpatialParamsOneP<FVGridGeometry, Scalar, ThisType>;
+    using Grid = typename FVGridGeometry::Grid;
+    using GridView = typename FVGridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+    //! Indices to access the parameters in the dgf file
+    enum DGFParamIndices {
+        orderIdx = 0,
+        rootIdIdx = 1,
+        surfaceIdx = 2,
+        massIdx = 3,
+        plantIdx = 5
+    };
+
+public:
+    // export permeability type
+    using PermeabilityType = Scalar;
+
+    RootSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+                      std::shared_ptr<const GridData<Grid>> gridData)
+    : ParentType(fvGridGeometry), gridData_(gridData)
+    {
+        porosity_ = getParam<Scalar>("Root.SpatialParams.Porosity", 0.4);
+        constantKx_ = getParam<Scalar>("Root.SpatialParams.Kx", 5.0968e-17);
+        constantKr_ = getParam<Scalar>("Root.SpatialParams.Kr", 2.04e-13);
+
+        const auto& gv = fvGridGeometry->gridView();
+        radii_.resize(gv.size(0));
+        for (const auto& element : elements(gv))
+        {
+            const auto eIdx = gv.indexSet().index(element);
+            auto level0element = element;
+            for(auto levelIdx = element.level(); levelIdx != 0; levelIdx--)
+                level0element = level0element.father();
+            const Scalar rootLength = element.geometry().volume();
+            const Scalar rootSurface = gridData_->parameters(level0element)[DGFParamIndices::surfaceIdx]/(1 << element.level());
+            radii_[eIdx] = rootSurface / rootLength / 2.0 / M_PI;
+        }
+    }
+
+    /*!
+     * \brief Return the intrinsic permeability for the current sub-control volume in [m^2].
+     *
+     * \param ipGlobal The integration point
+     * \note Kx has units [m^4/(Pa*s)] so we have to divide by the cross-section area
+     *       and multiply with a characteristic viscosity
+     */
+    template<class ElementSolution>
+    PermeabilityType permeability(const Element& element,
+                                  const SubControlVolume& scv,
+                                  const ElementSolution& elemSol) const
+    {
+        const Scalar r = radius(this->fvGridGeometry().gridView().indexSet().index(element));
+        return constantKx_ / (M_PI*r*r) * Components::SimpleH2O<Scalar>::liquidViscosity(285.15, 1e5);
+    }
+
+    /*!
+     * \brief Return the radius of the circular pipe for the current sub-control volume in [m].
+     *
+     * \param the index of the element
+     */
+    Scalar radius(std::size_t eIdxGlobal) const
+    {
+        return radii_[eIdxGlobal];
+    }
+
+    /*!
+     * \brief The radial permeability
+     *
+     * \param the index of the element
+     */
+    Scalar Kr(std::size_t eIdxGlobal) const
+    {
+        return constantKr_;
+    }
+
+    const std::vector<Scalar>& getRadii() const
+    { return radii_; }
+
+    /*!
+     * \brief Returns the porosity \f$[-]\f$
+     *
+     * \param globalPos the scv center
+     */
+    Scalar porosityAtPos(const GlobalPosition& globalPos) const
+    {
+        return porosity_;
+    }
+
+private:
+    std::shared_ptr<const GridData<Grid>> gridData_;
+    Scalar porosity_, constantKx_, constantKr_;
+    std::vector<Scalar> radii_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/soilproblem.hh b/test/multidomain/embedded/1d3d/1p2c_richards2c/soilproblem.hh
new file mode 100644
index 0000000000..294687531a
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/soilproblem.hh
@@ -0,0 +1,337 @@
+// -*- 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 2 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 OnePTests
+ * \brief Definition of a problem, for the 1p2c problem:
+ * Component transport of oxygen in interstitial fluid.
+ */
+#ifndef DUMUX_TISSUE_PROBLEM_HH
+#define DUMUX_TISSUE_PROBLEM_HH
+
+#include <dune/geometry/quadraturerules.hh>
+#include <dune/geometry/referenceelements.hh>
+#include <dune/grid/yaspgrid.hh>
+#include <dune/grid/uggrid.hh>
+#include <dune/localfunctions/lagrange/pqkfactory.hh>
+
+#include <dumux/common/math.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/properties.hh>
+#include <dumux/discretization/cellcentered/tpfa/properties.hh>
+
+#include <dumux/porousmediumflow/richardsnc/model.hh>
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/material/components/simpleh2o.hh>
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/liquidphase2c.hh>
+
+#include "soilspatialparams.hh"
+
+namespace Dumux {
+
+template <class TypeTag>
+class SoilProblem;
+
+namespace Properties {
+
+NEW_TYPE_TAG(SoilTypeTag, INHERITS_FROM(CCTpfaModel, RichardsNC));
+
+// Set the grid type
+SET_TYPE_PROP(SoilTypeTag, Grid, Dune::UGGrid<3>);
+
+SET_BOOL_PROP(SoilTypeTag, EnableFVGridGeometryCache, true);
+SET_BOOL_PROP(SoilTypeTag, EnableGridVolumeVariablesCache, true);
+SET_BOOL_PROP(SoilTypeTag, EnableGridFluxVariablesCache, true);
+SET_BOOL_PROP(SoilTypeTag, SolutionDependentAdvection, false);
+SET_BOOL_PROP(SoilTypeTag, SolutionDependentMolecularDiffusion, false);
+SET_BOOL_PROP(SoilTypeTag, SolutionDependentHeatConduction, false);
+
+// Set the problem property
+SET_TYPE_PROP(SoilTypeTag, Problem, SoilProblem<TypeTag>);
+
+// Set the spatial parameters
+SET_TYPE_PROP(SoilTypeTag, SpatialParams, SoilSpatialParams<typename GET_PROP_TYPE(TypeTag, FVGridGeometry),
+                                                            typename GET_PROP_TYPE(TypeTag, Scalar)>);
+
+// Set the fluid system
+SET_PROP(SoilTypeTag, FluidSystem)
+{
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+    using type = FluidSystems::LiquidPhaseTwoC<Scalar, Components::SimpleH2O<Scalar>,
+                                                       Components::Constant<1, Scalar>>;
+};
+
+SET_BOOL_PROP(SoilTypeTag, UseMoles, true);
+
+} // end namespace Properties
+
+
+/*!
