diff --git a/CHANGELOG.md b/CHANGELOG.md
index f7e47b154239a3938aea9d92bba5360540bb3192..16ed7dbf9b1dbb7eedd2e2c11dae6989ea743e03 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,7 @@ Differences Between DuMuX 3.1 and DuMuX 3.0
 ### Improvements and Enhancements
 
 - Added new porous medium model for the energy balance of a porous solid (general heat equation)
+- __Multidomain__: It is now possible to use the facet coupling module together with the mpfa-o scheme in the bulk domain.
 
 ### Immediate interface changes not allowing/requiring a deprecation period
 
diff --git a/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh b/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh
index eae2b64ac8de896801f31cae0c55c2f1141921b3..c0fa9de3a3ba275383942186204ec778a15d25cf 100644
--- a/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh
+++ b/dumux/discretization/cellcentered/mpfa/dualgridindexset.hh
@@ -45,7 +45,7 @@ struct NodalIndexSetDefaultTraits
 {
     using GridView = GV;
     using GridIndexType = typename IndexTraits<GV>::GridIndex;
-    using LocalIndexType = typename IndexTraits<GV>::SmallLocalIndex;
+    using LocalIndexType = typename IndexTraits<GV>::LocalIndex;
 
     //! per default, we use dynamic data containers (iv size unknown)
     template< class T > using NodalScvDataStorage = std::vector< T >;
diff --git a/dumux/discretization/cellcentered/mpfa/fvgridgeometrytraits.hh b/dumux/discretization/cellcentered/mpfa/fvgridgeometrytraits.hh
index b3bd755401aa444cef85e7bc6f84803e749b0a9b..6e9b2aa53a5d609c22fd3ddbf5a453de30e6b747 100644
--- a/dumux/discretization/cellcentered/mpfa/fvgridgeometrytraits.hh
+++ b/dumux/discretization/cellcentered/mpfa/fvgridgeometrytraits.hh
@@ -55,7 +55,7 @@ struct CCMpfaFVGridGeometryTraits : public DefaultMapperTraits<GV>
     //! Per default, we use high values that are hopefully enough for all cases
     //! We assume simplex grids where stencils can get quite large but the size is unknown
     static constexpr int maxElementStencilSize = int(GV::dimension) == 3 ? 150 :
-                                                 (int(GV::dimension)<int(GV::dimensionworld) ? 45 : 15);
+                                                 (int(GV::dimension)<int(GV::dimensionworld) ? 45 : 20);
     //! type definitions depending on the FVGridGeometry itself
     template< class FVGridGeom >
     using MpfaHelper = CCMpfaHelper< FVGridGeom >;
diff --git a/dumux/discretization/cellcentered/mpfa/localassemblerhelper.hh b/dumux/discretization/cellcentered/mpfa/localassemblerhelper.hh
index 536e38db173ac78c6f9e9eb1f8060ecfb90452d8..33e6386c57d386eab296b9721738f2f2b1cc82f1 100644
--- a/dumux/discretization/cellcentered/mpfa/localassemblerhelper.hh
+++ b/dumux/discretization/cellcentered/mpfa/localassemblerhelper.hh
@@ -26,7 +26,9 @@
 #ifndef DUMUX_DISCRETIZATION_CC_MPFA_LOCAL_ASSEMBLER_HELPER_HH
 #define DUMUX_DISCRETIZATION_CC_MPFA_LOCAL_ASSEMBLER_HELPER_HH
 
+#include <algorithm>
 #include <vector>
+#include <cassert>
 #include <utility>
 #include <type_traits>
 
@@ -67,6 +69,86 @@ class InteractionVolumeAssemblerHelper
     { return decltype( isValid(HasVectorResize())(std::declval<Vector>()) )::value; }
 
 public:
+    /*!
+     * \brief Solves a previously assembled iv-local system of equations
+     *        and stores the resulting transmissibilities in the provided
+     *        containers within the interaction volume data handle.
+     *
+     * \param fvGeometry The bound element finite volume geometry
+     * \param handle The data handle in which the matrices are stored
+     * \param iv The interaction volume
+     */
+    template< class FVElementGeometry, class DataHandle, class IV >
+    static void solveLocalSystem(const FVElementGeometry& fvGeometry,
+                                 DataHandle& handle,
+                                 IV& iv)
+    {
+        assert(iv.numUnknowns() > 0);
+
+        // T = C*(A^-1)*B + D
+        handle.A().invert();
+        handle.CA().rightmultiply(handle.A());
+        handle.T() += multiplyMatrices(handle.CA(), handle.AB());
+        handle.AB().leftmultiply(handle.A());
+
+        // On surface grids, compute the "outside" transmissibilities
+        using GridView = typename IV::Traits::GridView;
+        static constexpr int dim = GridView::dimension;
+        static constexpr int dimWorld = GridView::dimensionworld;
+        if (dim < dimWorld)
+        {
+            // bring outside tij container to the right size
+            auto& tijOut = handle.tijOutside();
+            tijOut.resize(iv.numFaces());
+            using LocalIndexType = typename IV::Traits::IndexSet::LocalIndexType;
+            for (LocalIndexType fIdx = 0; fIdx < iv.numFaces(); ++fIdx)
+            {
+                const auto& curGlobalScvf = fvGeometry.scvf(iv.localScvf(fIdx).gridScvfIndex());
+                const auto numOutsideFaces = curGlobalScvf.boundary() ? 0 : curGlobalScvf.numOutsideScvs();
+                // resize each face entry to the right number of outside faces
+                tijOut[fIdx].resize(numOutsideFaces);
+                std::for_each(tijOut[fIdx].begin(),
+                              tijOut[fIdx].end(),
+                              [&](auto& v) { resizeVector(v, iv.numKnowns()); });
+            }
+
+            // compute outside transmissibilities
+            for (const auto& localFaceData : iv.localFaceData())
+            {
+                // continue only for "outside" faces
+                if (!localFaceData.isOutsideFace())
+                    continue;
+
+                const auto scvIdx = localFaceData.ivLocalInsideScvIndex();
+                const auto scvfIdx = localFaceData.ivLocalScvfIndex();
+                const auto idxInOut = localFaceData.scvfLocalOutsideScvfIndex();
+
+                const auto& wijk = handle.omegas()[scvfIdx][idxInOut+1];
+                auto& tij = tijOut[scvfIdx][idxInOut];
+
+                tij = 0.0;
+                for (unsigned int dir = 0; dir < dim; dir++)
+                {
+                    // the scvf corresponding to this local direction in the scv
+                    const auto& scvf = iv.localScvf(iv.localScv(scvIdx).localScvfIndex(dir));
+
+                    // on interior faces the coefficients of the AB matrix come into play
+                    if (!scvf.isDirichlet())
+                    {
+                        auto tmp = handle.AB()[scvf.localDofIndex()];
+                        tmp *= wijk[dir];
+                        tij -= tmp;
+                    }
+                    else
+                        tij[scvf.localDofIndex()] -= wijk[dir];
+
+                    // add entry from the scv unknown
+                    tij[scvIdx] += wijk[dir];
+                }
+            }
+        }
+    }
+
     /*!
      * \brief Assembles the vector of face unknowns within an interaction volume.
      * \note  This requires the data handle to be fully assembled already.
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh
index c512da8f4d4b31de09c5e645935c4e5bc60904a2..82d737ff958a87422ef58f7dd9f7546cc6605b8c 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh
@@ -31,9 +31,7 @@
 #include <dune/common/fvector.hh>
 #include <dune/common/reservedvector.hh>
 
-#include <dumux/common/math.hh>
 #include <dumux/discretization/cellcentered/mpfa/interactionvolumebase.hh>
-#include <dumux/discretization/cellcentered/mpfa/dualgridindexset.hh>
 #include <dumux/discretization/cellcentered/mpfa/localfacedata.hh>
 #include <dumux/discretization/cellcentered/mpfa/methods.hh>
 
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh
index 339c95aae7c664f1fc8e21601a705ab14c9c0e51..f5485a38eb7c0ae77cfd06b2bb38fc1873677378 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/interactionvolumeindexset.hh
@@ -141,6 +141,13 @@ public:
     std::size_t numScvs() const
     { return nodalIndexSet_.numScvs(); }
 
+    //! returns a grid scv idx for a given iv-local scv index
+    GridIndexType gridScvIndex(LocalIndexType ivLocalScvIdx) const
+    {
+        assert(ivLocalScvIdx < numScvs());
+        return gridScvIndices()[ivLocalScvIdx];
+    }
+
     //! returns a grid scvf idx for a given iv-local scvf index
     GridIndexType gridScvfIndex(LocalIndexType ivLocalScvfIdx) const
     {
diff --git a/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh b/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh
index 4903b13395a9f7213daaf405e66f419e96bdf1f5..4a81776e6115331222cf63bfd8bbe36c6a31d82f 100644
--- a/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh
+++ b/dumux/discretization/cellcentered/mpfa/omethod/localassembler.hh
@@ -25,16 +25,11 @@
 #ifndef DUMUX_DISCRETIZATION_CC_MPFA_O_LOCAL_ASSEMBLER_HH
 #define DUMUX_DISCRETIZATION_CC_MPFA_O_LOCAL_ASSEMBLER_HH
 
-#include <dune/common/reservedvector.hh>
-
-#include <dumux/common/math.hh>
-#include <dumux/discretization/cellcentered/mpfa/methods.hh>
 #include <dumux/discretization/cellcentered/mpfa/localassemblerbase.hh>
 #include <dumux/discretization/cellcentered/mpfa/localassemblerhelper.hh>
 #include <dumux/discretization/cellcentered/mpfa/computetransmissibility.hh>
 
-namespace Dumux
-{
+namespace Dumux {
 
 /*!
  * \ingroup CCMpfaDiscretization
@@ -61,10 +56,6 @@ public:
      *        expressions and the local system of equations
      *        within an interaction volume in an mpfa-o type way.
      *
-     * \tparam IV The interaction volume type implementation
-     * \tparam TensorFunc Lambda to obtain the tensor w.r.t.
-     *                    which the local system is to be solved
-     *
      * \param handle The data handle in which the matrices are stored
      * \param iv The interaction volume
      * \param getT Lambda to evaluate the scv-wise tensors
@@ -76,79 +67,13 @@ public:
 
         // maybe solve the local system
         if (iv.numUnknowns() > 0)
-        {
-            // T = C*(A^-1)*B + D
-            handle.A().invert();
-            handle.CA().rightmultiply(handle.A());
-            handle.T() += multiplyMatrices(handle.CA(), handle.AB());
-            handle.AB().leftmultiply(handle.A());
-
-            // On surface grids, compute the "outside" transmissibilities
-            using GridView = typename IV::Traits::GridView;
-            static constexpr int dim = GridView::dimension;
-            static constexpr int dimWorld = GridView::dimensionworld;
-            if (dim < dimWorld)
-            {
-                // bring outside tij container to the right size
-                auto& tijOut = handle.tijOutside();
-                tijOut.resize(iv.numFaces());
-                using LocalIndexType = typename IV::Traits::IndexSet::LocalIndexType;
-                for (LocalIndexType fIdx = 0; fIdx < iv.numFaces(); ++fIdx)
-                {
-                    const auto& curGlobalScvf = this->fvGeometry().scvf(iv.localScvf(fIdx).gridScvfIndex());
-                    const auto numOutsideFaces = curGlobalScvf.boundary() ? 0 : curGlobalScvf.numOutsideScvs();
-                    // resize each face entry to the right number of outside faces
-                    tijOut[fIdx].resize(numOutsideFaces);
-                    std::for_each(tijOut[fIdx].begin(),
-                                  tijOut[fIdx].end(),
-                                  [&](auto& v) { Helper::resizeVector(v, iv.numKnowns()); });
-                }
-
-                // compute outside transmissibilities
-                for (const auto& localFaceData : iv.localFaceData())
-                {
-                    // continue only for "outside" faces
-                    if (!localFaceData.isOutsideFace())
-                        continue;
-
-                    const auto scvIdx = localFaceData.ivLocalInsideScvIndex();
-                    const auto scvfIdx = localFaceData.ivLocalScvfIndex();
-                    const auto idxInOut = localFaceData.scvfLocalOutsideScvfIndex();
-
-                    const auto& wijk = handle.omegas()[scvfIdx][idxInOut+1];
-                    auto& tij = tijOut[scvfIdx][idxInOut];
-
-                    tij = 0.0;
-                    for (unsigned int dir = 0; dir < dim; dir++)
-                    {
-                        // the scvf corresponding to this local direction in the scv
-                        const auto& scvf = iv.localScvf(iv.localScv(scvIdx).localScvfIndex(dir));
-
-                        // on interior faces the coefficients of the AB matrix come into play
-                        if (!scvf.isDirichlet())
-                        {
-                            auto tmp = handle.AB()[scvf.localDofIndex()];
-                            tmp *= wijk[dir];
-                            tij -= tmp;
-                        }
-                        else
-                            tij[scvf.localDofIndex()] -= wijk[dir];
-
-                        // add entry from the scv unknown
-                        tij[scvIdx] += wijk[dir];
-                    }
-                }
-            }
-        }
+            Helper::solveLocalSystem(this->fvGeometry(), handle, iv);
     }
 
     /*!
      * \brief Assembles the vector of primary (cell) unknowns and (maybe)
      *        Dirichlet boundary conditions within an interaction volume.
      *
-     * \tparam IV The interaction volume type implementation
-     * \tparam GetU Lambda to obtain the cell unknowns from grid indices
-     *
      * \param handle The data handle in which the vector is stored
      * \param iv The mpfa-o interaction volume
      * \param getU Lambda to obtain the desired cell/Dirichlet value from vol vars
@@ -181,8 +106,7 @@ private:
      * \note  The matrices are expected to have been resized beforehand.
      *
      * \tparam IV The interaction volume type implementation
-     * \tparam TensorFunc Lambda to obtain the tensor w.r.t.
-     *                    which the local system is to be solved
+     * \tparam TensorFunc Lambda to obtain the tensor w.r.t. which the local system is to be solved
      *
      * \param A The A matrix of the iv-local equation system
      * \param B The B matrix of the iv-local equation system
diff --git a/dumux/multidomain/facet/box/couplingmanager.hh b/dumux/multidomain/facet/box/couplingmanager.hh
index 2e998d925158d574921b8b7de652c12b1ccc3e43..33c5db7315e1f154b7b072597fd7a7e7a6d9fa4a 100644
--- a/dumux/multidomain/facet/box/couplingmanager.hh
+++ b/dumux/multidomain/facet/box/couplingmanager.hh
@@ -89,6 +89,8 @@ class FacetCouplingManager<MDTraits, CouplingMapper, bulkDomainId, lowDimDomainI
     static constexpr auto bulkGridId = CouplingMapper::template gridId<bulkDim>();
     static constexpr auto lowDimGridId = CouplingMapper::template gridId<lowDimDim>();
 
+    static constexpr bool lowDimUsesBox = FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box;
+
     /*!
      * \brief The coupling context of the bulk domain. Contains all data of the lower-
      *        dimensional domain which is required for the computation of a bulk element
@@ -291,7 +293,7 @@ public:
         const auto& idxInContext = std::distance( s.begin(), std::find(s.begin(), s.end(), lowDimElemIdx) );
         assert(std::find(s.begin(), s.end(), lowDimElemIdx) != s.end());
 
-        if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+        if (lowDimUsesBox)
             return bulkContext_.lowDimElemVolVars[idxInContext][coupledScvIdx];
         else
             return bulkContext_.lowDimElemVolVars[idxInContext][lowDimElemIdx];
@@ -302,13 +304,22 @@ public:
      */
     const Element<lowDimId> getLowDimElement(const Element<bulkId>& element,
                                              const SubControlVolumeFace<bulkId>& scvf) const
+    {
+        const auto lowDimElemIdx = getLowDimElementIndex(element, scvf);
+        return this->problem(lowDimId).fvGridGeometry().element(lowDimElemIdx);
+    }
+
+    /*!
+     * \brief returns the index of the lower-dimensional element coinciding with a bulk scvf.
+     */
+    const GridIndexType<lowDimId> getLowDimElementIndex(const Element<bulkId>& element,
+                                                        const SubControlVolumeFace<bulkId>& scvf) const
     {
         const auto eIdx = this->problem(bulkId).fvGridGeometry().elementMapper().index(element);
-        assert(bulkContext_.isSet);
-        assert(bulkElemIsCoupled_[eIdx]);
 
+        assert(bulkElemIsCoupled_[eIdx]);
         const auto& map = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
-        const auto& couplingData = map.find(eIdx)->second;
+        const auto& couplingData = map.at(eIdx);
 
         // search the low dim element idx this scvf is embedded in
         auto it = std::find_if( couplingData.elementToScvfMap.begin(),
@@ -321,8 +332,7 @@ public:
                                 } );
 
         assert(it != couplingData.elementToScvfMap.end());
-        const auto lowDimElemIdx = it->first;
-        return this->problem(lowDimId).fvGridGeometry().element(lowDimElemIdx);
+        return it->first;
     }
 
     /*!
@@ -413,7 +423,6 @@ public:
             return sources;
 
         assert(lowDimContext_.isSet);
-        const auto& bulkMap = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
         for (unsigned int i = 0; i < it->second.embedments.size(); ++i)
         {
             const auto& embedment = it->second.embedments[i];
@@ -421,8 +430,7 @@ public:
             // list of scvfs in the bulk domain whose fluxes enter this scv
             // if low dim domain uses tpfa, this is all scvfs lying on this element
             // if it uses box, it is the one scvf coinciding with the given scv
-            static constexpr bool lowDimUsesBox = FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box;
-            const auto& coincidingScvfs = bulkMap.find(embedment.first)->second.elementToScvfMap.at(lowDimContext_.elementIdx);
+            const auto& coincidingScvfs = embedment.second;
             const auto& scvfList = lowDimUsesBox ? std::vector<GridIndexType<lowDimId>>{ coincidingScvfs[scv.localDofIndex()] }
                                                  : coincidingScvfs;
 
@@ -574,7 +582,7 @@ public:
             // find the low-dim elements in coupling stencil, where this dof is contained in
             const auto couplingElements = [&] ()
             {
-                if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+                if (lowDimUsesBox)
                 {
                     std::vector< Element<lowDimId> > lowDimElems;
                     std::for_each( couplingElemStencil.begin(), couplingElemStencil.end(),
diff --git a/dumux/multidomain/facet/box/couplingmapper.hh b/dumux/multidomain/facet/box/couplingmapper.hh
index 9ccb833908dbd286b19ae0ecafa2d88e37ba2aef..a16b93359ca1d31384b4ce699f89ab40fd272762 100644
--- a/dumux/multidomain/facet/box/couplingmapper.hh
+++ b/dumux/multidomain/facet/box/couplingmapper.hh
@@ -79,9 +79,9 @@ public:
         using GridAdapter = CodimOneGridAdapter<Embeddings, bulkGridId, facetGridId>;
         update(bulkFvGridGeometry, lowDimFvGridGeometry, embeddings, GridAdapter(embeddings));
     }
+
     /*!
-     * \brief Update coupling maps. This is the standard
-     *        interface required by any mapper implementation.
+     * \brief Update coupling maps with a given grid adapter.
      *
      * \param bulkFvGridGeometry The finite-volume grid geometry of the bulk grid
      * \param lowDimFvGridGeometry The finite-volume grid geometry of the lower-dimensional grid
@@ -159,7 +159,7 @@ public:
                     if (scvf.interiorBoundary() && scvf.facetIndexInElement() == coupledFacetIndex)
                     {
                         // we want to order the set of scvfs lying on the lower-dimensional element such that the i-th scvf
-                        // coincides with the i-th low dim element corner. This will help later  to identify which scvf fluxes
+                        // coincides with the i-th low dim element corner. This will help later to identify which scvf fluxes
                         // enter which scv of the low dim element if the lower-dimensional domain uses the box scheme
                         const auto vIdxLocal = bulkRefElem.subEntity(coupledFacetIndex, 1, scvf.indexInElementFacet(), bulkDim);
                         const auto vIdxGlobal = bulkFvGridGeometry.vertexMapper().vertexIndex(bulkElement, vIdxLocal, bulkDim);
@@ -177,9 +177,9 @@ public:
 
