diff --git a/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt b/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d4e5246062d3240b2dd2d517b6f129c168e943b8
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt
@@ -0,0 +1,44 @@
+dune_symlink_to_source_files(FILES "grids" "params.input")
+
+# test gravity using different values for xi
+add_executable(test_md_facet_1p1p_gravity_tpfa EXCLUDE_FROM_ALL main.cc)
+target_compile_definitions(test_md_facet_1p1p_gravity_tpfa
+                           PUBLIC BULKTYPETAG=OnePBulkTpfa
+                                  LOWDIMTYPETAG=OnePLowDimTpfa
+                                  LOWDIMGRIDTYPE=Dune::FoamGrid<1,2>
+                                  BULKGRIDTYPE=Dune::ALUGrid<2,2,Dune::cube,Dune::nonconforming>)
+
+dune_add_test(NAME test_md_facet_1p1p_gravity_xi1_tpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_gravity_tpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_bulk-00000.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_bulk-00001.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_lowdim-00000.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_lowdim-00001.vtp
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_tpfa params.input")
+
+dune_add_test(NAME test_facet_1p1p_tpfa_gravity_xi066_tpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_gravity_tpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_bulk-00000.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_bulk-00001.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_lowdim-00000.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_lowdim-00001.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_tpfa params.input  \
+                                                               -FacetCoupling.Xi 0.66 -Vtk.OutputName test_md_facet_1p1p_gravity_xi066")
+
+set(CMAKE_BUILD_TYPE Release)
+
+#install sources
+install(FILES
+main.cc
+problem_bulk.hh
+problem_lowdim.hh
+spatialparams.hh
+DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/test/multidomain/facet/1p_1p/gravity)
diff --git a/test/multidomain/facet/1p_1p/gravity/grids/gravity.geo b/test/multidomain/facet/1p_1p/gravity/grids/gravity.geo
new file mode 100644
index 0000000000000000000000000000000000000000..b8dcabbbc87e3661def5518d3b1e6974155aabee
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/grids/gravity.geo
@@ -0,0 +1,34 @@
+// domain measures
+xmax = 1.0;
+ymax = 3.0;
+
+// use zmax != 0 to produce a surface grid
+zmax = 0.0;
+
+// discretization specifics
+numCellsX = 30;
+numCellsY = 90;
+
+Point(1) = {0.0, 0.0, 0.0};
+Point(2) = {xmax, 0.0, 0.0};
+Point(3) = {xmax, ymax/2.0, zmax/2.0};
+Point(4) = {xmax, ymax, zmax};
+Point(5) = {0.0, ymax, zmax};
+Point(6) = {0.0, ymax/2.0, zmax/2.0};
+
+Line(1) = {1, 2}; Transfinite Line{1} = numCellsX;
+Line(2) = {2, 3}; Transfinite Line{2} = numCellsY/2;
+Line(3) = {3, 4}; Transfinite Line{3} = numCellsY/2;
+Line(4) = {4, 5}; Transfinite Line{4} = numCellsX;
+Line(5) = {5, 6}; Transfinite Line{5} = numCellsY/2;
+Line(6) = {6, 1}; Transfinite Line{6} = numCellsY/2;
+Line(7) = {3, 6}; Transfinite Line{7} = numCellsX;
+
+Line Loop(1) = {1, 2, 7, 6};
+Line Loop(2) = {3, 4, 5, -7};
+Plane Surface(1) = {1};
+Plane Surface(2) = {2};
+Physical Line(1) = {7};
+Physical Surface(1) = {1, 2};
+Transfinite Surface "*";
+Recombine Surface "*";
diff --git a/test/multidomain/facet/1p_1p/gravity/grids/gravity.msh b/test/multidomain/facet/1p_1p/gravity/grids/gravity.msh
new file mode 100644
index 0000000000000000000000000000000000000000..892a75f3d5c956645a615064e39c26f5f45460ab
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/grids/gravity.msh
@@ -0,0 +1,5260 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$Nodes
+2670