+ * \ingroup OnePTests
+ */
+template <class TypeTag>
+class SoilProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+    using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
+    using FVElementGeometry = typename FVGridGeometry::LocalView;
+    using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+    using GridView = typename FVGridGeometry::GridView;
+    using GlobalPosition = typename FVGridGeometry::GlobalCoordinate;
+    using PrimaryVariables = typename GET_PROP_TYPE(TypeTag, PrimaryVariables);
+    using NumEqVector = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+    using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
+    using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+    using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+    using PointSource = typename GET_PROP_TYPE(TypeTag, PointSource);
+    using Element = typename GridView::template Codim<0>::Entity;
+
+    using CouplingManager = typename GET_PROP_TYPE(TypeTag, CouplingManager);
+
+public:
+    using FluidSystem = typename GET_PROP_TYPE(TypeTag, FluidSystem);
+    enum Indices {
+        // world dimension
+        dim = GridView::dimension,
+        dimWorld = GridView::dimensionworld,
+
+        pressureIdx = 0,
+        transportCompIdx = 1,
+
+        conti0EqIdx = 0,
+        transportEqIdx = 1,
+
+        liquidPhaseIdx = FluidSystem::liquidPhaseIdx
+    };
+
+    SoilProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+                std::shared_ptr<CouplingManager> couplingManager)
+    : ParentType(fvGridGeometry)
+    , couplingManager_(couplingManager)
+    {
+        //read parameters from input file
+        name_ = getParam<std::string>("Problem.Name") + "_3d";
+        contaminantMoleFraction_ = getParam<Scalar>("Problem.ContaminantMoleFraction");
+
+        // for initial conditions
+        const Scalar sw = getParam<Scalar>("Problem.InitTopSaturation", 0.3); // start with 30% saturation on top
+        using MaterialLaw = typename GET_PROP_TYPE(TypeTag, SpatialParams)::MaterialLaw;
+        pcTop_ = MaterialLaw::pc(this->spatialParams().materialLawParamsAtPos(fvGridGeometry->bBoxMax()), sw);
+    }
+
+    /*!
+     * \name Problem parameters
+     */
+    // \{
+
+    /*!
+     * \brief The problem name.
+     *
+     * This is used as a prefix for files generated by the simulation.
+     */
+    const std::string& name() const
+    { return name_; }
+
+    /*!
+     * \brief Returns the temperature within the domain [K].
+     *
+     * This problem assumes a temperature of 10 degrees Celsius.
+     */
+    Scalar temperature() const
+    { return 273.15 + 10; } // in [K]
+
+    /*
+      * \brief Returns the reference pressure [Pa] of the non-wetting
+     *        fluid phase within a finite volume
+     *
+     * This problem assumes a constant reference pressure of 1 bar.
+     */
+    Scalar nonWettingReferencePressure() const
+    { return 1.0e5; }
+
+
+    // \}
+
+    /*!
+     * \name Boundary conditions
+     */
+    // \{
+
+    /*!
+     * \brief Specifies which kind of boundary condition should be
+     *        used for which equation on a given boundary segment.
+     *
+     * \param globalPos The position for which the bc type should be evaluated
+     */
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        return values;
+    }
+
+    /*!
+     * \brief Evaluate the boundary conditions for a dirichlet
+     *        boundary segment.
+     *
+     * \param globalPos The position for which the bc type should be evaluated
+     *
+     * For this method, the \a values parameter stores primary variables.
+     */
+    PrimaryVariables dirichletAtPos(const GlobalPosition &globalPos) const
+    { return initialAtPos(globalPos); }
+
+    // \}
+
+    /*!
+     * \name Volume terms
+     */
+    // \{
+
+    /*!
+     * \brief Applies a vector of point sources. The point sources
+     *        are possibly solution dependent.
+     *
+     * \param pointSources A vector of Dumux::PointSource s that contain
+              source values for all phases and space positions.
+     *
+     * For this method, the \a values method of the point source
+     * has to return the absolute mass rate in kg/s. Positive values mean
+     * that mass is created, negative ones mean that it vanishes.
+     */
+    void addPointSources(std::vector<PointSource>& pointSources) const
+    { pointSources = this->couplingManager().bulkPointSources(); }
+
+    /*!
+     * \brief Evaluate the point sources (added by addPointSources)
+     *        for all phases within a given sub-control-volume.
+     *
+     * This is the method for the case where the point source is
+     * solution dependent and requires some quantities that
+     * are specific to the fully-implicit method.
+     *
+     * \param pointSource A single point source
+     * \param element The finite element
+     * \param fvGeometry The finite-volume geometry
+     * \param elemVolVars All volume variables for the element
+     * \param scv The sub-control volume within the element
+     *
+     * For this method, the \a values() method of the point sources returns
+     * the absolute rate mass generated or annihilate in kg/s. Positive values mean
+     * that mass is created, negative ones mean that it vanishes.