                 // add each dof in the low dim element to coupling stencil of the bulk element
                 auto& bulkData = this->couplingMap_(bulkGridId, facetGridId)[bulkElemIdx];
-                const auto lowDimElementDofs = LowDimFVG::discMethod == DiscretizationMethod::cctpfa
-                                               ? std::vector<LowDimIndexType>({lowDimElemIdx})
-                                               : this->extractNodalDofs_(lowDimElement, lowDimFvGridGeometry);
+                const auto lowDimElementDofs = LowDimFVG::discMethod == DiscretizationMethod::box
+                                               ? this->extractNodalDofs_(lowDimElement, lowDimFvGridGeometry)
+                                               : std::vector<LowDimIndexType>({lowDimElemIdx});
 
                 for (auto lowDimDofIdx : lowDimElementDofs)
                 {
diff --git a/dumux/multidomain/facet/box/fvgridgeometry.hh b/dumux/multidomain/facet/box/fvgridgeometry.hh
index e27d643fa9df5e9d620a8bda4473fbad7060092e..c4019de51cfe952e23aa8f4c7f48e8c31941e3a7 100644
--- a/dumux/multidomain/facet/box/fvgridgeometry.hh
+++ b/dumux/multidomain/facet/box/fvgridgeometry.hh
@@ -470,7 +470,6 @@ public:
 
                 if (isOnFacet || boundary)
                 {
-                    const auto isGeometry = intersection.geometry();
                     numScvf_ += numFaceCorners;
                     numBoundaryScvf_ += int(boundary)*numFaceCorners;
 
diff --git a/dumux/multidomain/facet/cellcentered/CMakeLists.txt b/dumux/multidomain/facet/cellcentered/CMakeLists.txt
index b0122c954b922a179db1270f9bd865fe8a01bfcd..c0e2edd755ec49c07feccbe3ff8ddad04ce9d78a 100644
--- a/dumux/multidomain/facet/cellcentered/CMakeLists.txt
+++ b/dumux/multidomain/facet/cellcentered/CMakeLists.txt
@@ -1,3 +1,4 @@
+add_subdirectory(mpfa)
 add_subdirectory(tpfa)
 