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diff --git a/test/multidomain/facet/1p_1p/gravity/main.cc b/test/multidomain/facet/1p_1p/gravity/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..ab8bb677c29fe4dc04ed5c23233dd6ab44886033
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/main.cc
@@ -0,0 +1,237 @@
+// -*- 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 one-phase facet coupling model
+ */
+#include <config.h>
+
+#include <iostream>
+
+#include <dune/common/parallel/mpihelper.hh>
+
+#include "problem_bulk.hh"
+#include "problem_lowdim.hh"
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/defaultusagemessage.hh>
+
+#include <dumux/assembly/diffmethod.hh>
+#include <dumux/linear/seqsolverbackend.hh>
+
+#include <dumux/multidomain/newtonsolver.hh>
+#include <dumux/multidomain/fvassembler.hh>
+#include <dumux/multidomain/traits.hh>
+
+#include <dumux/multidomain/facet/gridmanager.hh>
+#include <dumux/multidomain/facet/couplingmapper.hh>
+#include <dumux/multidomain/facet/couplingmanager.hh>
+
+#include <dumux/io/vtkoutputmodule.hh>
+
+// obtain/define some types to be used below in the property definitions and in main
+template< class BulkTypeTag, class LowDimTypeTag >
+class TestTraits
+{
+    using BulkFVGridGeometry = typename GET_PROP_TYPE(BulkTypeTag, FVGridGeometry);
+    using LowDimFVGridGeometry = typename GET_PROP_TYPE(LowDimTypeTag, FVGridGeometry);
+public:
+    using MDTraits = Dumux::MultiDomainTraits<BulkTypeTag, LowDimTypeTag>;
+    using CouplingMapper = Dumux::FacetCouplingMapper<BulkFVGridGeometry, LowDimFVGridGeometry>;
+    using CouplingManager = Dumux::FacetCouplingManager<MDTraits, CouplingMapper>;
+};
+
+namespace Dumux {
+namespace Properties {
+
+// set cm property in the sub-problems
+using TpfaTraits = TestTraits<TTAG(OnePBulkTpfa), TTAG(OnePLowDimTpfa)>;
+SET_TYPE_PROP(OnePBulkTpfa, CouplingManager, typename TpfaTraits::CouplingManager);
+SET_TYPE_PROP(OnePLowDimTpfa, CouplingManager, typename TpfaTraits::CouplingManager);
+
+} // end namespace Properties
+} // end namespace Dumux
+
+// main program
+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);
+
+    // initialize parameter tree
+    Parameters::init(argc, argv);
+
+    //////////////////////////////////////////////////////
+    // try to create the grids (from the given grid file)
+    //////////////////////////////////////////////////////
+    using BulkProblemTypeTag = TTAG(BULKTYPETAG);
+    using LowDimProblemTypeTag = TTAG(LOWDIMTYPETAG);
+    using BulkGrid = typename GET_PROP_TYPE(BulkProblemTypeTag, Grid);
+    using LowDimGrid = typename GET_PROP_TYPE(LowDimProblemTypeTag, Grid);
+
+    using GridManager = FacetCouplingGridManager<BulkGrid, LowDimGrid>;
+    GridManager gridManager;
+    gridManager.init();
+    gridManager.loadBalance();
+
+    ////////////////////////////////////////////////////////////
+    // run stationary, non-linear problem on this grid
+    ////////////////////////////////////////////////////////////
+
+    // we compute on the leaf grid views
+    const auto& bulkGridView = gridManager.template grid<0>().leafGridView();
+    const auto& lowDimGridView = gridManager.template grid<1>().leafGridView();
+
+    // create the finite volume grid geometries
+    using BulkFVGridGeometry = typename GET_PROP_TYPE(BulkProblemTypeTag, FVGridGeometry);
+    using LowDimFVGridGeometry = typename GET_PROP_TYPE(LowDimProblemTypeTag, FVGridGeometry);
+    auto bulkFvGridGeometry = std::make_shared<BulkFVGridGeometry>(bulkGridView);
+    auto lowDimFvGridGeometry = std::make_shared<LowDimFVGridGeometry>(lowDimGridView);
+    bulkFvGridGeometry->update();
+    lowDimFvGridGeometry->update();
+
+    // the coupling mapper
+    using TestTraits = TestTraits<BulkProblemTypeTag, LowDimProblemTypeTag>;