+     */
+    template<class ElementVolumeVariables>
+    void pointSource(PointSource& source,
+                     const Element &element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const SubControlVolume &scv) const
+    {
+        NumEqVector sourceValues;
+
+        // compute source at every integration point
+        const auto priVars3D = this->couplingManager().bulkPriVars(source.id());
+        const auto priVars1D = this->couplingManager().lowDimPriVars(source.id());
+        const Scalar pressure3D = priVars3D[pressureIdx];
+        const Scalar pressure1D = priVars1D[pressureIdx];
+
+        const auto& spatialParams = this->couplingManager().problem(Dune::index_constant<1>{}).spatialParams();
+        const auto lowDimElementIdx = this->couplingManager().pointSourceData(source.id()).lowDimElementIdx();
+        const Scalar Kr = spatialParams.Kr(lowDimElementIdx);
+        const Scalar rootRadius = spatialParams.radius(lowDimElementIdx);
+
+        // sink defined as radial flow Jr * density [m^2 s-1]* [kg m-3]
+        const auto molarDensityH20 = 1000 / 0.018;
+        sourceValues[conti0EqIdx] = 2 * M_PI * rootRadius * Kr * (pressure1D - pressure3D) * molarDensityH20;
+
+        const Scalar x3D = priVars3D[transportCompIdx];
+        const Scalar x1D = priVars1D[transportCompIdx];
+
+        //! advective transport over root wall
+        // compute correct upwind concentration
+        if (sourceValues[conti0EqIdx] > 0)
+            sourceValues[transportEqIdx] = sourceValues[conti0EqIdx]*x1D;
+        else
+            sourceValues[transportEqIdx] = sourceValues[conti0EqIdx]*x3D;
+
+        //! diffusive transport over root wall
+        const auto molarDensityD20 = 1000 / 0.020;
+        sourceValues[transportEqIdx] += 2 * M_PI * rootRadius * 1.0e-8 * (x1D - x3D) * molarDensityD20;
+
+        sourceValues *= source.quadratureWeight()*source.integrationElement();
+        source = sourceValues;
+    }
+
+    /*!
+     * \brief Evaluate the initial value for a control volume.
+     *
+     * \param values The initial values for the primary variables
+     * \param globalPos The position for which the initial condition should be evaluated
+     *
+     * For this method, the \a values parameter stores primary
+     * variables.
+     */
+    PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+    {
+        const auto& gg = this->fvGridGeometry();
+        static const Scalar extend = 0.15*(gg.bBoxMax()[0]-gg.bBoxMin()[0]);
+        const auto xTracer = [&]()
+        {
+            auto contaminationPos = gg.bBoxMax()-gg.bBoxMin();
+            contaminationPos[0] *= 0.26;
+            contaminationPos[1] *= 0.56;
+            contaminationPos[2] *= 0.26;
+            contaminationPos += gg.bBoxMin();
+
+            if ((globalPos - contaminationPos).infinity_norm() <  extend + eps_)
+                return contaminantMoleFraction_;
+            else
+                return 0.0;
+        }();
+
+        PrimaryVariables priVars(0.0);
+        //! hydrostatic pressure profile
+        priVars[pressureIdx] = (nonWettingReferencePressure() - pcTop_)
+                                -9.81*1000*(globalPos[dimWorld-1] - gg.bBoxMax()[dimWorld-1]);
+        priVars[transportCompIdx] = xTracer;
+        return priVars;
+    }
+
+    //! Set the coupling manager
+    void setCouplingManager(std::shared_ptr<CouplingManager> cm)
+    { couplingManager_ = cm; }
+
+    //! Get the coupling manager
+    const CouplingManager& couplingManager() const
+    { return *couplingManager_; }
+
+private:
+    Scalar pcTop_, contaminantMoleFraction_;
+
+    static constexpr Scalar eps_ = 1.5e-7;
+    std::string name_;
+
+    std::shared_ptr<CouplingManager> couplingManager_;
+};
+
+} //end namespace Dumux
+
+#endif
diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/soilspatialparams.hh b/test/multidomain/embedded/1d3d/1p2c_richards2c/soilspatialparams.hh
new file mode 100644
index 0000000000..e681354881
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/soilspatialparams.hh
@@ -0,0 +1,123 @@
+// -*- 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 2 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 OneTests
+ * \brief Definition of the spatial parameters for the tissue problem
+ */
+#ifndef DUMUX_SOIL_SPATIAL_PARAMS_HH
+#define DUMUX_SOIL_SPATIAL_PARAMS_HH
+
+#include <dumux/common/parameters.hh>
+#include <dumux/material/spatialparams/fv.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/regularizedvangenuchten.hh>
+#include <dumux/material/fluidmatrixinteractions/2p/efftoabslaw.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup OnePTests
+ * \brief Definition of the spatial parameters for the tissue problem
+ */
+template<class FVGridGeometry, class Scalar>
+class SoilSpatialParams
+: public FVSpatialParams<FVGridGeometry,Scalar, SoilSpatialParams<FVGridGeometry, Scalar>>
+{
+    using ThisType = SoilSpatialParams<FVGridGeometry, Scalar>;
+    using ParentType = FVSpatialParams<FVGridGeometry, Scalar, ThisType>;
+    using GridView = typename FVGridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+    // export permeability type
+    using PermeabilityType = Scalar;
+    // export material law type
+    using MaterialLaw = EffToAbsLaw<RegularizedVanGenuchten<Scalar>>;
+    // export material law params
+    using MaterialLawParams = typename MaterialLaw::Params;
+
+    SoilSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+    : ParentType(fvGridGeometry)
+    {
+        // residual saturations
+        materialParams_.setSwr(0.05);
+        materialParams_.setSnr(0.0);
+
+        // parameters for the Van Genuchten law
+        // alpha and n
+        materialParams_.setVgAlpha(2.956e-4);
+        materialParams_.setVgn(1.5);
+
+        // perm and poro
+        permeability_ = getParam<Scalar>("Soil.SpatialParams.Permeability");
+        porosity_ = getParam<Scalar>("Soil.SpatialParams.Porosity");
+    }
+
+    /*!