 install(FILES
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/CMakeLists.txt b/dumux/multidomain/facet/cellcentered/mpfa/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..29c2e60f59bc48e54df105bbc4d276973e9ac8f8
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/CMakeLists.txt
@@ -0,0 +1,8 @@
+install(FILES
+couplingmanager.hh
+couplingmapper.hh
+interactionvolume.hh
+localassembler.hh
+localsubcontrolentities.hh
+properties.hh
+DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/multidomain/facet/cellcentered/mpfa)
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/couplingmanager.hh b/dumux/multidomain/facet/cellcentered/mpfa/couplingmanager.hh
new file mode 100644
index 0000000000000000000000000000000000000000..b894a758b7bb9a5720e4814ea329ccbcf8a1edaf
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/couplingmanager.hh
@@ -0,0 +1,454 @@
+// -*- 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 FacetCoupling
+ * \copydoc Dumux::FacetCouplingManager
+ */
+#ifndef DUMUX_CCMPFA_FACETCOUPLING_MANAGER_HH
+#define DUMUX_CCMPFA_FACETCOUPLING_MANAGER_HH
+
+#include <algorithm>
+#include <cassert>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/indextraits.hh>
+#include <dumux/common/numericdifferentiation.hh>
+#include <dumux/assembly/numericepsilon.hh>
+
+#include <dumux/discretization/method.hh>
+#include <dumux/discretization/elementsolution.hh>
+#include <dumux/multidomain/couplingmanager.hh>
+#include <dumux/multidomain/facet/cellcentered/tpfa/couplingmanager.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief Manages the coupling between bulk elements and lower dimensional elements
+ *        where the coupling occurs across the facets of the bulk grid. This implementation
+ *        is to be used in conjunction with models using the cell-centered mpfa scheme.
+ *
+ * \tparam MDTraits The multidomain traits containing the types on all sub-domains
+ * \tparam CouplingMapper Class containing maps on the coupling between dofs of different grids
+ * \tparam bulkDomainId The domain id of the bulk problem
+ * \tparam lowDimDomainId The domain id of the lower-dimensional problem
+ */
+template<class MDTraits, class CouplingMapper, std::size_t bulkDomainId, std::size_t lowDimDomainId>
+class FacetCouplingManager<MDTraits, CouplingMapper, bulkDomainId, lowDimDomainId, DiscretizationMethod::ccmpfa>
+: public FacetCouplingManager<MDTraits, CouplingMapper, bulkDomainId, lowDimDomainId, DiscretizationMethod::cctpfa>
+{
+    using ParentType = FacetCouplingManager<MDTraits, CouplingMapper, bulkDomainId, lowDimDomainId, DiscretizationMethod::cctpfa>;
+
+    // domain id instances
+    using BulkIdType = typename MDTraits::template SubDomain<bulkDomainId>::Index;
+    using LowDimIdType = typename MDTraits::template SubDomain<lowDimDomainId>::Index;
+    static constexpr auto bulkId = BulkIdType();
+    static constexpr auto lowDimId = LowDimIdType();
+
+    // the sub-domain type tags
+    template<std::size_t id> using SubDomainTypeTag = typename MDTraits::template SubDomain<id>::TypeTag;
+
+    // further types specific to the sub-problems
+    template<std::size_t id> using Scalar = GetPropType<SubDomainTypeTag<id>, Properties::Scalar>;
+    template<std::size_t id> using Problem = GetPropType<SubDomainTypeTag<id>, Properties::Problem>;
+    template<std::size_t id> using NumEqVector = GetPropType<SubDomainTypeTag<id>, Properties::NumEqVector>;
+    template<std::size_t id> using FVGridGeometry = GetPropType<SubDomainTypeTag<id>, Properties::FVGridGeometry>;
+    template<std::size_t id> using FVElementGeometry = typename FVGridGeometry<id>::LocalView;
+    template<std::size_t id> using SubControlVolume = typename FVGridGeometry<id>::SubControlVolume;
+    template<std::size_t id> using SubControlVolumeFace = typename FVGridGeometry<id>::SubControlVolumeFace;
+    template<std::size_t id> using GridView = typename FVGridGeometry<id>::GridView;
+    template<std::size_t id> using GridIndexType = typename IndexTraits< GridView<id> >::GridIndex;
+    template<std::size_t id> using Element = typename GridView<id>::template Codim<0>::Entity;
+    template<std::size_t id> using LocalResidual = GetPropType<SubDomainTypeTag<id>, Properties::LocalResidual>;
+
+    template<std::size_t id> using GridVariables = GetPropType<SubDomainTypeTag<id>, Properties::GridVariables>;
+    template<std::size_t id> using GridVolumeVariables = typename GridVariables<id>::GridVolumeVariables;
+    template<std::size_t id> using ElementVolumeVariables = typename GridVolumeVariables<id>::LocalView;
+
+    // grid ids
+    static constexpr int bulkDim = GridView<bulkDomainId>::dimension;
+    static constexpr int lowDimDim = GridView<lowDimDomainId>::dimension;
+    static constexpr auto bulkGridId = CouplingMapper::template gridId<bulkDim>();
+    static constexpr auto lowDimGridId = CouplingMapper::template gridId<lowDimDim>();
+
+    static constexpr bool lowDimUsesBox = FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box;
+
+public:
+
+    //! the type of the solution vector
+    using SolutionVector = typename MDTraits::SolutionVector;
+
+    /*!
+     * \brief Initialize the coupling manager.
+     *
+     * \param bulkProblem The problem to be solved on the bulk domain
+     * \param lowDimProblem The problem to be solved on the lower-dimensional domain
+     * \param couplingMapper The mapper object containing the connectivity between the domains
+     * \param curSol The current solution
+     */
+    void init(std::shared_ptr< Problem<bulkId> > bulkProblem,
+              std::shared_ptr< Problem<lowDimId> > lowDimProblem,
+              std::shared_ptr< CouplingMapper > couplingMapper,
+              const SolutionVector& curSol)
+    {
+        // Initialize the parent class
+        ParentType::init(bulkProblem, lowDimProblem, couplingMapper, curSol);
+
+        // determine all bulk scvfs that coincide with low dim elements
+        bulkScvfIsOnFacetElement_.resize(bulkProblem->fvGridGeometry().numScvf(), false);
+        const auto& bulkMap = couplingMapper->couplingMap(bulkGridId, lowDimGridId);
+        for (const auto& entry : bulkMap)
+            for (const auto& couplingEntry : entry.second.elementToScvfMap)
+                for (const auto& scvfIdx : couplingEntry.second)
+                    bulkScvfIsOnFacetElement_[scvfIdx] = true;
+
+        // store pointer to mapper
+        couplingMapperPtr_ = couplingMapper;
+    }
+
+    /*!
+     * \brief returns true if a bulk scvf coincides with a facet element.
+     */
+    bool isOnInteriorBoundary(const Element<bulkId>& element,
+                              const SubControlVolumeFace<bulkId>& scvf) const
+    { return bulkScvfIsOnFacetElement_[scvf.index()]; }
+
+    /*!
+     * \brief returns the tensor within the low dim element coinciding with
+     *        the given bulk scvf according to the provided lambda to obtain
+     *        the tensor.
+     *
+     * \tparam TensorFunc lambda to obtain a tensorial or scalar spatial parameter.
+     */
+    template<class TensorFunc>
+    auto getLowDimTensor(const Element<bulkId>& element,
+                         const SubControlVolumeFace<bulkId>& scvf,
+                         const TensorFunc& getT) const
+    {
+        const auto lowDimElemIdx = this->getLowDimElementIndex(element, scvf);
+
+        const auto& map = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
+        const auto& s = map.find(this->bulkCouplingContext().elementIdx)->second.couplingElementStencil;
+        const auto& idxInContext = std::distance( s.begin(), std::find(s.begin(), s.end(), lowDimElemIdx) );
+        assert(std::find(s.begin(), s.end(), lowDimElemIdx) != s.end());
+
+        const auto& lowDimProblem = this->problem(lowDimId);
+        const auto& lowDimElement = lowDimProblem.fvGridGeometry().element(lowDimElemIdx);
+        const auto& lowDimVolVars = this->bulkCouplingContext().lowDimVolVars[idxInContext];
+        const auto& lowDimFvGeometry = this->bulkCouplingContext().lowDimFvGeometries[idxInContext];
+
+        // we assume constant parameters on the element and use the first scv within the low dim element.
+        return getT(lowDimProblem, lowDimElement, lowDimVolVars, lowDimFvGeometry, *scvs(lowDimFvGeometry).begin());
+    }
+
+    using ParentType::evalCouplingResidual;
+    /*!
+     * \brief Evaluates the coupling element residual of a lower-dimensional domain element
+     *        with respect to a dof in the bulk domain (dofIdxGlobalJ). This is essentially
+     *        the fluxes across the facets of the neighboring bulk elements.
+     * \note  The coupling residual is independent of w.r.t. which bulk dof it is computed
+     */
+    template< class LowDimLocalAssembler >
+    typename LocalResidual<lowDimId>::ElementResidualVector
+    evalCouplingResidual(LowDimIdType,
+                         const LowDimLocalAssembler& lowDimLocalAssembler,
+                         BulkIdType,
+                         GridIndexType<bulkId> dofIdxGlobalJ)
+    { return evalCouplingResidual(lowDimId, lowDimLocalAssembler, bulkId); }
+
+    /*!
+     * \brief Evaluates the coupling element residual of a lower-dimensional domain element
+     *        with respect to a dof in the bulk domain (dofIdxGlobalJ). This is essentially
+     *        the fluxes across the facets of the neighboring bulk elements.
+     */
+    template< class LowDimLocalAssembler >
+    typename LocalResidual<lowDimId>::ElementResidualVector
+    evalCouplingResidual(LowDimIdType, const LowDimLocalAssembler& lowDimLocalAssembler, BulkIdType)
+    {
+        // make sure this is called for the element for which the context was set
+        assert(this->lowDimCouplingContext().isSet);
+        assert(this->problem(lowDimId).fvGridGeometry().elementMapper().index(lowDimLocalAssembler.element()) == this->lowDimCouplingContext().elementIdx);
+
+        // fill element residual vector with the sources
+        typename LowDimLocalAssembler::LocalResidual::ElementResidualVector res(lowDimLocalAssembler.fvGeometry().numScv());
+        res = 0.0;
+        for (const auto& scv : scvs(lowDimLocalAssembler.fvGeometry()))
+             res[scv.localDofIndex()] -= evalSourcesFromBulk(lowDimLocalAssembler.element(),
+                                                             lowDimLocalAssembler.fvGeometry(),
+                                                             lowDimLocalAssembler.curElemVolVars(),
+                                                             scv);
+        return res;
+    }
+
+    /*!
+     * \brief Computes the sources in a lower-dimensional sub-control volume stemming from the bulk domain.
+     */
+    NumEqVector<lowDimId> evalSourcesFromBulk(const Element<lowDimId>& element,
+                                              const FVElementGeometry<lowDimId>& fvGeometry,
+                                              const ElementVolumeVariables<lowDimId>& elemVolVars,
+                                              const SubControlVolume<lowDimId>& scv)
+    {
+        // make sure the this is called for the element of the context
+        assert(this->problem(lowDimId).fvGridGeometry().elementMapper().index(element) == this->lowDimCouplingContext().elementIdx);
+
+        NumEqVector<lowDimId> sources(0.0);
+
+        const auto& map = couplingMapperPtr_->couplingMap(lowDimGridId, bulkGridId);
+        auto it = map.find(this->lowDimCouplingContext().elementIdx);
+        if (it == map.end())
+            return sources;
+
+        assert(this->lowDimCouplingContext().isSet);
+        for (const auto& embedment : it->second.embedments)
+        {
+            // list of scvfs in the bulk domain whose fluxes enter this scv
+            // if low dim domain uses a cc scheme, this is all scvfs lying on this element
+            // if it uses box, it is the one scvf coinciding with the given scv
+            const auto& coincidingScvfs = embedment.second;
+            const auto& scvfList = lowDimUsesBox ? std::vector<GridIndexType<lowDimId>>{ coincidingScvfs[scv.localDofIndex()] }
+                                                 : coincidingScvfs;
+
+            sources += this->evalBulkFluxes(this->problem(bulkId).fvGridGeometry().element(embedment.first),
+                                            *this->lowDimCouplingContext().bulkFvGeometry,
+                                            *this->lowDimCouplingContext().bulkElemVolVars,
+                                            *this->lowDimCouplingContext().bulkElemFluxVarsCache,
+                                            *this->lowDimCouplingContext().bulkLocalResidual,
+                                            scvfList);
+        }
+
+        return sources;
+    }
+
+    /*!
+     * \brief Extend the jacobian pattern of the diagonal block of the lowdim domain
+     *        by the elements that are in the coupling stencil of the neighboring bulk elements
+     */
+    template<class JacobianPattern>
+    void extendJacobianPattern(LowDimIdType, JacobianPattern& pattern) const
+    {
+        const auto& lowDimFVGridGeometry = this->problem(lowDimId).fvGridGeometry();
+        for (const auto& element : elements(lowDimFVGridGeometry.gridView()))
+        {
+
+            const auto eIdx = lowDimFVGridGeometry.elementMapper().index(element);
+            const auto& map = couplingMapperPtr_->couplingMap(lowDimGridId, bulkGridId);
+            auto it = map.find(eIdx);
+
+            // if element is coupled, take one of the neighbors and add coupling stencil to pattern
+            if (it != map.end())
+            {
+                // coupling stencil of the first neighbor
+                const auto bulkElemIdx = it->second.embedments[0].first;
+                const auto& bulkMapEntry = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId).at(bulkElemIdx);
+                const auto& couplingStencil = bulkMapEntry.couplingStencil;
+
+                for (auto globalJ : couplingStencil)
+                {
+                    if (lowDimUsesBox)
+                    {
+                        for (int i = 0; i < element.subEntities(lowDimDim); ++i)
+                            pattern.add(lowDimFVGridGeometry.vertexMapper().subIndex(element, i, lowDimDim), globalJ);
+                    }
+                    else
+                        pattern.add(eIdx, globalJ);
+                }
+            }
+        }
+    }
+
+    //! The bulk domain has no extended jacobian pattern
+    template<class JacobianPattern>
+    void extendJacobianPattern(BulkIdType, JacobianPattern& pattern) const
+    {}
+
+    /*!
+     * \brief evaluate additional derivatives of the element residual of the low-dim domain with respect
+     *        to dofs in the same domain that are not in the regular stencil (see extendJacobianPattern)
+     * \note Here, this is the change of the source term with respect to changes in the variables of the
+     *       other elements in the coupling stencil of the neighboring bulk elements.
+     */
+    template<class LowDimLocalAssembler, class JacobianMatrixDiagBlock, class GridVariables>
+    void evalAdditionalDomainDerivatives(LowDimIdType,
+                                         const LowDimLocalAssembler& lowDimLocalAssembler,
+                                         const typename LowDimLocalAssembler::LocalResidual::ElementResidualVector&,
+                                         JacobianMatrixDiagBlock& A,
+                                         GridVariables& gridVariables)
+    {
+        // Since coupling only occurs via the fluxes, there are no
+        // additional derivatives for explicit time integration schemes
+        if (!LowDimLocalAssembler::isImplicit())
+            return;
+
+        // lambda to update the coupling context for a given lowDim element/dofIdx
+        auto updateContext = [&] (auto elemIdx, auto dofIdx, auto priVars, auto pvIdx)
+        {
+            // deflect the solution
+            auto& ldSol = this->curSol()[lowDimId];
+            ldSol[dofIdx][pvIdx] = priVars[pvIdx];
+
+            // update the corresponding vol vars in the bulk context
+            assert(this->bulkCouplingContext().isSet);
+            const auto& bulkMap = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
+            const auto& couplingElementStencil = bulkMap.find(this->bulkCouplingContext().elementIdx)->second.couplingElementStencil;
+
+            auto it = std::find(couplingElementStencil.begin(), couplingElementStencil.end(), elemIdx);
+            assert(it != couplingElementStencil.end());
+            const auto idxInContext = std::distance(couplingElementStencil.begin(), it);
+
+            auto& volVars = this->bulkCouplingContext().lowDimVolVars[idxInContext];
+            const auto& fvGeom = this->bulkCouplingContext().lowDimFvGeometries[idxInContext];
+            const auto& element = this->problem(lowDimId).fvGridGeometry().element(elemIdx);
+
+            // if low dim domain uses the box scheme, we have to create interpolated vol vars
+            if (lowDimUsesBox)
+            {
+                const auto elemGeom = element.geometry();
+                FacetCoupling::makeInterpolatedVolVars(volVars, this->problem(lowDimId), ldSol, fvGeom, element, elemGeom, elemGeom.center());
+            }
+            // if low dim domain uses a cc scheme we can directly update the vol vars
+            else
+                volVars.update( elementSolution(element, ldSol, this->problem(lowDimId).fvGridGeometry()),
+                                this->problem(lowDimId),
+                                element,
+                                fvGeom.scv(this->lowDimCouplingContext().elementIdx) );
+
+            // update the element flux variables cache (tij depend on low dim values in context)
+            const auto contextElem = this->problem(bulkId).fvGridGeometry().element(this->bulkCouplingContext().elementIdx);
+            this->lowDimCouplingContext().bulkElemFluxVarsCache->update(contextElem,
+                                                                        *this->lowDimCouplingContext().bulkFvGeometry,
+                                                                        *this->lowDimCouplingContext().bulkElemVolVars);
+        };
+
+        const auto eIdx = this->problem(lowDimId).fvGridGeometry().elementMapper().index(lowDimLocalAssembler.element());
+
+        // bug tracking
+        assert(this->lowDimCouplingContext().isSet);
+        assert(this->lowDimCouplingContext().elementIdx == eIdx);
+
+        // if the element is coupled, evaluate additional source derivatives
+        const auto& map = couplingMapperPtr_->couplingMap(lowDimGridId, bulkGridId);
+        auto it = map.find(eIdx);
+        if (it != map.end())
+            evalLowDimSourceDerivatives_(updateContext, lowDimLocalAssembler, A);
+    }
+
+    //! The bulk domain has no additional derivatives
+    template<class LocalAssemblerI, class JacobianMatrixDiagBlock, class GridVariables>
+    void evalAdditionalDomainDerivatives(BulkIdType,
+                                         const LocalAssemblerI& localAssemblerI,
+                                         const typename LocalAssemblerI::LocalResidual::ElementResidualVector& origResiduals,
+                                         JacobianMatrixDiagBlock& A,
+                                         GridVariables& gridVariables)
+    {}
+
+private:
+    //! evaluates the additional source derivatives w.r.t. to neighboring elements
+    template<class UpdateContext, class LowDimLocalAssembler, class JacobianMatrixDiagBlock>
+    void evalLowDimSourceDerivatives_(const UpdateContext& updateContext,
+                                      const LowDimLocalAssembler& lowDimLocalAssembler,
+                                      JacobianMatrixDiagBlock& A)
+    {
+        const auto& lowDimFVGridGeometry = this->problem(lowDimId).fvGridGeometry();
+        const auto eIdx = lowDimFVGridGeometry.elementMapper().index(lowDimLocalAssembler.element());
+
+        // coupling stencil of the first neighbor
+        const auto bulkElemIdx = this->bulkCouplingContext().elementIdx;
+        const auto& bulkMapEntry = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId).at(bulkElemIdx);
+        const auto& couplingStencil = bulkMapEntry.couplingStencil;
+        const auto& couplingElementStencil = bulkMapEntry.couplingElementStencil;
+
+        // compute the undeflected residual (reuse coupling residual function)
+        const auto origResidual = evalCouplingResidual(lowDimId, lowDimLocalAssembler, bulkId);
+
+        // container of dofs within this element
+        std::vector< std::decay_t<decltype(couplingStencil[0])> > elemDofs;
+        elemDofs.reserve(lowDimLocalAssembler.fvGeometry().numScv());
+        for (const auto& scv : scvs(lowDimLocalAssembler.fvGeometry()))
+            elemDofs.push_back(scv.dofIndex());
+
+        // compute derivate for all additional dofs in the stencil
+        for (const auto couplingElemIdx : couplingElementStencil)
+        {
+            // skip the same element
+            if (couplingElemIdx == eIdx)
+                continue;
+
+            // container of dofs within the other element
+            std::vector< std::decay_t<decltype(couplingStencil[0])> > elemDofsJ;
+            if (lowDimUsesBox)
+            {
+                const auto& elemJ = lowDimFVGridGeometry.element(couplingElemIdx);
+                for (int i = 0; i < elemJ.subEntities(lowDimDim); ++i)
+                    elemDofsJ.push_back(lowDimFVGridGeometry.vertexMapper().subIndex(elemJ, i, lowDimDim));
+            }
+            else
+                elemDofsJ.push_back(couplingElemIdx);
+
+            for (auto dofIndex : elemDofsJ)
+            {
+                auto partialDerivs = origResidual;
+                const auto origPriVars = this->curSol()[lowDimId][dofIndex];
+
+                // calculate derivatives w.r.t to the privars at the dof at hand
+                static constexpr auto numEq = std::decay_t<decltype(origPriVars)>::dimension;
+                for (int pvIdx = 0; pvIdx < numEq; pvIdx++)
+                {
+                    // reset partial derivatives
+                    partialDerivs = 0.0;
+
+                    auto evalResiduals = [&](Scalar<lowDimId> priVar)
+                    {
+                        auto priVars = origPriVars;
+                        priVars[pvIdx] = priVar;
+
+                        // Update context to deflected solution and reevaluate residual
+                        updateContext(couplingElemIdx, dofIndex, priVars, pvIdx);
+                        return this->evalCouplingResidual(lowDimId, lowDimLocalAssembler, bulkId);
+                    };
+
+                    static const int numDiffMethod = getParamFromGroup<int>(this->problem(lowDimId).paramGroup(), "Assembly.NumericDifferenceMethod");
+                    static const NumericEpsilon< Scalar<lowDimId>, numEq > eps{this->problem(lowDimId).paramGroup()};
+                    NumericDifferentiation::partialDerivative(evalResiduals, origPriVars[pvIdx], partialDerivs,
+                                                              origResidual, eps(origPriVars, pvIdx), numDiffMethod);
+
+                    // update the global stiffness matrix with the current partial derivatives
+                    // A[i][col][eqIdx][pvIdx] is the rate of change of the residual of equation
+                    // 'eqIdx' at dof 'i' depending on the primary variable 'pvIdx' at dof 'col'.
+                    for (const auto& scv : scvs(lowDimLocalAssembler.fvGeometry()))
+                        for (int eqIdx = 0; eqIdx < numEq; eqIdx++)
+                            A[scv.dofIndex()][dofIndex][eqIdx][pvIdx] += partialDerivs[scv.indexInElement()][eqIdx];
+
+                    // restore the original coupling context
+                    updateContext(couplingElemIdx, dofIndex, origPriVars, pvIdx);
+                }
+            }
+        }
+    }
+
+    //! store which scvfs coincide with facet element
+    std::vector<bool> bulkScvfIsOnFacetElement_;
+
+    //! store shared_ptr to coupling mapper
+    std::shared_ptr< CouplingMapper > couplingMapperPtr_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/couplingmapper.hh b/dumux/multidomain/facet/cellcentered/mpfa/couplingmapper.hh
new file mode 100644
index 0000000000000000000000000000000000000000..8905592da9b621e6245773ce346c74e67e8a3aab
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/couplingmapper.hh
@@ -0,0 +1,261 @@
+/*****************************************************************************
+ *   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 FacetCoupling
+ * \copydoc Dumux::FacetCouplingMapper
+ */
+#ifndef DUMUX_CCMPFA_FACETCOUPLING_MAPPER_HH
+#define DUMUX_CCMPFA_FACETCOUPLING_MAPPER_HH
+
+#include <dune/common/indices.hh>
+#include <dune/common/float_cmp.hh>
+
+#include <dumux/common/indextraits.hh>
+#include <dumux/discretization/method.hh>
+#include <dumux/multidomain/facet/couplingmapper.hh>
+#include <dumux/multidomain/facet/couplingmapperbase.hh>
+#include <dumux/multidomain/facet/codimonegridadapter.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief Base class for the coupling mapper that sets up and stores
+ *        the coupling maps between two domains of dimension d and (d-1).
+ *        This specialization is for the bulk domain using the cell-centered
+ *        scheme with multi-point flux approximation.
+ *
+ * \tparam BulkFVG The d-dimensional finite-volume grid geometry
+ * \tparam LowDimFVG The (d-1)-dimensional finite-volume grid geometry
+ * \tparam bulkId The index of the bulk grid within the hierarchy of grids
+ * \tparam lowDimId The index of the facet grid within the hierarchy of grids
+ */
+template<class BulkFVG, class LowDimFVG, std::size_t bulkId, std::size_t lowDimId>
+class FacetCouplingMapper<BulkFVG, LowDimFVG, bulkId, lowDimId, DiscretizationMethod::ccmpfa>
+: public virtual FacetCouplingMapperBase<BulkFVG, LowDimFVG, bulkId, lowDimId>
+{
+    using ParentType = FacetCouplingMapperBase<BulkFVG, LowDimFVG, bulkId, lowDimId>;
+
+    using BulkFVElementGeometry = typename BulkFVG::LocalView;
+    using BulkSubControlVolumeFace = typename BulkFVG::SubControlVolumeFace;
+
+    using BulkIndexType = typename IndexTraits<typename BulkFVG::GridView>::GridIndex;
+    using LowDimIndexType = typename IndexTraits<typename LowDimFVG::GridView>::GridIndex;
+
+    using LowDimElement = typename LowDimFVG::GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename LowDimElement::Geometry::GlobalCoordinate;
+    static constexpr int lowDimDim = LowDimFVG::GridView::dimension;
+
+public:
+    //! export domain ids
+    using ParentType::bulkGridId;
+    using ParentType::facetGridId;
+
+    /*!
+     * \brief Update coupling maps. This is the standard
+     *        interface required by any mapper implementation.
+     *
+     * \param bulkFvGridGeometry The finite-volume grid geometry of the bulk grid
+     * \param lowDimFvGridGeometry The finite-volume grid geometry of the lower-dimensional grid
+     * \param embeddings Class that contains the embedments among the grids and entity insertion indices
+     */
+    template< class Embeddings >
+    void update(const BulkFVG& bulkFvGridGeometry,
+                const LowDimFVG& lowDimFvGridGeometry,
+                std::shared_ptr<const Embeddings> embeddings)
+    {
+        // forward to update function with instantiated vertex adapter
+        using GridAdapter = CodimOneGridAdapter<Embeddings, bulkGridId, facetGridId>;
+        update(bulkFvGridGeometry, lowDimFvGridGeometry, embeddings, GridAdapter(embeddings));
+    }
+
+    /*!
+     * \brief Update coupling maps. This is the standard
+     *        interface required by any mapper implementation.
+     *
+     * \param bulkFvGridGeometry The finite-volume grid geometry of the bulk grid
+     * \param lowDimFvGridGeometry The finite-volume grid geometry of the lower-dimensional grid
+     * \param embeddings Class that contains the embedments among the grids and entity insertion indices
+     * \param codimOneGridAdapter Allows direct access to data on the bulk grid for lowdim grid entities
+     */
+    template< class Embeddings, class CodimOneGridAdapter >
+    void update(const BulkFVG& bulkFvGridGeometry,
+                const LowDimFVG& lowDimFvGridGeometry,
+                std::shared_ptr<const Embeddings> embeddings,
+                const CodimOneGridAdapter& codimOneGridAdapter)
+    {
+        // define the policy how to add map entries for given lowdim element and adjoined entity indices
+        auto addCouplingEntryPolicy = [&] (auto&& adjoinedEntityIndices,
+                                           const LowDimElement& lowDimElement,
+                                           const LowDimFVG& lowDimFvGridGeometry,
+                                           const BulkFVG& bulkFvGridGeometry)
+        {
+            const auto lowDimElemIdx = lowDimFvGridGeometry.elementMapper().index(lowDimElement);
+            auto& lowDimData = this->couplingMap_(facetGridId, bulkGridId)[lowDimElemIdx];
+
+            // determine corner indices (in bulk grid indices)
+            const auto& lowDimGeometry = lowDimElement.geometry();
+            const auto numElementCorners = lowDimElement.subEntities(lowDimDim);
+            std::vector<BulkIndexType> elemCornerIndices(numElementCorners);
+            for (int i = 0; i < numElementCorners; ++i)
+                elemCornerIndices[i] = codimOneGridAdapter.bulkGridVertexIndex(lowDimElement.template subEntity<lowDimDim>(i));
+
+            // Find the scvfs in the adjoined entities coinciding with the low dim element
+            for (auto bulkElemIdx : adjoinedEntityIndices)
+            {
+                const auto bulkElement = bulkFvGridGeometry.element(bulkElemIdx);
+
+                auto fvGeometry = localView(bulkFvGridGeometry);
+                fvGeometry.bind(bulkElement);
+
+                std::vector<BulkIndexType> embeddedScvfIndices;
+                for (const auto& scvf : scvfs(fvGeometry))
+                {
+                    // for non-boundary faces, it suffices to check if one
+                    // of the outside scv indices is in the set of embedments
+                    if (!scvf.boundary())
+                    {
+                        if ( std::count(adjoinedEntityIndices.begin(), adjoinedEntityIndices.end(), scvf.outsideScvIdx()) )
+                            embeddedScvfIndices.push_back(scvf.index());
+                    }
+
+                    // otherwise, do float comparison of element and scvf facet corner
+                    else
+                    {
+                        const auto eps = lowDimGeometry.volume()*1e-8;
+                        const auto diffVec = lowDimGeometry.center()-scvf.facetCorner();
+
+                        if ( Dune::FloatCmp::eq<GlobalPosition, Dune::FloatCmp::CmpStyle::absolute>(diffVec, GlobalPosition(0.0), eps) )
+                            embeddedScvfIndices.push_back(scvf.index());
+                    }
+                }
+
+                // Error tracking. The boundary scvf detection might has to be improved for very fine grids!?
+                if ( embeddedScvfIndices.size() != numElementCorners )
+                    DUNE_THROW(Dune::InvalidStateException, "Could not find all coupling scvfs in embedment");
+
+                // add each dof in the low dim element to coupling stencil of the bulk element and vice versa
+                auto& bulkData = this->couplingMap_(bulkGridId, facetGridId)[bulkElemIdx];
+                const auto lowDimElementDofs = LowDimFVG::discMethod == DiscretizationMethod::box
+                                               ? this->extractNodalDofs_(lowDimElement, lowDimFvGridGeometry)
+                                               : std::vector<LowDimIndexType>( {lowDimElemIdx} );
+
+                // add coupling info to all elements/scvfs in interaction volumes
+                for (auto dofIdx : lowDimElementDofs)
+                    for (auto scvfIdx : embeddedScvfIndices)
+                        this->addCouplingsFromIV_(bulkFvGridGeometry, fvGeometry.scvf(scvfIdx), fvGeometry, lowDimElemIdx, dofIdx);
+
+                // sort the scvfs according to the corners of the low dim element if box is used
+                // that allows identifying which scvf flux enters which low dim scv later
+                if (LowDimFVG::discMethod == DiscretizationMethod::box)
+                {
+                    const auto copy = embeddedScvfIndices;
+
+                    for (unsigned int i = 0; i < numElementCorners; ++i)
+                    {
+                        const auto& scvf = fvGeometry.scvf(copy[i]);
+                        auto it = std::find(elemCornerIndices.begin(), elemCornerIndices.end(), scvf.vertexIndex());
+                        assert(it != elemCornerIndices.end());
+                        embeddedScvfIndices[ std::distance(elemCornerIndices.begin(), it) ] = copy[i];
+                    }
+                }
+
+                // add info on which scvfs coincide with which low dim element
+                auto& elemToScvfMap = bulkData.elementToScvfMap[lowDimElemIdx];
+                elemToScvfMap.insert(elemToScvfMap.end(), embeddedScvfIndices.begin(), embeddedScvfIndices.end());
+
+                // add embedment
+                lowDimData.embedments.emplace_back( bulkElemIdx, std::move(embeddedScvfIndices) );
+            }
+        };
+
+        // let the parent do the update subject to the execution policy defined above
+        ParentType::update_(bulkFvGridGeometry, lowDimFvGridGeometry, embeddings, addCouplingEntryPolicy);
+
+        // lambda to make a container unique
+        auto makeUnique = [] (auto& c)
+        {
+            std::sort(c.begin(), c.end());
+            c.erase( std::unique(c.begin(), c.end()), c.end() );
+        };
+
+        // lambda to make bulk coupling map entry unique
+        auto makeBulkMapEntryUnique = [&makeUnique] (auto& data)
+        {
+            makeUnique(data.second.couplingStencil);
+            makeUnique(data.second.couplingElementStencil);
+            std::for_each(data.second.dofToCouplingScvfMap.begin(),
+                          data.second.dofToCouplingScvfMap.end(),
+                          [&makeUnique] (auto& pair) { makeUnique(pair.second); });
+        };
+
+        // make bulk map unique
+        auto& bulkCouplingData = this->couplingMap_(bulkGridId, facetGridId);
+        std::for_each(bulkCouplingData.begin(), bulkCouplingData.end(), makeBulkMapEntryUnique);
+
+        // coupling stencils might not be unique in lowdim domain
+        auto& lowDimCouplingData = this->couplingMap_(facetGridId, bulkGridId);
+        std::for_each(lowDimCouplingData.begin(),
+                      lowDimCouplingData.end(),
+                      [&makeUnique] (auto& pair) { makeUnique(pair.second.couplingStencil); });
+    }
+
+private:
+    void addCouplingsFromIV_(const BulkFVG& bulkFvGridGeometry,
+                             const BulkSubControlVolumeFace& scvf,
+                             const BulkFVElementGeometry& fvGeometry,
+                             LowDimIndexType lowDimElemIdx,
+                             LowDimIndexType lowDimDofIdx)
+    {
+        const auto& gridIvIndexSets = bulkFvGridGeometry.gridInteractionVolumeIndexSets();
+        if (bulkFvGridGeometry.vertexUsesSecondaryInteractionVolume(scvf.vertexIndex()))
+            addCouplingsFromIVIndexSet_(gridIvIndexSets.secondaryIndexSet(scvf), fvGeometry, lowDimElemIdx, lowDimDofIdx);
+        else
+            addCouplingsFromIVIndexSet_(gridIvIndexSets.primaryIndexSet(scvf), fvGeometry, lowDimElemIdx, lowDimDofIdx);
+    }
+
+    template< class IVIndexSet >
+    void addCouplingsFromIVIndexSet_(const IVIndexSet& indexSet,
+                                     const BulkFVElementGeometry& fvGeometry,
+                                     LowDimIndexType lowDimElemIdx,
+                                     LowDimIndexType lowDimDofIdx)
+    {
+        auto& lowDimData = this->couplingMap_(facetGridId, bulkGridId)[lowDimElemIdx];
+        for (auto bulkElemIdx : indexSet.gridScvIndices())
+        {
+            auto& bulkData = this->couplingMap_(bulkGridId, facetGridId)[bulkElemIdx];
+
+            lowDimData.couplingStencil.push_back( bulkElemIdx );
+            bulkData.couplingStencil.push_back( lowDimDofIdx );
+            bulkData.couplingElementStencil.push_back( lowDimElemIdx );
+        }
+
+        // insert scvf couplings stemming from this interaction volume
+        for (auto scvfIdx : indexSet.gridScvfIndices())
+        {
+            const auto& scvf = fvGeometry.scvf(scvfIdx);
+            auto& bulkData = this->couplingMap_(bulkGridId, facetGridId)[scvf.insideScvIdx()];
+            auto& couplingScvfs = bulkData.dofToCouplingScvfMap[lowDimDofIdx];
+            couplingScvfs.insert(couplingScvfs.end(), scvfIdx);
+        }
+    }
+};
+
+} // end namespace Dumux
+
+#endif // DUMUX_FACETCOUPLING_CCMPFA_COUPLING_MAPPER_HH
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/interactionvolume.hh b/dumux/multidomain/facet/cellcentered/mpfa/interactionvolume.hh
new file mode 100644
index 0000000000000000000000000000000000000000..fbe84ad76f9101d0f77a2dcfb80623afdee43af2
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/interactionvolume.hh
@@ -0,0 +1,365 @@
+// -*- 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 FacetCoupling
+ * \copydoc Dumux::CCMpfaOFacetCouplingInteractionVolume
+ */
+#ifndef DUMUX_MULTIDOMAIN_FACET_CC_MPFA_O_INTERACTIONVOLUME_HH
+#define DUMUX_MULTIDOMAIN_FACET_CC_MPFA_O_INTERACTIONVOLUME_HH
+
+#include <dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh>
+#include <dumux/discretization/cellcentered/mpfa/omethod/scvgeometryhelper.hh>
+#include <dumux/discretization/cellcentered/mpfa/interactionvolumebase.hh>
+#include <dumux/discretization/cellcentered/mpfa/localfacedata.hh>
+#include <dumux/discretization/cellcentered/mpfa/methods.hh>
+
+#include "localassembler.hh"
+#include "localsubcontrolentities.hh"
+
+namespace Dumux {
+
+//! Forward declaration of the facet coupling MPFA-O interaction volume
+template< class Traits > class CCMpfaOFacetCouplingInteractionVolume;
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief The default interaction volume traits class for the mpfa-o method
+ *        in the context of facet coupling. This uses dynamic types types for
+ *        matrices/vectors in order to work on general grids.
+ *
+ * \tparam NodalIndexSet The type used for the dual grid's nodal index sets
+ * \tparam Scalar The Type used for scalar values
+ */
+template< class NodalIndexSet, class Scalar >
+struct CCMpfaOFacetCouplingDefaultInteractionVolumeTraits
+: public CCMpfaODefaultInteractionVolumeTraits< NodalIndexSet, Scalar >
+{
+private:
+    //! export the type for the interaction volume index set
+    using IVIndexSet = CCMpfaOInteractionVolumeIndexSet< NodalIndexSet >;
+
+    static constexpr int dim = NodalIndexSet::Traits::GridView::dimension;
+    static constexpr int dimWorld = NodalIndexSet::Traits::GridView::dimensionworld;
+
+public:
+    //! export the type of interaction-volume local scvs
+    using LocalScvType = CCMpfaOFacetCouplingInteractionVolumeLocalScv< IVIndexSet, Scalar, dim, dimWorld >;
+    //! export the type of interaction-volume local scvfs
+    using LocalScvfType = CCMpfaOFacetCouplingInteractionVolumeLocalScvf< IVIndexSet >;
+
+    //! Use the assembler that considers the coupled domain
+    template<class Problem, class FVElementGeometry, class ElemVolVars>
+    using LocalAssembler = MpfaOFacetCouplingInteractionVolumeAssembler<Problem, FVElementGeometry, ElemVolVars>;
+};
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief Class for the interaction volume of the mpfa-o scheme in the
+ *        context of models involving coupling to a lower-dimensional
+ *        domain across the element facets.
+ */
+template< class Traits >
+class CCMpfaOFacetCouplingInteractionVolume
+: public CCMpfaInteractionVolumeBase< Traits >
+{
+    using GridView = typename Traits::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+
+    using IndexSet = typename Traits::IndexSet;
+    using GridIndexType = typename IndexSet::GridIndexType;
+    using LocalIndexType = typename IndexSet::LocalIndexType;
+    using Stencil = typename IndexSet::NodalGridStencilType;
+
+    using LocalScvType = typename Traits::LocalScvType;
+    using LocalScvfType = typename Traits::LocalScvfType;
+    using LocalFaceData = typename Traits::LocalFaceData;
+
+public:
+    //! Reuse standard o-scheme's Dirichlet Data class
+    using DirichletData = typename CCMpfaOInteractionVolume<Traits>::DirichletData;
+
+    //! Define data structure to store which scvfs lie on interior boundaries
+    class InteriorBoundaryData
+    {
+        GridIndexType scvfIdx_;
+
+    public:
+        //! Constructor
+        InteriorBoundaryData(GridIndexType scvfIdx) : scvfIdx_(scvfIdx) {}
+
+        //! Return corresponding scvf index
+        GridIndexType scvfIndex() const { return scvfIdx_; }
+    };
+
+    //! publicly state the mpfa-scheme this interaction volume is associated with
+    static constexpr MpfaMethods MpfaMethod = MpfaMethods::oMethod;
+
+    //! Sets up the local scope for a given iv index set
+    template< class Problem, class FVElementGeometry >
+    void bind(const IndexSet& indexSet,
+              const Problem& problem,
+              const FVElementGeometry& fvGeometry)
+    {
+        // for the o-scheme, the stencil is equal to the scv
+        // index set of the dual grid's nodal index set
+        stencil_ = &indexSet.nodalIndexSet().gridScvIndices();
+
+        // find out how many facet elements appear in this iv
+        std::size_t numFacetElems = 0;
+        std::size_t numOutsideFaces = 0;
+        std::vector<bool> isOnInteriorBoundary(indexSet.numFaces(), false);
+        for (LocalIndexType fIdx = 0; fIdx < indexSet.numFaces(); ++fIdx)
+        {
+            const auto& scvf = fvGeometry.scvf(indexSet.gridScvfIndex(fIdx));
+            const auto element = fvGeometry.fvGridGeometry().element(scvf.insideScvIdx());
+            if (problem.couplingManager().isOnInteriorBoundary(element, scvf))
+            {
+                numFacetElems++;
+                numOutsideFaces += scvf.numOutsideScvs();
+                isOnInteriorBoundary[fIdx] = true;
+                interiorBoundaryData_.emplace_back( scvf.index() );
+            }
+        }
+
+        // number of interaction-volume-local scvs(=node-local for o-scheme) and scvfs
+        numFaces_ = indexSet.numFaces() + numOutsideFaces;
+        const auto numLocalScvs = indexSet.numScvs();
+        const auto numGlobalScvfs = indexSet.nodalIndexSet().numScvfs();
+
+        // reserve memory for local entities
+        elements_.clear();      elements_.reserve(numLocalScvs);
+        scvs_.clear();          scvs_.reserve(numLocalScvs);
+        scvfs_.clear();         scvfs_.reserve(numFaces_);
+        localFaceData_.clear(); localFaceData_.reserve(numGlobalScvfs);
+        dirichletData_.clear(); dirichletData_.reserve(numFaces_);
+
+        // keep track of the number of unknowns etc
+        numUnknowns_ = 0;
+        numKnowns_ = numLocalScvs + numFacetElems;
+
+        // index map from grid scvf index to local scvf index
+        std::unordered_map<GridIndexType, LocalIndexType> scvfIndexMap;
+
+        // set up objects related to sub-control volume faces
+        LocalIndexType facetElementCounter = 0;
+        for (LocalIndexType faceIdxLocal = 0; faceIdxLocal < indexSet.numFaces(); ++faceIdxLocal)
+        {