+    auto couplingMapper = std::make_shared<typename TestTraits::CouplingMapper>();
+    couplingMapper->update(*bulkFvGridGeometry, *lowDimFvGridGeometry, gridManager.getEmbeddings());
+
+    // the coupling manager
+    using CouplingManager = typename TestTraits::CouplingManager;
+    auto couplingManager = std::make_shared<CouplingManager>();
+
+    // the problems (boundary conditions)
+    using BulkProblem = typename GET_PROP_TYPE(BulkProblemTypeTag, Problem);
+    using LowDimProblem = typename GET_PROP_TYPE(LowDimProblemTypeTag, Problem);
+    auto bulkSpatialParams = std::make_shared<typename BulkProblem::SpatialParams>(bulkFvGridGeometry, "Bulk");
+    auto bulkProblem = std::make_shared<BulkProblem>(bulkFvGridGeometry, bulkSpatialParams, couplingManager, "Bulk");
+    auto lowDimSpatialParams = std::make_shared<typename LowDimProblem::SpatialParams>(lowDimFvGridGeometry, "LowDim");
+    auto lowDimProblem = std::make_shared<LowDimProblem>(lowDimFvGridGeometry, lowDimSpatialParams, couplingManager, "LowDim");
+
+    // the solution vector
+    using MDTraits = typename TestTraits::MDTraits;
+    using SolutionVector = typename MDTraits::SolutionVector;
+    SolutionVector x;
+
+    static const auto bulkId = typename MDTraits::template SubDomain<0>::Index();
+    static const auto lowDimId = typename MDTraits::template SubDomain<1>::Index();
+    x[bulkId].resize(bulkFvGridGeometry->numDofs());
+    x[lowDimId].resize(lowDimFvGridGeometry->numDofs());
+    bulkProblem->applyInitialSolution(x[bulkId]);
+    lowDimProblem->applyInitialSolution(x[lowDimId]);
+
+    // initialize coupling manager
+    couplingManager->init(bulkProblem, lowDimProblem, couplingMapper, x);
+
+    // the grid variables
+    using BulkGridVariables = typename GET_PROP_TYPE(BulkProblemTypeTag, GridVariables);
+    using LowDimGridVariables = typename GET_PROP_TYPE(LowDimProblemTypeTag, GridVariables);
+    auto bulkGridVariables = std::make_shared<BulkGridVariables>(bulkProblem, bulkFvGridGeometry);
+    auto lowDimGridVariables = std::make_shared<LowDimGridVariables>(lowDimProblem, lowDimFvGridGeometry);
+    bulkGridVariables->init(x[bulkId]);
+    lowDimGridVariables->init(x[lowDimId]);
+
+    // intialize the vtk output module
+    using BulkSolutionVector = std::decay_t<decltype(x[bulkId])>;
+    using LowDimSolutionVector = std::decay_t<decltype(x[lowDimId])>;
+    VtkOutputModule<BulkGridVariables, BulkSolutionVector> bulkVtkWriter(*bulkGridVariables, x[bulkId], bulkProblem->name(), "Bulk");
+    VtkOutputModule<LowDimGridVariables, LowDimSolutionVector> lowDimVtkWriter(*lowDimGridVariables, x[lowDimId], lowDimProblem->name(), "LowDim");
+
+    // container for the output of the exact solutions
+    std::vector<typename GET_PROP_TYPE(BulkProblemTypeTag, Scalar)> bulkExact;
+    std::vector<typename GET_PROP_TYPE(LowDimProblemTypeTag, Scalar)> lowDimExact;
+
+    // Add model specific output fields
+    using BulkIOFields = typename GET_PROP_TYPE(BulkProblemTypeTag, IOFields);
+    using LowIOFields = typename GET_PROP_TYPE(LowDimProblemTypeTag, IOFields);
+    BulkIOFields::initOutputModule(bulkVtkWriter);
+    LowIOFields::initOutputModule(lowDimVtkWriter);
+
+    // write initial solution
+    bulkVtkWriter.write(0.0);
+    lowDimVtkWriter.write(0.0);
+
+    // the assembler
+    using Assembler = MultiDomainFVAssembler<MDTraits, CouplingManager, DiffMethod::numeric, /*implicit?*/true>;
+    auto assembler = std::make_shared<Assembler>( std::make_tuple(bulkProblem, lowDimProblem),
+                                                  std::make_tuple(bulkFvGridGeometry, lowDimFvGridGeometry),
+                                                  std::make_tuple(bulkGridVariables, lowDimGridVariables),