+     * \brief Define the intrinsic permeability \f$\mathrm{[m^2]}\f$.
+     *
+     * \param element The element
+     * \param scv The sub control volume
+     * \param elemSol the element solution vector
+     */
+    template<class ElementSolution>
+    PermeabilityType permeability(const Element& element,
+                                  const SubControlVolume& scv,
+                                  const ElementSolution& elemSol) const
+    {
+        return permeability_;
+    }
+
+    /*!
+     * \brief Define the porosity \f$\mathrm{[-]}\f$.
+     *
+     * \param element The current finite element
+     * \param scv The sub control volume
+     * \param elemSol The current element solution vector
+     */
+    template<class ElementSolution>
+    Scalar porosity(const Element& element,
+                    const SubControlVolume& scv,
+                    const ElementSolution& elemSol) const
+    {
+        return porosity_;
+    }
+
+    /*!
+     * \brief Returns the parameters for the material law at a given location
+     *
+     * This method is not actually required by the Richards model, but provided
+     * for the convenience of the RichardsLensProblem
+     *
+     * \param globalPos A global coordinate vector
+     */
+    const MaterialLawParams& materialLawParamsAtPos(const GlobalPosition &globalPos) const
+    { return materialParams_; }
+
+private:
+    MaterialLawParams materialParams_;
+    Scalar permeability_;
+    Scalar porosity_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.cc b/test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.cc
new file mode 100644
index 0000000000..68853d64fd
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.cc
@@ -0,0 +1,487 @@
+// -*- 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 2 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
+ *
+ * \brief Test for the 1d-3d embedded mixed-dimension model coupling two
+ *        one-phase porous medium flow problems
+ */
+#include <config.h>
+
+#include <ctime>
+#include <iostream>
+#include <fstream>
+
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/timer.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/linear/seqsolverbackend.hh>
+#include <dumux/assembly/fvassembler.hh>
+#include <dumux/assembly/diffmethod.hh>
+#include <dumux/discretization/methods.hh>
+#include <dumux/io/vtkoutputmodule.hh>
+#include <dumux/io/grid/gridmanager.hh>
+
+#include <dumux/multidomain/traits.hh>
+#include <dumux/multidomain/fvassembler.hh>
+#include <dumux/multidomain/newtonsolver.hh>
+#include <dumux/multidomain/embedded/couplingmanager1d3d.hh>
+#include <dumux/multidomain/embedded/mixeddimensionglue.hh>
+
+#include "rootproblem.hh"
+#include "soilproblem.hh"
+
+namespace Dumux {
+namespace Properties {
+
+SET_PROP(SoilTypeTag, CouplingManager)
+{
+    using Traits = MultiDomainTraits<TypeTag, TTAG(RootTypeTag)>;
+    using type = EmbeddedCouplingManager1d3d<Traits, EmbeddedCouplingMode::average>;
+};
+
+SET_PROP(RootTypeTag, CouplingManager)
+{
+    using Traits = MultiDomainTraits<TTAG(SoilTypeTag), TypeTag>;
+    using type = EmbeddedCouplingManager1d3d<Traits, EmbeddedCouplingMode::average>;
+};
+
+SET_TYPE_PROP(SoilTypeTag, PointSource, typename GET_PROP_TYPE(TypeTag, CouplingManager)::PointSourceTraits::template PointSource<0>);
+SET_TYPE_PROP(RootTypeTag, PointSource, typename GET_PROP_TYPE(TypeTag, CouplingManager)::PointSourceTraits::template PointSource<1>);
+SET_TYPE_PROP(SoilTypeTag, PointSourceHelper, typename GET_PROP_TYPE(TypeTag, CouplingManager)::PointSourceTraits::template PointSourceHelper<0>);
+SET_TYPE_PROP(RootTypeTag, PointSourceHelper, typename GET_PROP_TYPE(TypeTag, CouplingManager)::PointSourceTraits::template PointSourceHelper<1>);
+
+} // end namespace Properties
+
+//! helper function for mass balance evaluations
+template<class Problem, class SolutionVector, class GridVariables>
+double computeSourceIntegral(const Problem& problem, const SolutionVector& sol, const GridVariables& gridVars)
+{
+    const auto& gg = problem.fvGridGeometry();
+    typename SolutionVector::block_type source(0.0);
+    for (const auto& element : elements(gg.gridView()))
+    {
+        auto fvGeometry = localView(gg);
+        fvGeometry.bindElement(element);
+
+        auto elemVolVars = localView(gridVars.curGridVolVars());
+        elemVolVars.bindElement(element, fvGeometry, sol);
+
+        for (auto&& scv : scvs(fvGeometry))
+        {
+            auto pointSources = problem.scvPointSources(element, fvGeometry, elemVolVars, scv);
+            // conversion to kg/s
+            const auto& volVars = elemVolVars[scv];
+            pointSources *= scv.volume()*volVars.extrusionFactor()
+                            * volVars.density(Problem::Indices::liquidPhaseIdx) / volVars.molarDensity(Problem::Indices::liquidPhaseIdx);
+
+            source += pointSources;
+        }
+    }
+
+    std::cout << "Global integrated source (" << problem.name() << "): " << source[Problem::Indices::conti0EqIdx] << " (kg/s) / "
+              <<                           source[Problem::Indices::conti0EqIdx]*3600*24*1000 << " (g/day)" << '\n';
+
+    return source[Problem::Indices::conti0EqIdx];
+}
+
+//! helper function for mass balance evaluations
+template<class Problem, class SolutionVector, class GridVariables>