+            const auto gridScvfIdx = indexSet.gridScvfIndex(faceIdxLocal);
+            const auto& flipScvfIdxSet = fvGeometry.fvGridGeometry().flipScvfIndexSet()[gridScvfIdx];
+            const auto& scvf = fvGeometry.scvf(gridScvfIdx);
+            const auto element = fvGeometry.fvGridGeometry().element(scvf.insideScvIdx());
+
+            // the neighboring scvs in local indices (order: 0 - inside scv, 1..n - outside scvs)
+            const auto& neighborScvIndicesLocal = indexSet.neighboringLocalScvIndices(faceIdxLocal);
+            const auto numNeighborScvs = neighborScvIndicesLocal.size();
+
+            // the ív-local scvf index of the face about to be created
+            const auto curLocalScvfIdx = scvfs_.size();
+            scvfIndexMap[gridScvfIdx] = curLocalScvfIdx;
+            localFaceData_.emplace_back(curLocalScvfIdx, neighborScvIndicesLocal[0], scvf.index());
+
+            // on interior boundaries, create local scvfs for inside AND all outside scvfs
+            if (isOnInteriorBoundary[faceIdxLocal])
+            {
+                const LocalIndexType facetLocalDofIdx = numLocalScvs + facetElementCounter++;
+                const bool isDirichlet = problem.interiorBoundaryTypes(element, scvf).hasOnlyDirichlet();
+
+                // create local scvf
+                if (isDirichlet)
+                    scvfs_.emplace_back(scvf, neighborScvIndicesLocal, facetLocalDofIdx, /*isDirichlet*/true, facetLocalDofIdx);
+                else
+                    scvfs_.emplace_back(scvf, neighborScvIndicesLocal, numUnknowns_++, /*isDirichlet*/false, facetLocalDofIdx);
+
+                // create "outside" local scvfs
+                for (LocalIndexType i = 1; i < numNeighborScvs; ++i)
+                {
+                    const auto outsideGridScvfIdx = flipScvfIdxSet[i-1];
+                    const auto& flipScvf = fvGeometry.scvf(outsideGridScvfIdx);
+                    const auto& outsideFlipScvfIdxSet = fvGeometry.fvGridGeometry().flipScvfIndexSet()[outsideGridScvfIdx];
+
+                    // rearrange the neighbor scv index vector corresponding to this scvfs flip scvf index set
+                    using std::swap;
+                    auto outsideNeighborScvIdxSet = neighborScvIndicesLocal;
+                    outsideNeighborScvIdxSet[0] = outsideNeighborScvIdxSet[i];
+                    for (LocalIndexType j = 0; j < outsideFlipScvfIdxSet.size(); ++j)
+                    {
+                        const auto flipScvfIdx = outsideFlipScvfIdxSet[j];
+                        auto it = std::find(flipScvfIdxSet.begin(), flipScvfIdxSet.end(), flipScvfIdx);
+
+                        // if we found the index, use corresponding local scv index
+                        if (it != flipScvfIdxSet.end())
+                            outsideNeighborScvIdxSet[j+1] = neighborScvIndicesLocal[std::distance(flipScvfIdxSet.begin(), it)+1];
+
+                        // otherwise this must be the "inside" scvf again
+                        else
+                        {
+                            assert(flipScvfIdx == gridScvfIdx);
+                            outsideNeighborScvIdxSet[j+1] = neighborScvIndicesLocal[0];
+                        }
+                    }
+
+                    scvfIndexMap[outsideGridScvfIdx] = curLocalScvfIdx+i;
+                    localFaceData_.emplace_back(curLocalScvfIdx+i, outsideNeighborScvIdxSet[0], flipScvf.index());
+                    if (isDirichlet)
+                        scvfs_.emplace_back(flipScvf, outsideNeighborScvIdxSet, facetLocalDofIdx, /*isDirichlet*/true, facetLocalDofIdx);
+                    else
+                        scvfs_.emplace_back(flipScvf, outsideNeighborScvIdxSet, numUnknowns_++, /*isDirichlet*/false, facetLocalDofIdx);
+                }
+            }
+
+            // otherwise crate boundary scvf ...
+            else if (scvf.boundary())
+            {
+                if (problem.boundaryTypes(element, scvf).hasOnlyDirichlet())
+                {
+                    scvfs_.emplace_back(scvf, neighborScvIndicesLocal, numKnowns_++, /*isDirichlet*/true);
+                    dirichletData_.emplace_back(scvf.outsideScvIdx());
+                }
+                else
+                    scvfs_.emplace_back(scvf, neighborScvIndicesLocal, numUnknowns_++, /*isDirichlet*/false);
+            }
+
+            // ... or interior scvf
+            else
+            {
+                scvfs_.emplace_back(scvf, neighborScvIndicesLocal, numUnknowns_++, /*isDirichlet*/false);
+
+                // add local face data objects for the outside faces
+                for (LocalIndexType i = 1; i < numNeighborScvs; ++i)
+                {
+                    // loop over scvfs in outside scv until we find the one coinciding with current scvf
+                    const auto outsideLocalScvIdx = neighborScvIndicesLocal[i];
+                    const auto& flipScvfIndex = fvGeometry.fvGridGeometry().flipScvfIndexSet()[scvf.index()][i-1];
+                    const auto& flipScvf = fvGeometry.scvf(flipScvfIndex);
+                    scvfIndexMap[flipScvfIndex] = curLocalScvfIdx;
+                    localFaceData_.emplace_back(curLocalScvfIdx,    // iv-local scvf idx
+                                                outsideLocalScvIdx, // iv-local scv index
+                                                i-1,                // scvf-local index in outside faces
+                                                flipScvf.index());  // global scvf index
+                }
+            }
+        }
+
+        // set up stuff related to sub-control volumes
+        for (LocalIndexType scvIdxLocal = 0; scvIdxLocal < numLocalScvs; scvIdxLocal++)
+        {
+            elements_.emplace_back(fvGeometry.fvGridGeometry().element( stencil()[scvIdxLocal] ));
+            scvs_.emplace_back(fvGeometry.fvGridGeometry().mpfaHelper(),
+                               fvGeometry,
+                               fvGeometry.scv( stencil()[scvIdxLocal] ),
+                               scvIdxLocal,
+                               indexSet,
+                               scvfIndexMap);
+        }
+    }
+
+    //! returns the number of primary scvfs of this interaction volume
+    std::size_t numFaces() const
+    { return numFaces_; }
+
+    //! returns the number of intermediate unknowns within this interaction volume
+    std::size_t numUnknowns() const
+    { return numUnknowns_; }
+
+    //! returns the number of (in this context) known solution values within this interaction volume
+    std::size_t numKnowns() const
+    { return numKnowns_; }
+
+    //! returns the number of scvs embedded in this interaction volume
+    std::size_t numScvs() const
+    { return scvs_.size(); }
+
+    //! returns the cell-stencil of this interaction volume
+    const Stencil& stencil() const
+    { return *stencil_; }
+
+    //! returns the grid element corresponding to a given iv-local scv idx
+    const Element& element(LocalIndexType ivLocalScvIdx) const
+    { return elements_[ivLocalScvIdx]; }
+
+    //! returns the local scvf entity corresponding to a given iv-local scvf idx
+    const LocalScvfType& localScvf(LocalIndexType ivLocalScvfIdx) const
+    { return scvfs_[ivLocalScvfIdx]; }
+
+    //! returns the local scv entity corresponding to a given iv-local scv idx
+    const LocalScvType& localScv(LocalIndexType ivLocalScvIdx) const
+    { return scvs_[ivLocalScvIdx]; }
+
+    //! returns a reference to the container with the local face data
+    const std::vector<LocalFaceData>& localFaceData() const
+    { return localFaceData_; }
+
+    //! returns a reference to the information container on Dirichlet BCs within this iv
+    const std::vector<DirichletData>& dirichletData() const
+    { return dirichletData_; }
+
+    //! returns a reference to the data container on interior boundaries
+    const std::vector<InteriorBoundaryData>& interiorBoundaryData() const
+    { return interiorBoundaryData_; }
+
+    //! returns the geometry of the i-th local scv
+    template< class FVElementGeometry >
+    auto getScvGeometry(LocalIndexType ivLocalScvIdx, const FVElementGeometry& fvGeometry) const
+    { return CCMpfaOScvGeometryHelper<LocalScvType>::computeScvGeometry(ivLocalScvIdx, *this, fvGeometry); }
+
+    //! returns the number of interaction volumes living around a vertex
+    template< class NI >
+    static constexpr std::size_t numIVAtVertex(const NI& nodalIndexSet)
+    { return 1; }
+
+    //! adds the iv index sets living around a vertex to a given container
+    //! and stores the the corresponding index in a map for each scvf
+    template< class IvIndexSetContainer,
+              class ScvfIndexMap,
+              class NodalIndexSet,
+              class FlipScvfIndexSet >
+    static void addIVIndexSets(IvIndexSetContainer& ivIndexSetContainer,
+                               ScvfIndexMap& scvfIndexMap,
+                               const NodalIndexSet& nodalIndexSet,
+                               const FlipScvfIndexSet& flipScvfIndexSet)
+    {
+        // reuse the function of the standard mpfa-o interaction volume
+        CCMpfaOInteractionVolume<Traits>::addIVIndexSets(ivIndexSetContainer,
+                                                         scvfIndexMap,
+                                                         nodalIndexSet,
+                                                         flipScvfIndexSet);
+    }
+
+private:
+    // pointer to cell stencil (in iv index set)
+    const Stencil* stencil_;
+
+    // Variables defining the local scope
+    std::vector<Element> elements_;
+    std::vector<LocalScvType> scvs_;
+    std::vector<LocalScvfType> scvfs_;
+    std::vector<LocalFaceData> localFaceData_;
+    std::vector<DirichletData> dirichletData_;
+    std::vector<InteriorBoundaryData> interiorBoundaryData_;
+
+    // sizes involved in the local system equations
+    std::size_t numFaces_;
+    std::size_t numUnknowns_;
+    std::size_t numKnowns_;
+};
+
+} // end namespace
+
+#endif
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/localassembler.hh b/dumux/multidomain/facet/cellcentered/mpfa/localassembler.hh
new file mode 100644
index 0000000000000000000000000000000000000000..9933b03148d28dfb33d7faeaae8f3ae492b90b0d
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/localassembler.hh
@@ -0,0 +1,459 @@
+// -*- 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 FacetCoupling
+ * \copydoc Dumux::MpfaOFacetCouplingInteractionVolumeAssembler
+ */
+#ifndef DUMUX_MULTIDOMAIN_FACET_CC_MPFA_O_LOCAL_ASSEMBLER_HH
+#define DUMUX_MULTIDOMAIN_FACET_CC_MPFA_O_LOCAL_ASSEMBLER_HH
+
+#include <dune/common/exceptions.hh>
+
+#include <dumux/common/math.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/discretization/cellcentered/mpfa/methods.hh>
+#include <dumux/discretization/cellcentered/mpfa/localassemblerbase.hh>
+#include <dumux/discretization/cellcentered/mpfa/localassemblerhelper.hh>
+#include <dumux/discretization/cellcentered/mpfa/computetransmissibility.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief Specialization of the interaction volume-local
+ *        assembler class for the schemes using an mpfa-o type
+ *        assembly in the context of facet coupling.
+ *
+ * \tparam P The problem type
+ * \tparam EG The element finite volume geometry
+ * \tparam EV The element volume variables type
+ */
+template< class P, class EG, class EV >
+class MpfaOFacetCouplingInteractionVolumeAssembler
+: public InteractionVolumeAssemblerBase< P, EG, EV >
+{
+    using ParentType = InteractionVolumeAssemblerBase< P, EG, EV >;
+    using Helper = InteractionVolumeAssemblerHelper;
+
+public:
+    //! Pull up constructor of the base class
+    using ParentType::ParentType;
+
+    /*!
+     * \brief Assembles the matrices involved in the flux expressions
+     *        and the local system of equations within an interaction volume.
+     *
+     * \param handle The data handle in which the matrices are stored
+     * \param iv The interaction volume
+     * \param getT Lambda to evaluate the scv-wise tensors
+     */
+    template< class DataHandle, class IV, class TensorFunc >
+    void assembleMatrices(DataHandle& handle, IV& iv, const TensorFunc& getT)
+    {
+        assembleLocalMatrices_(handle.A(), handle.AB(), handle.CA(), handle.T(), handle.omegas(), iv, getT);
+
+        // maybe solve the local system
+        if (iv.numUnknowns() > 0)
+            Helper::solveLocalSystem(this->fvGeometry(), handle, iv);
+    }
+
+    /*!
+     * \brief Assembles the vector of primary (cell) unknowns and (maybe)
+     *        Dirichlet boundary conditions within an interaction volume.
+     *
+     * \param handle The data handle in which the vector is stored
+     * \param iv The interaction volume
+     * \param getU Lambda to obtain the desired cell/Dirichlet value from vol vars
+     */
+    template< class DataHandle, class IV, class GetU >
+    void assembleU(DataHandle& handle, const IV& iv, const GetU& getU)
+    {
+        auto& u = handle.uj();
+        Helper::resizeVector(u, iv.numKnowns());
+
+        // put the cell unknowns first ...
+        typename IV::Traits::IndexSet::LocalIndexType i = 0;
+        for (; i < iv.numScvs(); i++)
+            u[i] = getU( this->elemVolVars()[iv.localScv(i).gridScvIndex()] );
+
+        // ... then put facet unknowns ...
+        for (const auto& data : iv.interiorBoundaryData())
+        {
+            const auto& scvf = this->fvGeometry().scvf(data.scvfIndex());
+            const auto element = this->fvGeometry().fvGridGeometry().element(scvf.insideScvIdx());
+            u[i++] = getU( this->problem().couplingManager().getLowDimVolVars(element, scvf) );
+        }
+
+        // ... then put the Dirichlet unknowns
+        for (const auto& data : iv.dirichletData())
+            u[i++] = getU( this->elemVolVars()[data.volVarIndex()] );
+    }
+
+    /*!
+     * \brief Assembles the gravitational flux contributions on the scvfs within an
+     *        interaction volume.
+     *
+     * \param handle The data handle in which the vector is stored
+     * \param iv The interaction volume
+     * \param getRho Lambda to obtain the density from volume variables
+     */
+    template< class DataHandle, class IV, class GetRho >
+    void assembleGravity(DataHandle& handle, const IV& iv, const GetRho& getRho)
+    {
+        using GridView = typename IV::Traits::GridView;
+        static constexpr int dim = GridView::dimension;
+        static constexpr int dimWorld = GridView::dimensionworld;
+        static constexpr bool isSurfaceGrid = dim < dimWorld;
+
+        // resize the gravity vectors
+        auto& g = handle.g();
+        auto& deltaG = handle.deltaG();
+        auto& outsideG = handle.gOutside();
+        Helper::resizeVector(g, iv.numFaces());
+        Helper::resizeVector(deltaG, iv.numUnknowns());
+        if (isSurfaceGrid)
+            Helper::resizeVector(outsideG, iv.numFaces());
+
+        //! For each face, we...
+        //! - arithmetically average the phase densities
+        //! - compute the term \f$ \alpha := \mathbf{A} \rho \ \mathbf{n}^T \mathbf{K} \mathbf{g} \f$ in each neighboring cell
+        //! - compute \f$ \alpha^* = \sum{\alpha_{outside, i}} - \alpha_{inside} \f$
+        using Scalar = typename IV::Traits::MatVecTraits::TMatrix::value_type;
+        using LocalIndexType = typename IV::Traits::IndexSet::LocalIndexType;
+
+        // xi factor for coupling conditions
+        static const Scalar xi = getParamFromGroup<Scalar>(this->problem().paramGroup(), "FacetCoupling.Xi", 1.0);
+
+        for (LocalIndexType faceIdx = 0; faceIdx < iv.numFaces(); ++faceIdx)
+        {
+            // gravitational acceleration on this face
+            const auto& curLocalScvf = iv.localScvf(faceIdx);
+            const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
+            const auto& gravity = this->problem().gravityAtPos(curGlobalScvf.ipGlobal());
+            const auto curIsInteriorBoundary = curLocalScvf.isOnInteriorBoundary();
+            const Scalar curXiFactor = curIsInteriorBoundary ? (curGlobalScvf.boundary() ? 1.0 : xi) : 1.0;
+
+            // get permeability tensor in "positive" sub volume
+            const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
+            const auto& posGlobalScv = this->fvGeometry().scv(iv.localScv(neighborScvIndices[0]).gridScvIndex());
+            const auto& posVolVars = this->elemVolVars()[posGlobalScv];
+            const auto alpha_inside = posVolVars.extrusionFactor()*vtmv(curGlobalScvf.unitOuterNormal(),
+                                                                        posVolVars.permeability(),
+                                                                        gravity);
+
+            const auto numOutsideFaces = !curGlobalScvf.boundary() ? curGlobalScvf.numOutsideScvs() : 0;
+            using OutsideAlphaStorage = std::conditional_t< isSurfaceGrid,
+                                                            std::vector<Scalar>,
+                                                            Dune::ReservedVector<Scalar, 1> >;
+            OutsideAlphaStorage alpha_outside; alpha_outside.resize(numOutsideFaces);
+            std::fill(alpha_outside.begin(), alpha_outside.end(), 0.0);
+            Scalar rho;
+
+            if (isSurfaceGrid && !curIsInteriorBoundary)
+                Helper::resizeVector(outsideG[faceIdx], numOutsideFaces);
+
+            if (!curLocalScvf.isDirichlet())
+            {
+                const auto localDofIdx = curLocalScvf.localDofIndex();
+                const Scalar curOneMinusXi = curIsInteriorBoundary ?  -(1.0 - xi) : 1.0;
+
+                rho = getRho(posVolVars);
+                deltaG[localDofIdx] = 0.0;
+
+                if (!curGlobalScvf.boundary())
+                {
+                    for (unsigned int idxInOutside = 0; idxInOutside < curGlobalScvf.numOutsideScvs(); ++idxInOutside)
+                    {
+                        // obtain outside tensor
+                        const auto negLocalScvIdx = neighborScvIndices[idxInOutside+1];
+                        const auto& negGlobalScv = this->fvGeometry().scv(iv.localScv(negLocalScvIdx).gridScvIndex());
+                        const auto& negVolVars = this->elemVolVars()[negGlobalScv];
+                        const auto& flipScvf = !isSurfaceGrid ? curGlobalScvf
+                                                              : this->fvGeometry().flipScvf(curGlobalScvf.index(), idxInOutside);
+
+                        alpha_outside[idxInOutside] = negVolVars.extrusionFactor()*vtmv(flipScvf.unitOuterNormal(),
+                                                                                        negVolVars.permeability(),
+                                                                                        gravity);
+                        if (isSurfaceGrid)
+                            alpha_outside[idxInOutside] *= -1.0;
+
+                        if (!curIsInteriorBoundary)
+                            rho += getRho(negVolVars);
+
+                        deltaG[localDofIdx] += curOneMinusXi*alpha_outside[idxInOutside];
+                    }
+                }
+
+                if (curIsInteriorBoundary)
+                {
+                    const auto posElement = this->fvGeometry().fvGridGeometry().element(posGlobalScv.elementIndex());
+                    const auto& facetVolVars = this->problem().couplingManager().getLowDimVolVars(posElement, curGlobalScvf);
+                    rho += getRho(facetVolVars);
+                    rho /= 2.0;
+                    const auto alphaFacet = posVolVars.extrusionFactor()*vtmv(curGlobalScvf.unitOuterNormal(),
+                                                                              facetVolVars.permeability(),
+                                                                              gravity);
+                    deltaG[localDofIdx] += alphaFacet;
+                }
+                else
+                    rho /= numOutsideFaces + 1;
+
+                deltaG[localDofIdx] -= curXiFactor*alpha_inside;
+                deltaG[localDofIdx] *= rho*curGlobalScvf.area();
+            }
+            // use average density between facet and cell density on interior Dirichlet boundaries
+            else if (curIsInteriorBoundary)
+            {
+                const auto posElement = this->fvGeometry().fvGridGeometry().element(posGlobalScv.elementIndex());
+                const auto& facetVolVars = this->problem().couplingManager().getLowDimVolVars(posElement, curGlobalScvf);
+                rho = 0.5*(getRho(facetVolVars) + getRho(posVolVars));
+            }
+            // use density resulting from Dirichlet BCs
+            else
+                rho = getRho(this->elemVolVars()[curGlobalScvf.outsideScvIdx()]);
+
+            // add "inside" & "outside" alphas to gravity containers
+            g[faceIdx] = alpha_inside*rho*curGlobalScvf.area();
+
+            if (isSurfaceGrid && !curIsInteriorBoundary)
+            {
+                unsigned int i = 0;
+                for (const auto& alpha : alpha_outside)
+                    outsideG[faceIdx][i++] = alpha*rho*curGlobalScvf.area();
+            }
+        }
+
+        // add iv-wide contributions to gravity vectors
+        handle.CA().umv(deltaG, g);
+        if (isSurfaceGrid)
+        {
+            using FaceVector = typename IV::Traits::MatVecTraits::FaceVector;
+            FaceVector AG;
+            Helper::resizeVector(AG, iv.numUnknowns());
+            handle.A().mv(deltaG, AG);
+
+            // compute gravitational accelerations
+            for (const auto& localFaceData : iv.localFaceData())
+            {
+                // continue only for "outside" faces
+                if (!localFaceData.isOutsideFace())
+                    continue;
+
+                const auto localScvIdx = localFaceData.ivLocalInsideScvIndex();
+                const auto localScvfIdx = localFaceData.ivLocalScvfIndex();
+                const auto idxInOutside = localFaceData.scvfLocalOutsideScvfIndex();
+                const auto& posLocalScv = iv.localScv(localScvIdx);
+                const auto& wijk = handle.omegas()[localScvfIdx][idxInOutside+1];
+
+                // add contributions from all local directions
+                for (LocalIndexType localDir = 0; localDir < dim; localDir++)
+                {
+                    // the scvf corresponding to this local direction in the scv
+                    const auto& curLocalScvf = iv.localScvf(posLocalScv.localScvfIndex(localDir));
+                    if (!curLocalScvf.isDirichlet())
+                        outsideG[localScvfIdx][idxInOutside] -= wijk[localDir]*AG[curLocalScvf.localDofIndex()];
+                }
+            }
+        }
+    }
+
+private:
+    /*!
+     * \copydoc Dumux::MpfaOInteractionVolumeAssembler::assembleLocalMatrices_
+     */
+    template< class IV, class TensorFunc >
+    void assembleLocalMatrices_(typename IV::Traits::MatVecTraits::AMatrix& A,
+                                typename IV::Traits::MatVecTraits::BMatrix& B,
+                                typename IV::Traits::MatVecTraits::CMatrix& C,
+                                typename IV::Traits::MatVecTraits::DMatrix& D,
+                                typename IV::Traits::MatVecTraits::OmegaStorage& wijk,
+                                IV& iv, const TensorFunc& getT)
+    {
+        using Scalar = typename IV::Traits::MatVecTraits::TMatrix::value_type;
+        using LocalIndexType = typename IV::Traits::IndexSet::LocalIndexType;
+        static constexpr int dim = IV::Traits::GridView::dimension;
+        static constexpr int dimWorld = IV::Traits::GridView::dimensionworld;
+
+        // xi factor for coupling conditions
+        static const Scalar xi = getParamFromGroup<Scalar>(this->problem().paramGroup(), "FacetCoupling.Xi", 1.0);
+
+        // resize omegas
+        Helper::resizeVector(wijk, iv.numFaces());
+
+        // if only Dirichlet faces are present in the iv,
+        // the matrices A, B & C are undefined and D = T
+        if (iv.numUnknowns() == 0)
+        {
+            // resize & reset D matrix
+            Helper::resizeMatrix(D, iv.numFaces(), iv.numKnowns()); D = 0.0;
+
+            // Loop over all the faces, in this case these are all dirichlet boundaries
+            for (LocalIndexType faceIdx = 0; faceIdx < iv.numFaces(); ++faceIdx)
+            {
+                const auto& curLocalScvf = iv.localScvf(faceIdx);
+                const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
+                const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
+
+                // get tensor in "positive" sub volume
+                const auto& posLocalScv = iv.localScv(neighborScvIndices[0]);
+                const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.gridScvIndex());
+                const auto& posVolVars = this->elemVolVars()[posGlobalScv];
+                const auto& posElement = iv.element(neighborScvIndices[0]);
+                const auto tensor = getT(this->problem(), posElement, posVolVars, this->fvGeometry(), posGlobalScv);
+
+                // the omega factors of the "positive" sub volume
+                Helper::resizeVector(wijk[faceIdx], /*no outside scvs present*/1);
+                wijk[faceIdx][0] = computeMpfaTransmissibility(posLocalScv, curGlobalScvf, tensor, posVolVars.extrusionFactor());
+
+                const auto posScvLocalDofIdx = posLocalScv.localDofIndex();
+                for (LocalIndexType localDir = 0; localDir < dim; localDir++)
+                {
+                    const auto& otherLocalScvf = iv.localScvf( posLocalScv.localScvfIndex(localDir) );
+                    const auto otherLocalDofIdx = otherLocalScvf.localDofIndex();
+                    D[faceIdx][otherLocalDofIdx] -= wijk[faceIdx][0][localDir];
+                    D[faceIdx][posScvLocalDofIdx] += wijk[faceIdx][0][localDir];
+                }
+            }
+        }
+        else
+        {
+            // resize & reset matrices
+            Helper::resizeMatrix(A, iv.numUnknowns(), iv.numUnknowns()); A = 0.0;
+            Helper::resizeMatrix(B, iv.numUnknowns(), iv.numKnowns());   B = 0.0;
+            Helper::resizeMatrix(C, iv.numFaces(), iv.numUnknowns());    C = 0.0;
+            Helper::resizeMatrix(D, iv.numFaces(), iv.numKnowns());      D = 0.0;
+
+            for (LocalIndexType faceIdx = 0; faceIdx < iv.numFaces(); ++faceIdx)
+            {
+                const auto& curLocalScvf = iv.localScvf(faceIdx);
+                const auto& curGlobalScvf = this->fvGeometry().scvf(curLocalScvf.gridScvfIndex());
+                const auto curIsDirichlet = curLocalScvf.isDirichlet();
+                const auto curLocalDofIdx = curLocalScvf.localDofIndex();
+                const auto curIsInteriorBoundary = curLocalScvf.isOnInteriorBoundary();
+                const Scalar curXiFactor = curIsInteriorBoundary ? (curGlobalScvf.boundary() ? 1.0 : xi) : 1.0;
+
+                // get tensor in "positive" sub volume
+                const auto& neighborScvIndices = curLocalScvf.neighboringLocalScvIndices();
+                const auto& posLocalScv = iv.localScv(neighborScvIndices[0]);
+                const auto& posGlobalScv = this->fvGeometry().scv(posLocalScv.gridScvIndex());
+                const auto& posVolVars = this->elemVolVars()[posGlobalScv];
+                const auto& posElement = iv.element(neighborScvIndices[0]);
+                const auto tensor = getT(this->problem(), posElement, posVolVars, this->fvGeometry(), posGlobalScv);
+
+                // the omega factors of the "positive" sub volume
+                Helper::resizeVector(wijk[faceIdx], neighborScvIndices.size());
+                wijk[faceIdx][0] = computeMpfaTransmissibility(posLocalScv, curGlobalScvf, tensor, posVolVars.extrusionFactor());
+
+                // go over the coordinate directions in the positive sub volume
+                for (unsigned int localDir = 0; localDir < dim; localDir++)
+                {
+                    const auto& otherLocalScvf = iv.localScvf( posLocalScv.localScvfIndex(localDir) );
+                    const auto otherLocalDofIdx = otherLocalScvf.localDofIndex();
+
+                    // if we are not on a Dirichlet face, add entries associated with unknown face pressures
+                    // i.e. in matrix C and maybe A (if current face is not a Dirichlet face)
+                    if (!otherLocalScvf.isDirichlet())
+                    {
+                        C[faceIdx][otherLocalDofIdx] -= wijk[faceIdx][0][localDir];
+                        if (!curIsDirichlet)
+                            A[curLocalDofIdx][otherLocalDofIdx] -= curXiFactor*wijk[faceIdx][0][localDir];
+                    }
+                    // the current face is a Dirichlet face and creates entries in D & maybe B
+                    else
+                    {
+                        D[faceIdx][otherLocalDofIdx] -= wijk[faceIdx][0][localDir];
+                        if (!curIsDirichlet)
+                            B[curLocalDofIdx][otherLocalDofIdx] += curXiFactor*wijk[faceIdx][0][localDir];
+                    }
+
+                    // add entries related to pressures at the scv centers (dofs)
+                    const auto posScvLocalDofIdx = posLocalScv.localDofIndex();
+                    D[faceIdx][posScvLocalDofIdx] += wijk[faceIdx][0][localDir];
+
+                    if (!curIsDirichlet)
+                        B[curLocalDofIdx][posScvLocalDofIdx] -= curXiFactor*wijk[faceIdx][0][localDir];
+                }
+
+                // handle the entries related to the coupled facet element
+                if (curIsInteriorBoundary && !curIsDirichlet)
+                {
+                    const auto facetVolVars = this->problem().couplingManager().getLowDimVolVars(posElement, curGlobalScvf);
+                    const auto facetTensor = this->problem().couplingManager().getLowDimTensor(posElement, curGlobalScvf, getT);
+
+                    // On surface grids we use the square root of the extrusion factor as approximation of the aperture
+                    using std::sqrt;
+                    const auto wFacet = 2.0*curGlobalScvf.area()*posVolVars.extrusionFactor()
+                                           *vtmv(curGlobalScvf.unitOuterNormal(), facetTensor, curGlobalScvf.unitOuterNormal())
+                                           / (dim < dimWorld ? sqrt(facetVolVars.extrusionFactor()) : facetVolVars.extrusionFactor());
+
+                    A[curLocalDofIdx][curLocalDofIdx] -= wFacet;
+                    B[curLocalDofIdx][curLocalScvf.coupledFacetLocalDofIndex()] -= wFacet;
+                }
+
+                // If we are on an interior face (which isn't coupled via Dirichlet Bs), add values from negative sub volume
+                if (!curGlobalScvf.boundary() && !curIsDirichlet)
+                {
+                    // the minus ensures the right sign of the coupling condition in the matrices
+                    const Scalar curOneMinusXi = curIsInteriorBoundary ?  -(1.0 - xi) : 1.0;
+
+                    // loop over all the outside neighbors of this face and add entries
+                    for (unsigned int idxInOutside = 0; idxInOutside < curGlobalScvf.numOutsideScvs(); ++idxInOutside)
+                    {
+                        const auto idxOnScvf = idxInOutside+1;
+                        const auto& negLocalScv = iv.localScv( neighborScvIndices[idxOnScvf] );
+                        const auto& negGlobalScv = this->fvGeometry().scv(negLocalScv.gridScvIndex());
+                        const auto& negVolVars = this->elemVolVars()[negGlobalScv];
+                        const auto& negElement = iv.element( neighborScvIndices[idxOnScvf] );
+                        const auto negTensor = getT(this->problem(), negElement, negVolVars, this->fvGeometry(), negGlobalScv);
+
+                        // On surface grids, use outside face for "negative" transmissibility calculation
+                        const auto& scvf = dim < dimWorld ? this->fvGeometry().flipScvf(curGlobalScvf.index(), idxInOutside)
+                                                          : curGlobalScvf;
+                        wijk[faceIdx][idxOnScvf] = computeMpfaTransmissibility(negLocalScv, scvf, negTensor, negVolVars.extrusionFactor());
+
+                        // flip sign on surface grids (since we used the "outside" normal)
+                        if (dim < dimWorld)
+                            wijk[faceIdx][idxOnScvf] *= -1.0;
+
+                        // go over the coordinate directions in the negative sub volume
+                        for (int localDir = 0; localDir < dim; localDir++)
+                        {
+                            const auto otherLocalScvfIdx = negLocalScv.localScvfIndex(localDir);
+                            const auto& otherLocalScvf = iv.localScvf(otherLocalScvfIdx);
+                            const auto otherLocalDofIdx = otherLocalScvf.localDofIndex();
+
+                            if (!otherLocalScvf.isDirichlet())
+                                A[curLocalDofIdx][otherLocalDofIdx] += curOneMinusXi*wijk[faceIdx][idxOnScvf][localDir];
+                            else
+                                B[curLocalDofIdx][otherLocalDofIdx] -= curOneMinusXi*wijk[faceIdx][idxOnScvf][localDir];
+
+                            // add entries to matrix B
+                            B[curLocalDofIdx][negLocalScv.localDofIndex()] += curOneMinusXi*wijk[faceIdx][idxOnScvf][localDir];
+                        }
+                    }
+                }
+            }
+        }
+    }
+};
+
+} // end namespace
+
+#endif
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/localsubcontrolentities.hh b/dumux/multidomain/facet/cellcentered/mpfa/localsubcontrolentities.hh
new file mode 100644
index 0000000000000000000000000000000000000000..e47c3823ff58e6155a9305adc99614c3a23ff3b5
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/localsubcontrolentities.hh
@@ -0,0 +1,159 @@
+// -*- 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 FacetCoupling
+ * \brief Classes for sub control entities of the
+ *        mpfa-o method in the context of facet coupling
+ */
+#ifndef DUMUX_MULTDOMAIN_FACET_CC_MPFA_O_LOCAL_SUBCONTROLENTITIES_HH
+#define DUMUX_MULTDOMAIN_FACET_CC_MPFA_O_LOCAL_SUBCONTROLENTITIES_HH
+
+#include <array>
+
+#include <dune/common/fvector.hh>
+#include <dumux/discretization/cellcentered/mpfa/omethod/localsubcontrolentities.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief Class for the interaction volume-local sub-control volume used
+ *        in the mpfa-o scheme in the context of facet coupling.
+ *
+ * \tparam IvIndexSet The type used for index sets within interaction volumes
+ * \tparam dim The dimensionality of the grid
+ * \tparam dimWorld The dimension of the world the grid is embedded in
+ */
+template< class IvIndexSet, class Scalar, int dim, int dimWorld>
+class CCMpfaOFacetCouplingInteractionVolumeLocalScv
+: public CCMpfaOInteractionVolumeLocalScv<IvIndexSet, Scalar, dim, dimWorld>
+{
+    using ParentType = CCMpfaOInteractionVolumeLocalScv<IvIndexSet, Scalar, dim, dimWorld>;
+
+public:
+    // export some types
+    using typename ParentType::LocalIndexType;
+
+    // export dimension
+    static constexpr int myDimension = dim;
+
+    //! The default constructor
+    CCMpfaOFacetCouplingInteractionVolumeLocalScv() = default;
+
+    /*!
+     * \brief The constructor
+     *
+     * \param helper Helper class for mpfa schemes
+     * \param fvGeometry The element finite volume geometry
+     * \param scv The grid sub-control volume
+     * \param localIndex The iv-local index of this scvIdx
+     * \param indexSet The interaction volume index set
+     * \param scvfGridToLocalIndexMap maps to grid scvf indices the iv-local scvf index
+     */
+    template<class MpfaHelper, class FVElementGeometry, class SubControlVolume, class IndexMap>
+    CCMpfaOFacetCouplingInteractionVolumeLocalScv(const MpfaHelper& helper,
+                                                  const FVElementGeometry& fvGeometry,
+                                                  const SubControlVolume& scv,
+                                                  const LocalIndexType localIndex,
+                                                  const IvIndexSet& indexSet,
+                                                  const IndexMap& scvfGridToLocalIndexMap)
+    : ParentType(helper, fvGeometry, scv, localIndex, indexSet)
+    {
+        // set up local scvf indices
+        const auto& nis = indexSet.nodalIndexSet();
+        for (unsigned int dir = 0; dir < myDimension; ++dir)
+            localScvfIndices_[dir] = scvfGridToLocalIndexMap.at(nis.gridScvfIndex(this->localDofIndex(), dir));
+    }
+
+    //! iv-local index of the coordir's scvf in this scv
+    LocalIndexType localScvfIndex(unsigned int coordDir) const
+    {
+        assert(coordDir < myDimension);
+        return localScvfIndices_[coordDir];
+    }
+
+private:
+    std::array<LocalIndexType, dim> localScvfIndices_;
+};
+
+/*!
+ * \ingroup FacetCoupling
+ * \brief Class for the interaction volume-local sub-control volume face
+ *        used in the mpfa-o scheme in the context of facet coupling.
+ *
+ * \tparam IvIndexSet The type used for index sets within interaction volumes
+ */
+template< class IvIndexSet >
+struct CCMpfaOFacetCouplingInteractionVolumeLocalScvf
+: public CCMpfaOInteractionVolumeLocalScvf< IvIndexSet >
+{
+  using ParentType = CCMpfaOInteractionVolumeLocalScvf< IvIndexSet >;
+  using ScvfNeighborLocalIndexSet = typename IvIndexSet::ScvfNeighborLocalIndexSet;
+
+public:
+    // pull up index types
+    using typename ParentType::LocalIndexType;
+    using typename ParentType::GridIndexType;
+
+    //! pull up parent's constructors
+    using ParentType::ParentType;
+
+    /*!
+     * \brief The constructor for interior boundary faces.
+     *
+     * \param scvf The grid sub-control volume face
+     * \param localScvIndices The iv-local neighboring scv indices
+     * \param localDofIdx This scvf's interaction volume-local dof index
+     * \param isDirichlet Specifies if this scv is on a Dirichlet boundary
+     * \param coupledFacetLocalDof The local index of the coupled facet element
+     *                             in the set of cell&Dirichlet values.
+     */
+    template< class SubControlVolumeFace >
+    CCMpfaOFacetCouplingInteractionVolumeLocalScvf(const SubControlVolumeFace& scvf,
+                                                   const ScvfNeighborLocalIndexSet& localScvIndices,
+                                                   const LocalIndexType localDofIdx,
+                                                   const bool isDirichlet,
+                                                   const LocalIndexType coupledFacetLocalDof)
+    : ParentType(scvf, neighborLocalScvIndices_, localDofIdx, isDirichlet)
+    , isInteriorBoundary_(true)
+    , coupledFacetLocalDofIndex_(coupledFacetLocalDof)
+    , neighborLocalScvIndices_(localScvIndices)
+    {}
+
+    //! Returns the iv-local dof index of the coupled facet element
+    LocalIndexType coupledFacetLocalDofIndex() const
+    { assert(isInteriorBoundary_); return coupledFacetLocalDofIndex_; }
+
+    //! Returns the local indices of the scvs neighboring this scvf
+    const ScvfNeighborLocalIndexSet& neighboringLocalScvIndices() const
+    { return isOnInteriorBoundary() ? neighborLocalScvIndices_ : ParentType::neighboringLocalScvIndices(); }
+
+    //! Returns true if this face is on an interior boundary
+    bool isOnInteriorBoundary() const { return isInteriorBoundary_; }
+
+private:
+    bool isInteriorBoundary_{false};
+    LocalIndexType coupledFacetLocalDofIndex_{0};
+    ScvfNeighborLocalIndexSet neighborLocalScvIndices_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/dumux/multidomain/facet/cellcentered/mpfa/properties.hh b/dumux/multidomain/facet/cellcentered/mpfa/properties.hh
new file mode 100644
index 0000000000000000000000000000000000000000..b2732f504954b0b764e2ba8eafeb6e9843f27812
--- /dev/null
+++ b/dumux/multidomain/facet/cellcentered/mpfa/properties.hh
@@ -0,0 +1,95 @@
+// -*- 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 FacetCoupling
+ * \brief Properties (and default properties) for all models using cell-centered
+ *        finite volume scheme with MPFA together with coupling across the grid element facets
+ * \note If n is the dimension of the lowest grid to be considered in the hierarchy,
+ *       all problem type tags for the grids with the dimension m > n must inherit
+ *       from these or other facet coupling properties (e.g. BoxFacetCouplingModel).
+ */
+
+#ifndef DUMUX_FACETCOUPLING_CC_MPFA_PROPERTIES_HH
+#define DUMUX_FACETCOUPLING_CC_MPFA_PROPERTIES_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/discretization/ccmpfa.hh>
+
+#include <dumux/multidomain/facet/cellcentered/upwindscheme.hh>
+#include <dumux/multidomain/facet/cellcentered/localresidual.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/interactionvolume.hh>
+
+#include <dumux/porousmediumflow/fluxvariables.hh>
+
+namespace Dumux {
+
+namespace Properties {
+
+//! Type tag for the cell-centered mpfa scheme with coupling to
+//! another sub-domain living on the grid facets.
+// Create new type tags
+namespace TTag {
+struct CCMpfaFacetCouplingModel { using InheritsFrom = std::tuple<CCMpfaModel>; };
+} // end namespace TTag
+
+//! Use the cc local residual for models with facet coupling
+template<class TypeTag>
+struct BaseLocalResidual<TypeTag, TTag::CCMpfaFacetCouplingModel> { using type = CCFacetCouplingLocalResidual<TypeTag>; };
+
+//! Use the facet coupling-specific mpfa-o interaction volume
+template<class TypeTag>
+struct PrimaryInteractionVolume<TypeTag, TTag::CCMpfaFacetCouplingModel>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using NodalIndexSet = GetPropType<TypeTag, Properties::DualGridNodalIndexSet>;
+
+    // use the default traits
+    using Traits = CCMpfaOFacetCouplingDefaultInteractionVolumeTraits< NodalIndexSet, Scalar >;
+public:
+    using type = CCMpfaOFacetCouplingInteractionVolume< Traits >;
+};
+
+//! Use the facet coupling-specific mpfa-o interaction volume
+template<class TypeTag>
+struct SecondaryInteractionVolume<TypeTag, TTag::CCMpfaFacetCouplingModel>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using NodalIndexSet = GetPropType<TypeTag, Properties::DualGridNodalIndexSet>;
+
+    // use the default traits
+    using Traits = CCMpfaOFacetCouplingDefaultInteractionVolumeTraits< NodalIndexSet, Scalar >;
+public:
+    using type = CCMpfaOFacetCouplingInteractionVolume< Traits >;
+};
+
+//! Per default, use the porous medium flow flux variables with the modified upwind scheme
+template<class TypeTag>
+struct FluxVariables<TypeTag, TTag::CCMpfaFacetCouplingModel>
+{
+    using type = PorousMediumFluxVariables<TypeTag,
+                                           CCFacetCouplingUpwindScheme<GetPropType<TypeTag, Properties::FVGridGeometry>>>;
+};
+
+} // namespace Properties
+} // namespace Dumux
+
+#endif
diff --git a/dumux/multidomain/facet/cellcentered/tpfa/couplingmanager.hh b/dumux/multidomain/facet/cellcentered/tpfa/couplingmanager.hh
index 32312fd2a3269405ba47fd37c177b107486c4bd6..96f508b2ea1a7d78889b66c0da976fc4f4a48d93 100644
--- a/dumux/multidomain/facet/cellcentered/tpfa/couplingmanager.hh
+++ b/dumux/multidomain/facet/cellcentered/tpfa/couplingmanager.hh
@@ -97,6 +97,8 @@ class FacetCouplingManager<MDTraits, CouplingMapper, bulkDomainId, lowDimDomainI
     static constexpr auto bulkGridId = CouplingMapper::template gridId<bulkDim>();
     static constexpr auto lowDimGridId = CouplingMapper::template gridId<lowDimDim>();
 