+                                                  couplingManager);
+
+    // the linear solver
+    using LinearSolver = ILU0BiCGSTABBackend;
+    auto linearSolver = std::make_shared<LinearSolver>();
+
+    // the non-linear solver
+    using NewtonSolver = Dumux::MultiDomainNewtonSolver<Assembler, LinearSolver, CouplingManager>;
+    auto newtonSolver = std::make_shared<NewtonSolver>(assembler, linearSolver, couplingManager);
+
+    // linearize & solve
+    newtonSolver->solve(x);
+
+    // update grid variables for output
+    bulkGridVariables->update(x[bulkId]);
+    lowDimGridVariables->update(x[lowDimId]);
+
+    // write vtk output
+    bulkVtkWriter.write(1.0);
+    lowDimVtkWriter.write(1.0);
+
+    ////////////////////////////////////////////////////////////
+    // finalize, print dumux message to say goodbye
+    ////////////////////////////////////////////////////////////
+    if (mpiHelper.rank() == 0)
+        DumuxMessage::print(/*firstCall=*/false);
+
+    return 0;
+}
+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/facet/1p_1p/gravity/params.input b/test/multidomain/facet/1p_1p/gravity/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..56bdd974aa9711a037d44ac7dbf8652346f62482
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/params.input
@@ -0,0 +1,27 @@
+[Problem]
+EnableGravity = true
+FractureAperture = 1e-3
+
+[Grid]
+File = ./grids/gravity.msh
+
+[Bulk]
+Problem.Name = bulk
+SpatialParams.Permeability = 1
+
+[LowDim]
+Problem.Name = lowdim
+SpatialParams.Permeability = 1e-4
+
+[FacetCoupling]
+Xi = 1.0
+
+[Vtk]
+OutputName = test_md_facet_1p1p_gravity_xi1
+
+[Assembly]
+NumericDifference.BaseEpsilon = 1e10
+
+[Component]
+LiquidDensity = 1.0
+LiquidKinematicViscosity = 1.0
diff --git a/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh b/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh
new file mode 100644
index 0000000000000000000000000000000000000000..cbd78b3b66af34b6935aa5e57279667d87cfa7be
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh
@@ -0,0 +1,175 @@
+// -*- 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 MultiDomain
+ * \ingroup FacetCoupling
+ * \brief The problem for the bulk domain in the single-phase facet coupling test
+ */
+#ifndef DUMUX_TEST_TPFAFACETCOUPLING_ONEP_BULKPROBLEM_HH
+#define DUMUX_TEST_TPFAFACETCOUPLING_ONEP_BULKPROBLEM_HH
+
+#include <dune/alugrid/grid.hh>
+
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/1pliquid.hh>
+
+#include <dumux/multidomain/facet/box/properties.hh>
+#include <dumux/multidomain/facet/cellcentered/tpfa/properties.hh>
+
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/porousmediumflow/1p/model.hh>
+
+#include "spatialparams.hh"
+
+// default for the bulk grid type
+#ifndef BULKGRIDTYPE
+#define BULKGRIDTYPE Dune::ALUGrid<2, 2, Dune::cube, Dune::nonconforming>
+#endif
+
+namespace Dumux {
+// forward declarations
+template<class TypeTag> class OnePBulkProblem;
+
+namespace Properties {
+// create the type tag nodes
+NEW_TYPE_TAG(OnePBulk, INHERITS_FROM(OneP));
+NEW_TYPE_TAG(OnePBulkTpfa, INHERITS_FROM(OnePBulk, CCTpfaFacetCouplingModel));
+
+// Set the grid type
+SET_TYPE_PROP(OnePBulk, Grid, BULKGRIDTYPE);
+// Set the problem type
+SET_TYPE_PROP(OnePBulk, Problem, OnePBulkProblem<TypeTag>);
+// set the spatial params
+SET_TYPE_PROP(OnePBulk, SpatialParams, OnePSpatialParams< typename GET_PROP_TYPE(TypeTag, FVGridGeometry),
+                                                          typename GET_PROP_TYPE(TypeTag, Scalar) >);
+
+// the fluid system
+SET_PROP(OnePBulk, FluidSystem)
+{
+private:
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+public:
+    using type = FluidSystems::OnePLiquid< Scalar, Components::Constant<1, Scalar> >;
+};
+
+} // end namespace Properties
+
+/*!