+double computeGlobalMass(const Problem& problem, const SolutionVector& sol, const GridVariables& gridVars)
+{
+    static constexpr int liquidPhaseIdx = Problem::Indices::liquidPhaseIdx;
+    static constexpr int transportCompIdx = Problem::Indices::transportCompIdx;
+    double mass = 0.0;
+
+    const auto& gg = problem.fvGridGeometry();
+    for (const auto& element : elements(gg.gridView()))
+    {
+        auto fvGeometry = localView(gg);
+        fvGeometry.bindElement(element);
+
+        auto elemVolVars = localView(gridVars.curGridVolVars());
+        elemVolVars.bindElement(element, fvGeometry, sol);
+
+        for (auto&& scv : scvs(fvGeometry))
+        {
+            const auto& volVars = elemVolVars[scv];
+            mass += volVars.massFraction(liquidPhaseIdx, transportCompIdx)*volVars.density(liquidPhaseIdx)
+                     *scv.volume() * volVars.porosity() * volVars.saturation(liquidPhaseIdx) * volVars.extrusionFactor();
+        }
+    }
+
+    return mass;
+}
+
+//! helper function for mass balance evaluations
+template<class Problem, class SolutionVector, class GridVariables>
+double computeGlobalBoundaryMass(const Problem& problem, const SolutionVector& sol, const GridVariables& gridVars, double dt)
+{
+    static constexpr int transportCompIdx = Problem::Indices::transportCompIdx;
+    static constexpr int transportEqIdx = Problem::Indices::transportEqIdx;
+    double mass = 0.0;
+
+    const auto& gg = problem.fvGridGeometry();
+    for (const auto& element : elements(gg.gridView()))
+    {
+        auto fvGeometry = localView(gg);
+        fvGeometry.bindElement(element);
+
+        auto elemVolVars = localView(gridVars.curGridVolVars());
+        elemVolVars.bindElement(element, fvGeometry, sol);
+
+        for (auto&& scvf : scvfs(fvGeometry))
+            if (scvf.boundary())
+                mass += problem.neumann(element, fvGeometry, elemVolVars, scvf)[transportEqIdx]
+                        * scvf.area() * elemVolVars[scvf.insideScvIdx()].extrusionFactor()
+                        * Problem::FluidSystem::molarMass(transportCompIdx)
+                        * dt;
+    }
+
+    return mass;
+}
+
+} // end namespace Dumux
+
+int main(int argc, char** argv) try
+{
+    using namespace Dumux;
+
+    // initialize MPI, finalize is done automatically on exit
+    const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+    // print dumux start message
+    if (mpiHelper.rank() == 0)
+        DumuxMessage::print(/*firstCall=*/true);
+
+    // parse command line arguments and input file
+    Parameters::init(argc, argv);
+
+    // Define the sub problem type tags
+    using BulkTypeTag = TTAG(SoilTypeTag);
+    using LowDimTypeTag = TTAG(RootTypeTag);
+
+    // try to create a grid (from the given grid file or the input file)
+    // for both sub-domains
+    using BulkGridManager = Dumux::GridManager<typename GET_PROP_TYPE(BulkTypeTag, Grid)>;
+    BulkGridManager bulkGridManager;
+    bulkGridManager.init("Soil"); // pass parameter group
+
+    using LowDimGridManager = Dumux::GridManager<typename GET_PROP_TYPE(LowDimTypeTag, Grid)>;
+    LowDimGridManager lowDimGridManager;
+    lowDimGridManager.init("Root"); // pass parameter group
+
+    // we compute on the leaf grid view
+    const auto& bulkGridView = bulkGridManager.grid().leafGridView();
+    const auto& lowDimGridView = lowDimGridManager.grid().leafGridView();
+
+    ////////////////////////////////////////////////////////////
+    // run instationary non-linear problem on this grid
+    ////////////////////////////////////////////////////////////
+
+    // create the finite volume grid geometry
+    using BulkFVGridGeometry = typename GET_PROP_TYPE(BulkTypeTag, FVGridGeometry);
+    auto bulkFvGridGeometry = std::make_shared<BulkFVGridGeometry>(bulkGridView);
+    bulkFvGridGeometry->update();
+    using LowDimFVGridGeometry = typename GET_PROP_TYPE(LowDimTypeTag, FVGridGeometry);
+    auto lowDimFvGridGeometry = std::make_shared<LowDimFVGridGeometry>(lowDimGridView);
+    lowDimFvGridGeometry->update();
+
+    // the mixed dimension type traits
+    using Traits = MultiDomainTraits<BulkTypeTag, LowDimTypeTag>;
+    constexpr auto bulkIdx = Traits::template DomainIdx<0>();
+    constexpr auto lowDimIdx = Traits::template DomainIdx<1>();
+
+    // the coupling manager
+    using CouplingManager = typename GET_PROP_TYPE(BulkTypeTag, CouplingManager);
+    auto couplingManager = std::make_shared<CouplingManager>(bulkFvGridGeometry, lowDimFvGridGeometry);
+
+    // the bulk problem (initial and boundary conditions)
+    using BulkProblem = typename GET_PROP_TYPE(BulkTypeTag, Problem);
+    auto bulkProblem = std::make_shared<BulkProblem>(bulkFvGridGeometry, couplingManager);
+
+    // the low dim spatial parameters
+    using LowDimSpatialParams = typename GET_PROP_TYPE(LowDimTypeTag, SpatialParams);
+    auto lowDimSpatialParams = std::make_shared<LowDimSpatialParams>(lowDimFvGridGeometry, lowDimGridManager.getGridData());
+
+    // the low dim problem (initial and boundary conditions)
+    using LowDimProblem = typename GET_PROP_TYPE(LowDimTypeTag, Problem);
+    auto lowDimProblem = std::make_shared<LowDimProblem>(lowDimFvGridGeometry, lowDimSpatialParams, couplingManager);
+