+    static constexpr bool lowDimUsesBox = FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box;
+
     /*!
      * \brief The coupling context of the bulk domain. Contains all data of the lower-
      *        dimensional domain which is required for the computation of a bulk element
@@ -249,25 +251,12 @@ public:
                                                       const SubControlVolumeFace<bulkId>& scvf) const
     {
         assert(bulkContext_.isSet);
-        assert(bulkScvfIsCoupled_[scvf.index()]);
-        assert(scvf.insideScvIdx() == this->problem(bulkId).fvGridGeometry().elementMapper().index(element));
 
+        const auto lowDimElemIdx = getLowDimElementIndex(element, scvf);
         const auto& map = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
-        const auto& couplingData = map.find(scvf.insideScvIdx())->second;
-
-        // search the low dim element idx this scvf is embedded in
-        auto it = std::find_if( couplingData.elementToScvfMap.begin(),
-                                couplingData.elementToScvfMap.end(),
-                                [&scvf] (auto& dataPair)
-                                {
-                                    const auto& scvfs = dataPair.second;
-                                    return std::find(scvfs.begin(), scvfs.end(), scvf.index()) != scvfs.end();
-                                } );
-
-        assert(it != couplingData.elementToScvfMap.end());
-        const auto lowDimElemIdx = it->first;
         const auto& s = map.find(bulkContext_.elementIdx)->second.couplingElementStencil;
         const auto& idxInContext = std::distance( s.begin(), std::find(s.begin(), s.end(), lowDimElemIdx) );
+
         assert(std::find(s.begin(), s.end(), lowDimElemIdx) != s.end());
         return bulkContext_.lowDimVolVars[idxInContext];
     }
@@ -278,12 +267,20 @@ public:
     const Element<lowDimId> getLowDimElement(const Element<bulkId>& element,
                                              const SubControlVolumeFace<bulkId>& scvf) const
     {
-        assert(bulkContext_.isSet);
+        const auto lowDimElemIdx = getLowDimElementIndex(element, scvf);
+        return this->problem(lowDimId).fvGridGeometry().element(lowDimElemIdx);
+    }
+
+    /*!
+     * \brief returns the index of the lower-dimensional element coinciding with a bulk scvf.
+     */
+    const GridIndexType<lowDimId> getLowDimElementIndex(const Element<bulkId>& element,
+                                                        const SubControlVolumeFace<bulkId>& scvf) const
+    {
         assert(bulkScvfIsCoupled_[scvf.index()]);
-        assert(scvf.insideScvIdx() == this->problem(bulkId).fvGridGeometry().elementMapper().index(element));
 