+ * \ingroup OnePTests
+ * \brief Test problem for the incompressible one-phase model
+ *        with coupling across the bulk grid facets
+ */
+template<class TypeTag>
+class OnePBulkProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+    using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+    using PrimaryVariables = typename GridVariables::PrimaryVariables;
+    using Scalar = typename GridVariables::Scalar;
+
+    using FVGridGeometry = typename GridVariables::GridGeometry;
+    using FVElementGeometry = typename FVGridGeometry::LocalView;
+    using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+    using SubControlVolumeFace = typename FVGridGeometry::SubControlVolumeFace;
+    using GridView = typename FVGridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+    using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+    using CouplingManager = typename GET_PROP_TYPE(TypeTag, CouplingManager);
+    using NumEqVector = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+
+    static constexpr int dimWorld = GridView::dimensionworld;
+
+public:
+    OnePBulkProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+                    std::shared_ptr<typename ParentType::SpatialParams> spatialParams,
+                    std::shared_ptr<CouplingManager> couplingManager,
+                    const std::string& paramGroup = "")
+    : ParentType(fvGridGeometry, spatialParams, paramGroup)
+    , couplingManagerPtr_(couplingManager)
+    {
+        problemName_  =  getParam<std::string>("Vtk.OutputName") + "_" +
+                         getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
+    }
+
+    //! The problem name.
+    const std::string& name() const
+    { return problemName_; }
+
+    //! Specifies the type of boundary condition at a given position
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        if (globalPos[1] < 1e-6 || globalPos[1] > this->fvGridGeometry().bBoxMax()[1] - 1e-6)
+            values.setAllDirichlet();
+        return values;
+    }
+
+    //! Specifies the type of interior boundary condition at a given position
+    BoundaryTypes interiorBoundaryTypes(const Element& element, const SubControlVolumeFace& scvf) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        return values;
+    }
+
+    //! Evaluate the source term at a given position
+    NumEqVector sourceAtPos(const GlobalPosition& globalPos) const
+    { return NumEqVector(0.0); }
+
+    //! evaluates the Dirichlet boundary condition for a given position
+    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+    { return initialAtPos(globalPos); }
+
+    //! evaluates the Neumann boundary condition for a boundary segment
+    template<class ElementVolumeVariables>
+    NumEqVector neumann(const Element& element,
+                        const FVElementGeometry& fvGeometry,
+                        const ElementVolumeVariables& elemVolVars,
+                        const SubControlVolumeFace& scvf) const
+    { return NumEqVector(0.0); }
+
+    //! evaluate the initial conditions
+    PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
+    {
+        const auto g = this->gravityAtPos(globalPos)[dimWorld-1];
+        const auto h = 1.0 - (3.0-globalPos[dimWorld-1])*g;
+        return PrimaryVariables(h);
+    }
+
+    //! returns the temperature in \f$\mathrm{[K]}\f$ in the domain
+    Scalar temperature() const
+    { return 283.15; /*10°*/ }
+
+    //! returns reference to the coupling manager.