+    // locally refine levels deep around the embedded grid
+    int levels = getParam<int>("Soil.Grid.LocalRefinement");
+    for (int i = 0; i < levels; ++i)
+    {
+        auto& soilGrid = bulkGridManager.grid();
+        using BulkGridView = typename GET_PROP_TYPE(BulkTypeTag, GridView);
+        using LowDimGridView = typename GET_PROP_TYPE(LowDimTypeTag, GridView);
+
+        MixedDimensionGlue<BulkGridView, LowDimGridView>
+            glue(bulkFvGridGeometry->boundingBoxTree(), lowDimFvGridGeometry->boundingBoxTree());
+
+        // refine all 3D cells intersected
+        for (const auto& is : intersections(glue))
+        {
+            for (unsigned int outsideIdx = 0; outsideIdx < is.neighbor(0); ++outsideIdx)
+            {
+                const auto cutElement = is.outside(outsideIdx);
+
+                // mark the cut element and all it's neighbors
+                soilGrid.mark(1, cutElement);
+                for (const auto& intersection : intersections(bulkGridView, cutElement))
+                    if (intersection.neighbor())
+                        soilGrid.mark(1, intersection.outside());
+            }
+
+        }
+
+        // refine all 3D cells that are where the contamination is
+        const double extend = 0.15*(bulkFvGridGeometry->bBoxMax()[0]-bulkFvGridGeometry->bBoxMin()[0]);
+        for (const auto& element : elements(bulkGridView))
+        {
+            const auto globalPos = element.geometry().center();
+            auto contaminationPos = bulkFvGridGeometry->bBoxMax()-bulkFvGridGeometry->bBoxMin();
+            contaminationPos[0] *= 0.25;
+            contaminationPos[1] *= 0.55;
+            contaminationPos[2] *= 0.25;
+            contaminationPos += bulkFvGridGeometry->bBoxMin();
+
+            if ((globalPos - contaminationPos).infinity_norm() <  extend + 1e-7)
+                soilGrid.mark(1, element);
+        }
+
+        soilGrid.preAdapt();
+        soilGrid.adapt();
+        soilGrid.postAdapt();
+
+        // make sure there is only one level difference
+        for (int i = 0; i < levels; ++i)
+        {
+            for (const auto& element : elements(bulkGridView))
+            {
+                for (const auto& intersection : intersections(bulkGridView, element))
+                {
+                    if (intersection.neighbor())
+                        if (intersection.outside().level()-1 > element.level())
+                            soilGrid.mark(1, element);
+                }
+            }
+
+            soilGrid.preAdapt();
+            soilGrid.adapt();
+            soilGrid.postAdapt();
+        }
+
+        // update the bounding box tree
+        bulkFvGridGeometry->update();
+    }
+
+    // update geometry after refinement
+    bulkFvGridGeometry->update();
+    lowDimFvGridGeometry->update();
+
+    // output min max h
+    double bulkHMin = 1.0; double bulkHMax = 0.0;
+    for (const auto& element : elements(bulkGridView))
+    {
+        const auto geometry = element.geometry();
+        const auto h = (geometry.corner(1)-geometry.corner(0)).two_norm();
+        bulkHMin = std::min(bulkHMin, h);
+        bulkHMax = std::max(bulkHMax, h);
+    }
+
+    double ldHMin = 1.0; double ldHMax = 0.0;
+    for (const auto& element : elements(lowDimGridView))
+    {
+        const auto geometry = element.geometry();
+        const auto h = (geometry.corner(1)-geometry.corner(0)).two_norm();
+        ldHMin = std::min(ldHMin, h);
+        ldHMax = std::max(ldHMax, h);
+    }
+
+    // the solution vector
+    Traits::SolutionVector sol;
+    sol[bulkIdx].resize(bulkFvGridGeometry->numDofs());
+    sol[lowDimIdx].resize(lowDimFvGridGeometry->numDofs());
+    bulkProblem->applyInitialSolution(sol[bulkIdx]);
+    lowDimProblem->applyInitialSolution(sol[lowDimIdx]);
+    auto oldSol = sol;
+
+    couplingManager->init(bulkProblem, lowDimProblem, sol);
+    bulkProblem->computePointSourceMap();
+    lowDimProblem->computePointSourceMap();
+
+    // the grid variables
+    using BulkGridVariables = typename GET_PROP_TYPE(BulkTypeTag, GridVariables);
+    auto bulkGridVariables = std::make_shared<BulkGridVariables>(bulkProblem, bulkFvGridGeometry);
+    bulkGridVariables->init(sol[bulkIdx], oldSol[bulkIdx]);
+    using LowDimGridVariables = typename GET_PROP_TYPE(LowDimTypeTag, GridVariables);
+    auto lowDimGridVariables = std::make_shared<LowDimGridVariables>(lowDimProblem, lowDimFvGridGeometry);
+    lowDimGridVariables->init(sol[lowDimIdx], oldSol[lowDimIdx]);
+
+    // get some time loop parameters
+    using Scalar = Traits::Scalar;
+    const auto tEnd = getParam<Scalar>("TimeLoop.TEnd");
+    const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize");
+    const auto episodeLength = getParam<Scalar>("TimeLoop.EpisodeLength");
+    auto dt = getParam<Scalar>("TimeLoop.DtInitial");
+
+    const bool outputVtk = getParam<bool>("Problem.EnableVtkOutput", true);
+
+    // intialize the vtk output module
+    VtkOutputModule<BulkTypeTag> bulkVtkWriter(*bulkProblem, *bulkFvGridGeometry, *bulkGridVariables, sol[bulkIdx], bulkProblem->name());
+    GET_PROP_TYPE(BulkTypeTag, VtkOutputFields)::init(bulkVtkWriter);
+    if (outputVtk) bulkVtkWriter.write(0.0);
+
+    VtkOutputModule<LowDimTypeTag> lowDimVtkWriter(*lowDimProblem, *lowDimFvGridGeometry, *lowDimGridVariables, sol[lowDimIdx], lowDimProblem->name());