         const auto& map = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
-        const auto& couplingData = map.find(scvf.insideScvIdx())->second;
+        const auto& couplingData = map.at(scvf.insideScvIdx());
 
         // search the low dim element idx this scvf is embedded in
         auto it = std::find_if( couplingData.elementToScvfMap.begin(),
@@ -295,15 +292,13 @@ public:
                                 } );
 
         assert(it != couplingData.elementToScvfMap.end());
-        const auto lowDimElemIdx = it->first;
-        return this->problem(lowDimId).fvGridGeometry().element(lowDimElemIdx);
+        return it->first;
     }
 
     /*!
      * \brief Evaluates the coupling element residual of a bulk domain element with respect
      *        to a dof in the lower-dimensional domain (dofIdxGlobalJ). This is essentially
-     *        the fluxes across the bulk element facets that coincide with the lower-dimensional
-     *        element whose dof idx is dofIdxGlobalJ.
+     *        the fluxes across the bulk element facets that depend on dofIdxGlobalJ.
      */
     template< class BulkLocalAssembler >
     typename LocalResidual<bulkId>::ElementResidualVector
@@ -321,20 +316,24 @@ public:
 
         typename LocalResidual<bulkId>::ElementResidualVector res(1);
         res = 0.0;
-        res[0] = evalBulkFluxes_(bulkLocalAssembler.element(),
-                                 bulkLocalAssembler.fvGeometry(),
-                                 bulkLocalAssembler.curElemVolVars(),
-                                 bulkLocalAssembler.elemFluxVarsCache(),
-                                 bulkLocalAssembler.localResidual(),
-                                 map.find(bulkContext_.elementIdx)->second.dofToCouplingScvfMap.at(dofIdxGlobalJ));
+        res[0] = evalBulkFluxes(bulkLocalAssembler.element(),
+                                bulkLocalAssembler.fvGeometry(),
+                                bulkLocalAssembler.curElemVolVars(),
+                                bulkLocalAssembler.elemFluxVarsCache(),
+                                bulkLocalAssembler.localResidual(),
+                                map.find(bulkContext_.elementIdx)->second.dofToCouplingScvfMap.at(dofIdxGlobalJ));
         return res;
     }
 