+    const CouplingManager& couplingManager() const
+    { return *couplingManagerPtr_; }
+
+private:
+    std::shared_ptr<CouplingManager> couplingManagerPtr_;
+    std::string problemName_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh b/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh
new file mode 100644
index 0000000000000000000000000000000000000000..e3030d32640ec2f97d0c247dbfca6876720b759a
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh
@@ -0,0 +1,170 @@
+// -*- 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 MultiDomain
+ * \ingroup FacetCoupling
+ * \brief The problem for the lower-dimensional domain in the single-phase facet coupling test
+ */
+#ifndef DUMUX_TEST_TPFAFACETCOUPLING_ONEP_LOWDIMPROBLEM_HH
+#define DUMUX_TEST_TPFAFACETCOUPLING_ONEP_LOWDIMPROBLEM_HH
+
+#include <dune/foamgrid/foamgrid.hh>
+
+#include <dumux/material/components/constant.hh>
+#include <dumux/material/fluidsystems/1pliquid.hh>
+
+#include <dumux/discretization/box.hh>
+#include <dumux/discretization/cctpfa.hh>
+
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/porousmediumflow/1p/model.hh>
+
+#include "spatialparams.hh"
+
+// default for the grid type
+#ifndef LOWDIMGRIDTYPE
+#define LOWDIMGRIDTYPE Dune::FoamGrid<1, 2>
+#endif
+
+namespace Dumux {
+// forward declarations
+template<class TypeTag> class OnePLowDimProblem;
+
+namespace Properties {
+// create the type tag nodes
+NEW_TYPE_TAG(OnePLowDim, INHERITS_FROM(OneP));
+NEW_TYPE_TAG(OnePLowDimTpfa, INHERITS_FROM(CCTpfaModel, OnePLowDim));
+
+// Set the grid type
+SET_TYPE_PROP(OnePLowDim, Grid, LOWDIMGRIDTYPE);
+// Set the problem type
+SET_TYPE_PROP(OnePLowDim, Problem, OnePLowDimProblem<TypeTag>);
+// set the spatial params
+SET_TYPE_PROP(OnePLowDim, SpatialParams, OnePSpatialParams< typename GET_PROP_TYPE(TypeTag, FVGridGeometry),
+                                                            typename GET_PROP_TYPE(TypeTag, Scalar) >);
+
+// the fluid system
+SET_PROP(OnePLowDim, FluidSystem)
+{
+private:
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+public:
+    using type = FluidSystems::OnePLiquid< Scalar, Components::Constant<1, Scalar> >;
+};
+} // end namespace Properties
+
+/*!
+ * \ingroup OnePTests
+ * \brief The lower-dimensional test problem for the incompressible
+ *        one-phase model with coupling across the bulk grid facets
+ */
+template<class TypeTag>
+class OnePLowDimProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+
+    using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+    using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView;
+    using PrimaryVariables = typename GridVariables::PrimaryVariables;
+    using Scalar = typename GridVariables::Scalar;
+
+    using FVGridGeometry = typename GridVariables::GridGeometry;
+    using FVElementGeometry = typename FVGridGeometry::LocalView;
+    using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+    using GridView = typename FVGridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+    using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+    using CouplingManager = typename GET_PROP_TYPE(TypeTag, CouplingManager);
+    using NumEqVector = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+
+    static constexpr int dimWorld = GridView::dimensionworld;
+
+public:
+    OnePLowDimProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry,
+                      std::shared_ptr<typename ParentType::SpatialParams> spatialParams,
+                      std::shared_ptr<CouplingManager> couplingManager,
+                      const std::string& paramGroup = "")
+    : ParentType(fvGridGeometry, spatialParams, paramGroup)
+    , couplingManagerPtr_(couplingManager)
+    , aperture_(getParam<Scalar>("Problem.FractureAperture"))
+    {
+        problemName_  =  getParam<std::string>("Vtk.OutputName") + "_" +
+                         getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
+    }
+
+    //! The problem name.