+    GET_PROP_TYPE(LowDimTypeTag, VtkOutputFields)::init(lowDimVtkWriter);
+    lowDimProblem->addVtkOutputFields(lowDimVtkWriter);
+    if (outputVtk) lowDimVtkWriter.write(0.0);
+
+    // instantiate time loop
+    auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>(0.0, dt, tEnd);
+    timeLoop->setMaxTimeStepSize(maxDt);
+
+    // the assembler with time loop for instationary problem
+    using Assembler = MultiDomainFVAssembler<Traits, CouplingManager, DiffMethod::numeric>;
+    auto assembler = std::make_shared<Assembler>(std::make_tuple(bulkProblem, lowDimProblem),
+                                                 std::make_tuple(bulkFvGridGeometry, lowDimFvGridGeometry),
+                                                 std::make_tuple(bulkGridVariables, lowDimGridVariables),
+                                                 couplingManager, timeLoop);
+
+    // the linear solver
+    using LinearSolver = BlockDiagILU0BiCGSTABSolver;
+    auto linearSolver = std::make_shared<LinearSolver>();
+
+    // the non-linear solver
+    using NewtonSolver = MultiDomainNewtonSolver<Assembler, LinearSolver, CouplingManager>;
+    NewtonSolver nonLinearSolver(assembler, linearSolver, couplingManager);
+
+    // keep track of mass that left the system
+    double massLeft = 0.0;
+
+    // output file
+    const auto outFileName = getParam<std::string>("Problem.OutFile");
+    std::ofstream outFile(outFileName, std::ios::out);
+
+    outFile << "[3D] hMax: " << bulkHMax << ", hMin: " << bulkHMin << std::endl;
+    outFile << "[1D] hMax: " << ldHMax << ", hMin: " << ldHMin << std::endl << std::endl;
+
+    double lowDimMass = computeGlobalMass(*lowDimProblem, sol[lowDimIdx], *lowDimGridVariables);
+    double bulkMass = computeGlobalMass(*bulkProblem, sol[bulkIdx], *bulkGridVariables);
+    const double initialMass = lowDimMass + bulkMass;
+
+    std::cout << "\033[1;33m" << "The domain initially contains " << (lowDimMass + bulkMass)*1e12 << " ng tracer"
+              << " (root: " << lowDimMass*1e12 << ", soil: " << bulkMass*1e12 << ")\033[0m" << '\n';
+
+    // time loop
+    timeLoop->setPeriodicCheckPoint(episodeLength);
+    timeLoop->start();
+    while (!timeLoop->finished())
+    {
+        std::cout << '\n' << "\033[1m" << "Simulation time in hours: " << timeLoop->time()/3600 << "\033[0m\n\n";
+
+        // set previous solution for storage evaluations
+        assembler->setPreviousSolution(oldSol);
+
+        // solve the non-linear system with time step control
+        nonLinearSolver.solve(sol, *timeLoop);
+
+        // make the new solution the old solution
+        oldSol = sol;
+        bulkGridVariables->advanceTimeStep();
+        lowDimGridVariables->advanceTimeStep();
+
+        // advance to the time loop to the next step
+        timeLoop->advanceTimeStep();
+
+        lowDimMass = computeGlobalMass(*lowDimProblem, sol[lowDimIdx], *lowDimGridVariables);
+        bulkMass = computeGlobalMass(*bulkProblem, sol[bulkIdx], *bulkGridVariables);
+        massLeft += computeGlobalBoundaryMass(*lowDimProblem, sol[lowDimIdx], *lowDimGridVariables, timeLoop->timeStepSize());
+
+        std::cout << "\033[1;33m" << "The domain contains " << (lowDimMass + bulkMass)*1e12 << " ng tracer"
+                  << " (root: " << lowDimMass*1e12 << ", soil: " << bulkMass*1e12 << ")\033[0m" << '\n';
+
+        std::cout << "\033[1;33m" << massLeft*1e12 << " ng left domain over the root collar -> "
+                  << ((lowDimMass + bulkMass) + massLeft)*1e12 << " ng balanced.\033[0m" << '\n';
+
+        std::cout << "\033[1;33m" << "Global mass balance error: "
+                  << (lowDimMass + bulkMass + massLeft - initialMass)*1e12 << " ng.\033[0m" << '\n';
+
+        outFile << timeLoop->time() << std::scientific << std::setprecision(8)
+                << " " << massLeft*1e12 << " " << lowDimMass + bulkMass + massLeft - initialMass << '\n';
+
+        // write vtk output
+        if (outputVtk && (timeLoop->isCheckPoint() || timeLoop->finished()))
+        {
+            bulkVtkWriter.write(timeLoop->time());
+            lowDimVtkWriter.write(timeLoop->time());
+        }
+
+        // report statistics of this time step
+        timeLoop->reportTimeStep();
+
+        // set new dt as suggested by newton controller
+        timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+    }
+
+    outFile.close();
+
+    timeLoop->finalize(mpiHelper.getCollectiveCommunication());
+
+    ////////////////////////////////////////////////////////////
+    // finalize, print dumux message to say goodbye
+    ////////////////////////////////////////////////////////////
+
+    // print dumux end message
+    if (mpiHelper.rank() == 0)
+    {
+        Parameters::print();
+        DumuxMessage::print(/*firstCall=*/false);
+    }
+
+    return 0;
+} // end main
+catch (Dumux::ParameterException &e)
+{
+    std::cerr << std::endl << e << " ---> Abort!" << std::endl;
+    return 1;
+}
+catch (Dune::DGFException & e)
+{
+    std::cerr << "DGF exception thrown (" << e <<
+                 "). Most likely, the DGF file name is wrong "
+                 "or the DGF file is corrupted, "
+                 "e.g. missing hash at end of file or wrong number (dimensions) of entries."