     /*!
      * \brief Evaluates the coupling element residual of a lower-dimensional domain element
      *        with respect to a dof in the bulk domain (dofIdxGlobalJ). This is essentially
-     *        the fluxes across the facets of the neighboring bulk element that coincide with
+     *        the fluxes across the facets of the neighboring bulk elements that coincide with
      *        the given element.
+     *
+     * \note The coupling residual in this case is always the entire transfer flux from bulk
+     *       to the lowDim domain. It is therefore independent of the given dof index in the
+     *       bulk domain, which is why we directly forward to the index-independent function.
      */
     template< class LowDimLocalAssembler >
     typename LocalResidual<lowDimId>::ElementResidualVector
@@ -342,6 +341,16 @@ public:
                          const LowDimLocalAssembler& lowDimLocalAssembler,
                          BulkIdType,
                          GridIndexType<bulkId> dofIdxGlobalJ)
+    { return evalCouplingResidual(lowDimId, lowDimLocalAssembler, bulkId); }
+
+    /*!
+     * \brief Evaluates the coupling element residual of a lower-dimensional domain element
+     *        with respect to a dof in the bulk domain (dofIdxGlobalJ). This is essentially
+     *        the fluxes across the facets of the neighboring bulk elements.
+     */
+    template< class LowDimLocalAssembler >
+    typename LocalResidual<lowDimId>::ElementResidualVector
+    evalCouplingResidual(LowDimIdType, const LowDimLocalAssembler& lowDimLocalAssembler, BulkIdType)
     {
         // make sure this is called for the element for which the context was set
         assert(lowDimContext_.isSet);
@@ -382,17 +391,16 @@ public:
             return sources;
 
         assert(lowDimContext_.isSet);
-        const auto& bulkMap = couplingMapperPtr_->couplingMap(bulkGridId, lowDimGridId);
         for (const auto& embedment : it->second.embedments)
-            sources += evalBulkFluxes_(this->problem(bulkId).fvGridGeometry().element(embedment.first),
-                                       *lowDimContext_.bulkFvGeometry,
-                                       *lowDimContext_.bulkElemVolVars,
-                                       *lowDimContext_.bulkElemFluxVarsCache,
-                                       *lowDimContext_.bulkLocalResidual,
-                                       bulkMap.find(embedment.first)->second.elementToScvfMap.at(lowDimContext_.elementIdx));
+            sources += evalBulkFluxes(this->problem(bulkId).fvGridGeometry().element(embedment.first),
+                                      *lowDimContext_.bulkFvGeometry,
+                                      *lowDimContext_.bulkElemVolVars,
+                                      *lowDimContext_.bulkElemFluxVarsCache,
+                                      *lowDimContext_.bulkLocalResidual,
+                                      embedment.second);
 
         // if lowdim domain uses box, we distribute the sources equally among the scvs
-        if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+        if (lowDimUsesBox)
             sources /= fvGeometry.numScv();
 
         return sources;
@@ -436,10 +444,10 @@ public:
                 VolumeVariables<lowDimId> volVars;
 
                 // if low dim domain uses the box scheme, we have to create interpolated vol vars
-                if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+                if (lowDimUsesBox)
                 {
                     const auto elemGeom = elemJ.geometry();
-                    makeInterpolatedVolVars(volVars, ldProblem, ldSol, fvGeom, elemJ, elemGeom, elemGeom.center());
+                    FacetCoupling::makeInterpolatedVolVars(volVars, ldProblem, ldSol, fvGeom, elemJ, elemGeom, elemGeom.center());
                 }
                 // if low dim domain uses a cc scheme we can directly update the vol vars
                 else
@@ -539,7 +547,7 @@ public:
             // find the low-dim elements in coupling stencil, where this dof is contained in
             const auto couplingElements = [&] ()
             {
-                if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+                if (lowDimUsesBox)
                 {
                     std::vector< Element<lowDimId> > lowDimElems;
                     std::for_each( couplingElemStencil.begin(), couplingElemStencil.end(),
@@ -571,10 +579,10 @@ public:
                 auto& volVars = bulkContext_.lowDimVolVars[idxInContext];
                 const auto& fvGeom = bulkContext_.lowDimFvGeometries[idxInContext];
                 // if low dim domain uses the box scheme, we have to create interpolated vol vars
-                if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+                if (lowDimUsesBox)
                 {
                     const auto elemGeom = element.geometry();
-                    makeInterpolatedVolVars(volVars, ldProblem, ldSol, fvGeom, element, elemGeom, elemGeom.center());
+                    FacetCoupling::makeInterpolatedVolVars(volVars, ldProblem, ldSol, fvGeom, element, elemGeom, elemGeom.center());
                 }
                 // if low dim domain uses a cc scheme we can directly update the vol vars
                 else
@@ -692,10 +700,10 @@ public:
             const auto& fvGeom = bulkContext_.lowDimFvGeometries[idxInContext];
             const auto& element = lowDimLocalAssembler.element();
             // if low dim domain uses the box scheme, we have to create interpolated vol vars
-            if (FVGridGeometry<lowDimId>::discMethod == DiscretizationMethod::box)
+            if (lowDimUsesBox)
             {
                 const auto elemGeom = element.geometry();
-                makeInterpolatedVolVars(volVars, ldProblem, ldSol, fvGeom, element, elemGeom, elemGeom.center());
+                FacetCoupling::makeInterpolatedVolVars(volVars, ldProblem, ldSol, fvGeom, element, elemGeom, elemGeom.center());
             }
             // if low dim domain uses a cc scheme we can directly update the vol vars
             else
@@ -755,15 +763,23 @@ public:
     getEmptyStencil(Dune::index_constant<id>) const
     { return std::get<(id == bulkId ? 0 : 1)>(emptyStencilTuple_); }
 
-private:
+protected:
+    //! Return const references to the bulk coupling contexts
+    const BulkCouplingContext& bulkCouplingContext() const { return bulkContext_; }
+    const LowDimCouplingContext& lowDimCouplingContext() const { return lowDimContext_; }
+
+    //! Return references to the bulk coupling contexts
+    BulkCouplingContext& bulkCouplingContext() { return bulkContext_; }
+    LowDimCouplingContext& lowDimCouplingContext() { return lowDimContext_; }
+
     //! evaluates the bulk-facet exchange fluxes for a given facet element
     template<class BulkScvfIndices>
-    NumEqVector<bulkId> evalBulkFluxes_(const Element<bulkId>& elementI,
-                                        const FVElementGeometry<bulkId>& fvGeometry,
-                                        const ElementVolumeVariables<bulkId>& elemVolVars,
-                                        const ElementFluxVariablesCache<bulkId>& elemFluxVarsCache,
-                                        const LocalResidual<bulkId>& localResidual,
-                                        const BulkScvfIndices& scvfIndices) const
+    NumEqVector<bulkId> evalBulkFluxes(const Element<bulkId>& elementI,
+                                       const FVElementGeometry<bulkId>& fvGeometry,
+                                       const ElementVolumeVariables<bulkId>& elemVolVars,
+                                       const ElementFluxVariablesCache<bulkId>& elemFluxVarsCache,
+                                       const LocalResidual<bulkId>& localResidual,
+                                       const BulkScvfIndices& scvfIndices) const
     {
 
         NumEqVector<bulkId> coupledFluxes(0.0);
@@ -777,6 +793,7 @@ private:
         return coupledFluxes;
     }
 
+private:
     std::shared_ptr<CouplingMapper> couplingMapperPtr_;
 
     //! store bools for all bulk elements/scvfs that indicate if they
diff --git a/dumux/multidomain/facet/cellcentered/tpfa/couplingmapper.hh b/dumux/multidomain/facet/cellcentered/tpfa/couplingmapper.hh
index 788c86d11d710fe6712ec5b051c310443f8fe7a1..1bd84f6991eabaa650092a1c06659fe49eff0f26 100644
--- a/dumux/multidomain/facet/cellcentered/tpfa/couplingmapper.hh
+++ b/dumux/multidomain/facet/cellcentered/tpfa/couplingmapper.hh
@@ -23,6 +23,7 @@
 #define DUMUX_CCTPFA_FACETCOUPLING_MAPPER_HH
 
 #include <dune/common/indices.hh>
+#include <dune/common/float_cmp.hh>
 
 #include <dumux/common/indextraits.hh>
 #include <dumux/discretization/method.hh>
@@ -49,6 +50,7 @@ class FacetCouplingMapper<BulkFVG, LowDimFVG, bulkId, lowDimId, DiscretizationMe
 {
     using ParentType = FacetCouplingMapperBase<BulkFVG, LowDimFVG, bulkId, lowDimId>;
     using LowDimElement = typename LowDimFVG::GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename LowDimElement::Geometry::GlobalCoordinate;
 
 public:
     //! export domain ids
@@ -77,6 +79,7 @@ public:
             using LowDimIndexType = typename IndexTraits<typename LowDimFVG::GridView>::GridIndex;
             using BulkIndexType = typename IndexTraits<typename BulkFVG::GridView>::GridIndex;
 
+            const auto lowDimGeometry = lowDimElement.geometry();
             const auto lowDimElemIdx = lowDimFvGridGeometry.elementMapper().index(lowDimElement);
             auto& lowDimData = this->couplingMap_(facetGridId, bulkGridId)[lowDimElemIdx];
 
@@ -109,12 +112,10 @@ public:
                     // otherwise, do float comparison of element and scvf center
                     else
                     {
-                        const auto lowDimGeom = lowDimElement.geometry();
-                        const auto eps = lowDimGeom.volume()*1e-8;
-                        const auto diffVec = lowDimGeom.center()-scvf.center();
+                        const auto eps = lowDimGeometry.volume()*1e-8;
+                        const auto diffVec = lowDimGeometry.center()-scvf.center();
 
-                        using std::abs;
-                        if ( std::all_of(diffVec.begin(), diffVec.end(), [eps] (auto coord) { return abs(coord) < eps; }) )
+                        if ( Dune::FloatCmp::eq<GlobalPosition, Dune::FloatCmp::CmpStyle::absolute>(diffVec, GlobalPosition(0.0), eps) )
                         {
                             embeddedScvfIdx = scvf.index();
                             found = true; break;
@@ -128,9 +129,9 @@ public:
 
                 // add each dof in the low dim element to coupling stencil of the bulk element
                 auto& bulkData = this->couplingMap_(bulkGridId, facetGridId)[bulkElemIdx];
-                const auto lowDimElementDofs = LowDimFVG::discMethod == DiscretizationMethod::cctpfa
-                                               ? std::vector<LowDimIndexType>( {lowDimElemIdx} )
-                                               : this->extractNodalDofs_(lowDimElement, lowDimFvGridGeometry);
+                const auto lowDimElementDofs = LowDimFVG::discMethod == DiscretizationMethod::box
+                                               ? this->extractNodalDofs_(lowDimElement, lowDimFvGridGeometry)
+                                               : std::vector<LowDimIndexType>( {lowDimElemIdx} );
 
                 for (auto dofIdx : lowDimElementDofs)
                 {
diff --git a/dumux/multidomain/facet/couplingmanager.hh b/dumux/multidomain/facet/couplingmanager.hh
index efe446eb740a205e9859903edd8a4a32a2bb3fc0..b6acef4e71904f97659e8d513b38e622144013b9 100644
--- a/dumux/multidomain/facet/couplingmanager.hh
+++ b/dumux/multidomain/facet/couplingmanager.hh
@@ -32,6 +32,7 @@
 #include <dumux/discretization/evalsolution.hh>
 
 namespace Dumux {
+namespace FacetCoupling{
 
 /*!
  * \ingroup FacetCoupling
@@ -69,6 +70,7 @@ void makeInterpolatedVolVars(VolumeVariables& volVars,
     // of this function has to be provided!
     volVars.update(elemSol, problem, element, *scvs(fvGeometry).begin());
 }
+} // end namespace FacetCoupling
 
 /*!
  * \ingroup FacetCoupling
@@ -134,6 +136,7 @@ class FacetCouplingThreeDomainManager
 
     template<std::size_t id> using FVGridGeometry = GetPropType<SubDomainTypeTag<id>, Properties::FVGridGeometry>;
     template<std::size_t id> using FVElementGeometry = typename FVGridGeometry<id>::LocalView;
+    template<std::size_t id> using SubControlVolumeFace = typename FVGridGeometry<id>::SubControlVolumeFace;
     template<std::size_t id> using GridView = typename FVGridGeometry<id>::GridView;
     template<std::size_t id> using GridIndexType = typename IndexTraits<GridView<id>>::GridIndex;
     template<std::size_t id> using Element = typename GridView<id>::template Codim<0>::Entity;
@@ -142,6 +145,11 @@ class FacetCouplingThreeDomainManager
     template<std::size_t id> using ElementVolumeVariables = typename GridVariables<id>::GridVolumeVariables::LocalView;
     template<std::size_t id> using ElementFluxVariablesCache = typename GridVariables<id>::GridFluxVariablesCache::LocalView;
 
+    // helper function to check if a domain uses mpfa
+    template<std::size_t id>
+    static constexpr bool usesMpfa(Dune::index_constant<id> domainId)
+    { return FVGridGeometry<domainId>::discMethod == DiscretizationMethod::ccmpfa; }
+
 public:
     //! types used for coupling stencils
     template<std::size_t i, std::size_t j>
@@ -184,6 +192,12 @@ public:
     using BulkFacetManager::getLowDimVolVars;
     using FacetEdgeManager::getLowDimVolVars;
 
+    using BulkFacetManager::getLowDimElement;
+    using FacetEdgeManager::getLowDimElement;
+
+    using BulkFacetManager::getLowDimElementIndex;
+    using FacetEdgeManager::getLowDimElementIndex;
+
     using BulkFacetManager::evalSourcesFromBulk;
     using FacetEdgeManager::evalSourcesFromBulk;
 
@@ -199,6 +213,40 @@ public:
     using BulkFacetManager::updateCoupledVariables;
     using FacetEdgeManager::updateCoupledVariables;
 
+    using BulkFacetManager::extendJacobianPattern;
+    using FacetEdgeManager::extendJacobianPattern;
+
+    using BulkFacetManager::evalAdditionalDomainDerivatives;
+    using FacetEdgeManager::evalAdditionalDomainDerivatives;
+
+    // extension of the jacobian pattern for the facet domain only occurs
+    // within the bulk-facet coupling & for mpfa being used in the bulk domain.
+    template<class JacobianPattern>
+    void extendJacobianPattern(FacetIdType, JacobianPattern& pattern) const
+    { BulkFacetManager::extendJacobianPattern(facetId, pattern); }
+
+    template<class FacetLocalAssembler, class JacobianMatrixDiagBlock, class GridVariables>
+    void evalAdditionalDomainDerivatives(FacetIdType,
+                                         const FacetLocalAssembler& facetLocalAssembler,
+                                         const typename FacetLocalAssembler::LocalResidual::ElementResidualVector& origResiduals,
+                                         JacobianMatrixDiagBlock& A,
+                                         GridVariables& gridVariables)
+    { BulkFacetManager::evalAdditionalDomainDerivatives(facetId, facetLocalAssembler, origResiduals, A, gridVariables); }
+
+    // Overload required for compatibility with mpfa
+    template<class GetTensor, bool mpfa = usesMpfa(bulkId), std::enable_if_t<mpfa, int> = 0>
+    auto getLowDimTensor(const Element<bulkId>& element,
+                         const SubControlVolumeFace<bulkId>& scvf,
+                         const GetTensor& getT) const
+    { return BulkFacetManager::getLowDimTensor(element, scvf, getT); }
+
+    // Overload required for compatibility with mpfa
+    template<class GetTensor, bool mpfa = usesMpfa(facetId), std::enable_if_t<mpfa, int> = 0>
+    auto getLowDimTensor(const Element<facetId>& element,
+                         const SubControlVolumeFace<facetId>& scvf,
+                         const GetTensor& getT) const
+    { return FacetEdgeManager::getLowDimTensor(element, scvf, getT); }
+
     /*!
      * \brief The coupling stencil of the bulk with the edge domain (empty stencil).
      */
@@ -327,5 +375,6 @@ public:
 // Here, we have to include all available implementations
 #include <dumux/multidomain/facet/box/couplingmanager.hh>
 #include <dumux/multidomain/facet/cellcentered/tpfa/couplingmanager.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/couplingmanager.hh>
 
 #endif
diff --git a/dumux/multidomain/facet/couplingmapper.hh b/dumux/multidomain/facet/couplingmapper.hh
index 149c7a2c31a9d30fa611016549e1c8ef555738fc..1daeb34e358b87cc0d0c08b2431a45c9cb436cfa 100644
--- a/dumux/multidomain/facet/couplingmapper.hh
+++ b/dumux/multidomain/facet/couplingmapper.hh
@@ -138,5 +138,6 @@ public:
 // Here, we have to include all available implementations
 #include <dumux/multidomain/facet/box/couplingmapper.hh>
 #include <dumux/multidomain/facet/cellcentered/tpfa/couplingmapper.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/couplingmapper.hh>
 
 #endif // DUMUX_FACETCOUPLING_COUPLING_MAPPER_HH
diff --git a/dumux/multidomain/facet/gmshreader.hh b/dumux/multidomain/facet/gmshreader.hh
index 6b3f3fd5e580d3a52a977cdbb0a844c8785096bf..60ffa2c19874661ea6d02942fbbea78023d8aa6d 100644
--- a/dumux/multidomain/facet/gmshreader.hh
+++ b/dumux/multidomain/facet/gmshreader.hh
@@ -364,11 +364,17 @@ private:
     {
         // triangles, lines & tetrahedra need no reordering
         if (gt == Dune::GeometryTypes::hexahedron)
-            DUNE_THROW(Dune::NotImplemented, "Reordering of corners for hexahedra");
+        {
+            using std::swap;
+            assert(cornerIndices.size() == 8);
+            swap(cornerIndices[2], cornerIndices[3]);
+            swap(cornerIndices[6], cornerIndices[7]);
+        }
         else if (gt == Dune::GeometryTypes::quadrilateral)
         {
+            using std::swap;
             assert(cornerIndices.size() == 4);
-            std::swap(cornerIndices[2], cornerIndices[3]);
+            swap(cornerIndices[2], cornerIndices[3]);
         }
     }
 
diff --git a/dumux/multidomain/facet/gridmanager.hh b/dumux/multidomain/facet/gridmanager.hh
index e0489cdd00adf6b8e7e6b87b87fc882fdf608627..5366ed14d488e6d48dce9720d6140a6e65fc8f3f 100644
--- a/dumux/multidomain/facet/gridmanager.hh
+++ b/dumux/multidomain/facet/gridmanager.hh
@@ -45,7 +45,7 @@
 #include "gmshreader.hh"
 
 namespace Dumux {
-namespace Detail {
+namespace FCGridManagerChecks {
 
     // The grid creator and grid data classes provided below
     // require that the grids passed as template arguments are
@@ -84,8 +84,8 @@ template<typename... Grids>
 class FacetCouplingGridDataWrapper
 {
     // make sure all grids have the same world dimension and are ordered in descending dimension
-    static_assert(Detail::FulfillConditions<false, Grids...>::value, "All grids must have the same world dimension!");
-    static_assert(Detail::FulfillConditions<true, Grids...>::value, "Grids must be ordered w.r.t the dimension in descending order!");
+    static_assert(FCGridManagerChecks::FulfillConditions<false, Grids...>::value, "All grids must have the same world dimension!");
+    static_assert(FCGridManagerChecks::FulfillConditions<true, Grids...>::value, "Grids must be ordered w.r.t the dimension in descending order!");
 
     //! determine the number of involved grids
     static constexpr std::size_t numGrids = sizeof...(Grids);
@@ -154,8 +154,8 @@ template<typename... Grids>
 class FacetCouplingEmbeddings
 {
     // make sure all grids have the same world dimension and are ordered in descending dimension
-    static_assert(Detail::FulfillConditions<false, Grids...>::value, "All grids must have the same world dimension!");
-    static_assert(Detail::FulfillConditions<true, Grids...>::value, "Grids must be ordered w.r.t the dimension in descending order!");
+    static_assert(FCGridManagerChecks::FulfillConditions<false, Grids...>::value, "All grids must have the same world dimension!");
+    static_assert(FCGridManagerChecks::FulfillConditions<true, Grids...>::value, "Grids must be ordered w.r.t the dimension in descending order!");
 