+    const std::string& name() const
+    { return problemName_; }
+
+    //! Specifies the type of boundary condition at a given position
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+        return values;
+    }
+
+    //! Evaluate the source term at a given position
+    NumEqVector source(const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const SubControlVolume& scv) const
+    {
+        // evaluate sources from bulk domain
+        auto source = couplingManagerPtr_->evalSourcesFromBulk(element, fvGeometry, elemVolVars, scv);
+        source /= scv.volume()*elemVolVars[scv].extrusionFactor();
+        return source;
+    }
+
+    //! evaluates the Dirichlet boundary condition for a given position
+    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+    { return initialAtPos(globalPos); }
+
+    //! Set the aperture as extrusion factor.
+    Scalar extrusionFactorAtPos(const GlobalPosition& globalPos) const
+    { return aperture_; }
+
+    //! evaluate the initial conditions
+    PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
+    {
+        const auto g = this->gravityAtPos(globalPos)[dimWorld-1];
+        const auto h = 1.0 - (3.0-globalPos[dimWorld-1])*g;
+        return PrimaryVariables(h);
+    }
+
+    //! returns the temperature in \f$\mathrm{[K]}\f$ in the domain
+    Scalar temperature() const
+    { return 283.15; /*10°*/ }
+
+    //! returns reference to the coupling manager.
+    const CouplingManager& couplingManager() const
+    { return *couplingManagerPtr_; }
+
+private:
+    std::shared_ptr<CouplingManager> couplingManagerPtr_;
+    Scalar aperture_;
+    std::string problemName_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/facet/1p_1p/gravity/spatialparams.hh b/test/multidomain/facet/1p_1p/gravity/spatialparams.hh
new file mode 100644
index 0000000000000000000000000000000000000000..e0b602ba341196de1c11d43529d5fa187afc6bb2
--- /dev/null
+++ b/test/multidomain/facet/1p_1p/gravity/spatialparams.hh
@@ -0,0 +1,72 @@
+// -*- 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 The spatial params the single-phase facet coupling test
+ */
+#ifndef DUMUX_TEST_TPFAFACETCOUPLING_ONEP_SPATIALPARAMS_HH
+#define DUMUX_TEST_TPFAFACETCOUPLING_ONEP_SPATIALPARAMS_HH
+
+#include <dumux/material/spatialparams/fv1p.hh>
+
+namespace Dumux
+{
+
+/*!
+ * \ingroup OnePTests
+ * \brief The spatial params the single-phase facet coupling test
+ */
+template< class FVGridGeometry, class Scalar >
+class OnePSpatialParams
+: public FVSpatialParamsOneP< FVGridGeometry, Scalar, OnePSpatialParams<FVGridGeometry, Scalar> >
+{
+    using ThisType = OnePSpatialParams< FVGridGeometry, Scalar >;
+    using ParentType = FVSpatialParamsOneP< FVGridGeometry, Scalar, ThisType >;
+
+    using GridView = typename FVGridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+    //! export the type used for permeabilities
+    using PermeabilityType = Scalar;
+
+    //! the constructor
+    OnePSpatialParams(std::shared_ptr<const FVGridGeometry> fvGridGeometry, const std::string& paramGroup = "")
+    : ParentType(fvGridGeometry)
+    {
+        permeability_ = getParamFromGroup<Scalar>(paramGroup, "SpatialParams.Permeability");
+    }
+
+    //! Function for defining the (intrinsic) permeability \f$[m^2]\f$.
+    PermeabilityType permeabilityAtPos(const GlobalPosition& globalPos) const
+    { return permeability_; }
+
+    //! Return the porosity
+    Scalar porosityAtPos(const GlobalPosition& globalPos) const
+    { return 1.0; }
+
+private:
+    PermeabilityType permeability_;
+};
+
+} // end namespace Dumux
+
+#endif