+                 << " ---> Abort!" << std::endl;
+    return 2;
+}
+catch (Dune::Exception &e)
+{
+    std::cerr << "Dune reported error: " << e << " ---> Abort!" << std::endl;
+    return 3;
+}
+catch (...)
+{
+    std::cerr << "Unknown exception thrown! ---> Abort!" << std::endl;
+    return 4;
+}
diff --git a/test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.input b/test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.input
new file mode 100644
index 0000000000..58fbd978d5
--- /dev/null
+++ b/test/multidomain/embedded/1d3d/1p2c_richards2c/test_1p2c_richards2c.input
@@ -0,0 +1,51 @@
+[MixedDimension]
+NumCircleSegments = 10
+
+[TimeLoop]
+DtInitial = 8640 # [s]
+TEnd = 259200 # [s]
+EpisodeLength = 86400 # [s]
+
+[Root.Grid]
+File = ../grids/lupine.dgf
+Refinement = 0
+
+[Soil.Grid]
+LowerLeft = -0.05 -0.05 -0.1
+UpperRight = 0.05 0.05 0
+Cells = 10 10 10
+ClosureType = None
+Refinement = 0
+LocalRefinement = 1
+
+[Problem]
+Name = test_soilroot
+ContaminantMoleFraction = 3e-7
+OutFile = "tracermass_fine.out"
+EnableVtkOutput = true
+EnableGravity = true
+InitTopSaturation = 0.3
+
+[Soil.SpatialParams]
+Permeability = 2.57e-12 # [m^2]
+Porosity = 0.4 # [-]
+
+[Root.SpatialParams]
+Kx = 5.0968e-17
+Kr = 2.04e-13
+
+[Component]
+LiquidDiffusionCoefficient = 2.3e-9
+Name = D2O
+MolarMass = 20e-3 # in kg/mol, molar mass heavy water D2O
+
+[BoundaryConditions]
+InitialRootPressure = -1.2e6 # [Pa]
+TranspirationRate = 2.15e-8 # [kg / s]
+
+[Assembly.NumericDifference]
+PriVarMagnitude = 1e6 1
+
+[LinearSolver]
+MaxIterations = 20000
+Verbosity = 0
diff --git a/test/multidomain/embedded/1d3d/CMakeLists.txt b/test/multidomain/embedded/1d3d/CMakeLists.txt
index 70dead5f49..5d6a78487b 100644
--- a/test/multidomain/embedded/1d3d/CMakeLists.txt
+++ b/test/multidomain/embedded/1d3d/CMakeLists.txt
@@ -1,4 +1,5 @@
 add_subdirectory(1p_1p)
 add_subdirectory(1p_richards)
+add_subdirectory(1p2c_richards2c)
 
 dune_symlink_to_source_files(FILES "grids")
diff --git a/test/references/test_embedded_1d3d_1p2c_richards2c_1d-reference.vtp b/test/references/test_embedded_1d3d_1p2c_richards2c_1d-reference.vtp
new file mode 100644
index 0000000000..4353175f99
--- /dev/null
+++ b/test/references/test_embedded_1d3d_1p2c_richards2c_1d-reference.vtp
@@ -0,0 +1,2359 @@
+<?xml version="1.0"?>
+<VTKFile type="PolyData" version="0.1" byte_order="LittleEndian">
+  <PolyData>
+    <Piece NumberOfLines="1738" NumberOfPoints="1739">
+      <CellData Scalars="pressure">
+        <DataArray type="Float32" Name="pressure" NumberOfComponents="1" format="ascii">
+          19306.8 19575.7 19640.3 19703.9 19766.7 19828.8 19890.3 19953.5 20018.4 20082.9 20146.9 20212
+          20278 20343.6 20408.8 20473.5 20537.8 20601.7 20664.3 20725.7 20786.7 20847.2 20903.6 20956
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+          21515 21549.5 21583.6 21617.4 21650.8 21683.8 21716.4 21748.7 21780.5 21812 21843.1 21873.9
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diff --git a/test/references/test_embedded_1d3d_1p2c_richards2c_3d-reference.vtu b/test/references/test_embedded_1d3d_1p2c_richards2c_3d-reference.vtu
new file mode 100644
index 0000000000..ede4614fc8
--- /dev/null
+++ b/test/references/test_embedded_1d3d_1p2c_richards2c_3d-reference.vtu
@@ -0,0 +1,7767 @@
+<?xml version="1.0"?>
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-- 
GitLab