     //! the i-th grid type
     template<std::size_t id> using Grid = typename std::tuple_element_t<id, std::tuple<Grids...>>;
@@ -284,8 +284,8 @@ template<typename... Grids>
 class FacetCouplingGridManager
 {
     // make sure all grids have the same world dimension and are ordered in descending dimension
-    static_assert(Detail::FulfillConditions<false, Grids...>::value, "All grids must have the same world dimension!");
-    static_assert(Detail::FulfillConditions<true, Grids...>::value, "Grids must be ordered w.r.t the dimension in descending order!");
+    static_assert(FCGridManagerChecks::FulfillConditions<false, Grids...>::value, "All grids must have the same world dimension!");
+    static_assert(FCGridManagerChecks::FulfillConditions<true, Grids...>::value, "Grids must be ordered w.r.t the dimension in descending order!");
 
     // we use a wrapper class for the grid data containing the data on all grids
     using GridDataWrapper = FacetCouplingGridDataWrapper<Grids...>;
diff --git a/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt b/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt
index 50a1bded8f6452a4a4f74c14242929aa7ce36aec..bb7170d24cf78741b6ce42fbba0399bc2a171977 100644
--- a/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt
+++ b/test/multidomain/facet/1p_1p/gravity/CMakeLists.txt
@@ -8,27 +8,64 @@ target_compile_definitions(test_md_facet_1p1p_gravity_tpfa
                                   LOWDIMGRIDTYPE=Dune::FoamGrid<1,2>
                                   BULKGRIDTYPE=Dune::ALUGrid<2,2,Dune::cube,Dune::nonconforming>)
 
+add_executable(test_md_facet_1p1p_gravity_mpfa EXCLUDE_FROM_ALL main.cc)
+target_compile_definitions(test_md_facet_1p1p_gravity_mpfa
+                           PUBLIC BULKTYPETAG=OnePBulkMpfa
+                                  LOWDIMTYPETAG=OnePLowDimMpfa
+                                  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")
+                        --files ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_tpfa_bulk-00000.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_tpfa_bulk-00001.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_tpfa_lowdim-00000.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_tpfa_lowdim-00001.vtp
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_tpfa params.input \
+                                                              -Vtk.OutputName test_md_facet_1p1p_gravity_xi1_tpfa")
 
-dune_add_test(NAME test_facet_1p1p_gravity_xi066_tpfa
+dune_add_test(NAME test_md_facet_1p1p_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
+                        --files ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_tpfa_bulk-00000.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_tpfa_bulk-00001.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_tpfa_lowdim-00000.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_tpfa_lowdim-00001.vtp
                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_tpfa params.input  \
-                                                               -FacetCoupling.Xi 0.66 -Vtk.OutputName test_md_facet_1p1p_gravity_xi066")
+                                                               -FacetCoupling.Xi 0.66 -Vtk.OutputName test_md_facet_1p1p_gravity_xi066_tpfa")
+
+
+
+dune_add_test(NAME test_md_facet_1p1p_gravity_xi1_mpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_gravity_mpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_mpfa_bulk-00000.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_mpfa_bulk-00001.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_mpfa_lowdim-00000.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi1_mpfa_lowdim-00001.vtp
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_mpfa params.input \
+                                                              -Vtk.OutputName test_md_facet_1p1p_gravity_xi1_mpfa")
+
+dune_add_test(NAME test_md_facet_1p1p_gravity_xi066_mpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_gravity_mpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_mpfa_bulk-00000.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_mpfa_bulk-00001.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_mpfa_lowdim-00000.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_xi066_mpfa_lowdim-00001.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_gravity_mpfa params.input  \
+                                                               -FacetCoupling.Xi 0.66
+                                                               -Vtk.OutputName test_md_facet_1p1p_gravity_xi066_mpfa")
diff --git a/test/multidomain/facet/1p_1p/gravity/main.cc b/test/multidomain/facet/1p_1p/gravity/main.cc
index 860c1e5136d1f0ee5c3675bded23a12b4369509c..2427a2d5b1c7c553eafc15bbf069cfcb8ca1a147 100644
--- a/test/multidomain/facet/1p_1p/gravity/main.cc
+++ b/test/multidomain/facet/1p_1p/gravity/main.cc
@@ -67,9 +67,11 @@ namespace Properties {
 
 // set cm property in the sub-problems
 using TpfaTraits = TestTraits<TTag::OnePBulkTpfa, TTag::OnePLowDimTpfa>;
+using MpfaTraits = TestTraits<TTag::OnePBulkMpfa, TTag::OnePLowDimMpfa>;
 template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePBulkTpfa> { using type = typename TpfaTraits::CouplingManager; };
 template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePLowDimTpfa> { using type = typename TpfaTraits::CouplingManager; };
-
+template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePBulkMpfa> { using type = typename MpfaTraits::CouplingManager; };
+template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePLowDimMpfa> { using type = typename MpfaTraits::CouplingManager; };
 } // end namespace Properties
 } // end namespace Dumux
 
diff --git a/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh b/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh
index 3d42f9c0612803f643db6ed1bda524c4003703aa..a029617b91129ceec18f1eb51d9386112d401cc2 100644
--- a/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh
+++ b/test/multidomain/facet/1p_1p/gravity/problem_bulk.hh
@@ -31,6 +31,7 @@
 
 #include <dumux/multidomain/facet/box/properties.hh>
 #include <dumux/multidomain/facet/cellcentered/tpfa/properties.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/properties.hh>
 
 #include <dumux/porousmediumflow/problem.hh>
 #include <dumux/porousmediumflow/1p/model.hh>
@@ -51,6 +52,7 @@ namespace Properties {
 namespace TTag {
 struct OnePBulk { using InheritsFrom = std::tuple<OneP>; };
 struct OnePBulkTpfa { using InheritsFrom = std::tuple<CCTpfaFacetCouplingModel, OnePBulk>; };
+struct OnePBulkMpfa { using InheritsFrom = std::tuple<CCMpfaFacetCouplingModel, OnePBulk>; };
 } // end namespace TTag
 
 // Set the grid type
diff --git a/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh b/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh
index 069a7ed1a31b04d6b9f4dc6e426a42d44fae738f..a2f1c82933bcfb1e1e3ffd43c620420f935ad348 100644
--- a/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh
+++ b/test/multidomain/facet/1p_1p/gravity/problem_lowdim.hh
@@ -52,6 +52,9 @@ namespace Properties {
 namespace TTag {
 struct OnePLowDim { using InheritsFrom = std::tuple<OneP>; };
 struct OnePLowDimTpfa { using InheritsFrom = std::tuple<OnePLowDim, CCTpfaModel>; };
+
+// we need an additional type tag for the test using mpfa in the bulk domain
+struct OnePLowDimMpfa { using InheritsFrom = std::tuple<OnePLowDim, CCTpfaModel>; };
 } // end namespace TTag
 
 // Set the grid type
diff --git a/test/multidomain/facet/1p_1p/linearprofile/CMakeLists.txt b/test/multidomain/facet/1p_1p/linearprofile/CMakeLists.txt
index 251a1dc764234ef900269f7c1a4e4ae1184acc62..01ec53a3247d226a29217f7245c4292844321ed6 100644
--- a/test/multidomain/facet/1p_1p/linearprofile/CMakeLists.txt
+++ b/test/multidomain/facet/1p_1p/linearprofile/CMakeLists.txt
@@ -14,6 +14,20 @@ target_compile_definitions(test_md_facet_1p1p_linearprofile_surface_tpfa
                                   LOWDIMGRIDTYPE=Dune::FoamGrid<1,3>
                                   BULKGRIDTYPE=Dune::ALUGrid<2,3,Dune::cube,Dune::nonconforming>)
 
+add_executable(test_md_facet_1p1p_linearprofile_mpfa EXCLUDE_FROM_ALL main.cc)
+target_compile_definitions(test_md_facet_1p1p_linearprofile_mpfa
+                           PUBLIC BULKTYPETAG=OnePBulkMpfa
+                                  LOWDIMTYPETAG=OnePLowDimMpfa
+                                  LOWDIMGRIDTYPE=Dune::FoamGrid<1,2>
+                                  BULKGRIDTYPE=Dune::ALUGrid<2,2,Dune::cube,Dune::nonconforming>)
+
+add_executable(test_md_facet_1p1p_linearprofile_surface_mpfa EXCLUDE_FROM_ALL main.cc)
+target_compile_definitions(test_md_facet_1p1p_linearprofile_surface_mpfa
+                            PUBLIC BULKTYPETAG=OnePBulkMpfa
+                                   LOWDIMTYPETAG=OnePLowDimMpfa
+                                   LOWDIMGRIDTYPE=Dune::FoamGrid<1,3>
+                                   BULKGRIDTYPE=Dune::ALUGrid<2,3,Dune::cube,Dune::nonconforming>)
+
 dune_add_test(NAME test_md_facet_1p1p_linearprofile_xi1_tpfa
               LABELS multidomain
               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
@@ -66,3 +80,57 @@ dune_add_test(NAME test_md_facet_1p1p_linearprofile_surface_xi066_tpfa
                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_tpfa params.input \
                                                                -FacetCoupling.Xi 0.66 \
                                                                -Vtk.OutputName test_md_facet_1p1p_linearprofile_surface_xi066_tpfa")
+
+dune_add_test(NAME test_md_facet_1p1p_linearprofile_xi1_mpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_linearprofile_mpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_tpfa_bulk-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_xi1_mpfa_bulk-00001.vtu
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_tpfa_lowdim-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_xi1_mpfa_lowdim-00001.vtp
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_mpfa params.input \
+                                                              -Vtk.OutputName test_md_facet_1p1p_linearprofile_xi1_mpfa")
+
+dune_add_test(NAME test_md_facet_1p1p_linearprofile_xi066_mpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_linearprofile_mpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_tpfa_bulk-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_xi066_mpfa_bulk-00001.vtu
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_tpfa_lowdim-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_xi066_mpfa_lowdim-00001.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_mpfa params.input \
+                                                            -FacetCoupling.Xi 0.66 \
+                                                            -Vtk.OutputName test_md_facet_1p1p_linearprofile_xi066_mpfa")
+
+dune_add_test(NAME test_md_facet_1p1p_linearprofile_surface_xi1_mpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_linearprofile_surface_mpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_surface_tpfa_bulk-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_xi1_mpfa_bulk-00001.vtu
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_surface_tpfa_lowdim-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_xi1_mpfa_lowdim-00001.vtp
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_mpfa params.input \
+                                                              -Vtk.OutputName test_md_facet_1p1p_linearprofile_surface_xi1_mpfa")
+
+dune_add_test(NAME test_md_facet_1p1p_linearprofile_surface_xi066_mpfa
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              TARGET test_md_facet_1p1p_linearprofile_surface_mpfa
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_surface_tpfa_bulk-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_xi066_mpfa_bulk-00001.vtu
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1p1p_linearprofile_surface_tpfa_lowdim-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_xi066_mpfa_lowdim-00001.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1p1p_linearprofile_surface_mpfa params.input \
+                                                               -FacetCoupling.Xi 0.66 \
+                                                               -Vtk.OutputName test_md_facet_1p1p_linearprofile_surface_xi066_mpfa")
diff --git a/test/multidomain/facet/1p_1p/linearprofile/grids/linear.geo b/test/multidomain/facet/1p_1p/linearprofile/grids/linear.geo
deleted file mode 100644
index 98e981970ce4ece29a9825ea354ffc57254c95b3..0000000000000000000000000000000000000000
--- a/test/multidomain/facet/1p_1p/linearprofile/grids/linear.geo
+++ /dev/null
@@ -1,34 +0,0 @@
-// domain measures
-xmax = 3.0;
-ymax = 1.0;
-
-// use zmax != 0 to produce a surface grid
-zmax = 0.0;
-
-// discretization specifics
-numCellsX = 120;
-numCellsY = 40;
-
-Point(1) = {0.0, 0.0, 0.0};
-Point(2) = {xmax/2.0, 0.0, zmax/2.0};
-Point(3) = {xmax, 0.0, zmax};
-Point(4) = {xmax, ymax, zmax};
-Point(5) = {xmax/2.0,ymax, zmax/2.0};
-Point(6) = {0.0, ymax, 0.0};
-
-Line(1) = {1, 2}; Transfinite Line{1} = numCellsX/2;
-Line(2) = {2, 3}; Transfinite Line{2} = numCellsX/2;
-Line(3) = {3, 4}; Transfinite Line{3} = numCellsY;
-Line(4) = {4, 5}; Transfinite Line{4} = numCellsX/2;
-Line(5) = {5, 6}; Transfinite Line{5} = numCellsX/2;
-Line(6) = {6, 1}; Transfinite Line{6} = numCellsY;
-Line(7) = {2, 5}; Transfinite Line{7} = numCellsY;
-
-Line Loop(1) = {1, 7, 5, 6};
-Line Loop(2) = {2, 3, 4, -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/linearprofile/main.cc b/test/multidomain/facet/1p_1p/linearprofile/main.cc
index 385cb4b3dc4c53acb21b263a2d186a99ad7a306f..5bab625497b569af6af43de13d37dde9b84e8445 100644
--- a/test/multidomain/facet/1p_1p/linearprofile/main.cc
+++ b/test/multidomain/facet/1p_1p/linearprofile/main.cc
@@ -66,9 +66,11 @@ namespace Properties {
 
 // set cm property in the sub-problems
 using TpfaTraits = TestTraits<TTag::OnePBulkTpfa, TTag::OnePLowDimTpfa>;
+using MpfaTraits = TestTraits<TTag::OnePBulkMpfa, TTag::OnePLowDimMpfa>;
 template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePBulkTpfa> { using type = typename TpfaTraits::CouplingManager; };
 template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePLowDimTpfa> { using type = typename TpfaTraits::CouplingManager; };
-
+template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePBulkMpfa> { using type = typename MpfaTraits::CouplingManager; };
+template<class TypeTag> struct CouplingManager<TypeTag, TTag::OnePLowDimMpfa> { using type = typename MpfaTraits::CouplingManager; };
 } // end namespace Properties
 } // end namespace Dumux
 
diff --git a/test/multidomain/facet/1p_1p/linearprofile/problem_bulk.hh b/test/multidomain/facet/1p_1p/linearprofile/problem_bulk.hh
index 9c05b4d0e4c25e2f17bf87a2143ee9ffbe1ef2cb..9d97606c64014315d540202aec8dd2dfe7ee5ab5 100644
--- a/test/multidomain/facet/1p_1p/linearprofile/problem_bulk.hh
+++ b/test/multidomain/facet/1p_1p/linearprofile/problem_bulk.hh
@@ -31,6 +31,7 @@
 
 #include <dumux/multidomain/facet/box/properties.hh>
 #include <dumux/multidomain/facet/cellcentered/tpfa/properties.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/properties.hh>
 
 #include <dumux/porousmediumflow/problem.hh>
 #include <dumux/porousmediumflow/1p/model.hh>
@@ -52,6 +53,7 @@ namespace Properties {
 namespace TTag {
 struct OnePBulk { using InheritsFrom = std::tuple<OneP>; };
 struct OnePBulkTpfa { using InheritsFrom = std::tuple<CCTpfaFacetCouplingModel, OnePBulk>; };
+struct OnePBulkMpfa { using InheritsFrom = std::tuple<CCMpfaFacetCouplingModel, OnePBulk>; };
 } // end namespace TTag
 
 // Set the grid type
diff --git a/test/multidomain/facet/1p_1p/linearprofile/problem_lowdim.hh b/test/multidomain/facet/1p_1p/linearprofile/problem_lowdim.hh
index dd77c2e7a7894750c86b6ff6683bbd8ac16363d3..73ce6e708b2e4087fa2fb3906dfd3060f5b87d21 100644
--- a/test/multidomain/facet/1p_1p/linearprofile/problem_lowdim.hh
+++ b/test/multidomain/facet/1p_1p/linearprofile/problem_lowdim.hh
@@ -52,6 +52,9 @@ namespace Properties {
 namespace TTag {
 struct OnePLowDim { using InheritsFrom = std::tuple<OneP>; };
 struct OnePLowDimTpfa { using InheritsFrom = std::tuple<OnePLowDim, CCTpfaModel>; };
+
+// for the test using mpfa in the bulk domain we need an additional type tag
+struct OnePLowDimMpfa { using InheritsFrom = std::tuple<OnePLowDim, CCTpfaModel>; };
 } // end namespace TTag
 
 // Set the grid type
diff --git a/test/multidomain/facet/CMakeLists.txt b/test/multidomain/facet/CMakeLists.txt
index fab4a712a60b417e065500c9e43d82f438c321ad..d5776afddb3af7870d34865025ac963b27855fc8 100644
--- a/test/multidomain/facet/CMakeLists.txt
+++ b/test/multidomain/facet/CMakeLists.txt
@@ -35,6 +35,24 @@ dune_add_test(NAME test_facetcouplingmapper_tpfa_ug
              COMMAND ./test_facetcouplingmapper_tpfa_ug
              CMD_ARGS test_gridmanager.input)
 
+dune_add_test(NAME test_facetcouplingmapper_mpfa_alu
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              COMPILE_DEFINITIONS BULKGRIDTYPE=Dune::ALUGrid<3,3,Dune::simplex,Dune::conforming>
+              COMPILE_DEFINITIONS USEMPFAINBULK=true
+              SOURCES test_facetcouplingmapper.cc
+              COMMAND ./test_facetcouplingmapper_mpfa_alu
+              CMD_ARGS test_gridmanager.input)
+
+dune_add_test(NAME test_facetcouplingmapper_mpfa_ug
+              LABELS multidomain
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              COMPILE_DEFINITIONS BULKGRIDTYPE=Dune::UGGrid<3>
+              COMPILE_DEFINITIONS USEMPFAINBULK=true
+              SOURCES test_facetcouplingmapper.cc
+              COMMAND ./test_facetcouplingmapper_mpfa_ug
+              CMD_ARGS test_gridmanager.input)
+
 dune_add_test(NAME test_facetcouplingmapper_box_alu
               LABELS multidomain
               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
diff --git a/test/multidomain/facet/test_facetcouplingmapper.cc b/test/multidomain/facet/test_facetcouplingmapper.cc
index 91a7dd8d3e67622f10ab637f14b0f2beaa3e62c0..bb903d4b7e02c0ea36ca8367e7bbee9db27591a8 100644
--- a/test/multidomain/facet/test_facetcouplingmapper.cc
+++ b/test/multidomain/facet/test_facetcouplingmapper.cc
@@ -19,7 +19,7 @@
 /*!
  * \file
  * \ingroup FacetTests
- * \brief Tests the grid creator class for models using facet coupling.
+ * \brief Tests the coupling mapper class for models using facet coupling.
  */
 
 #include <config.h>
@@ -36,6 +36,10 @@
 #include <dumux/common/parameters.hh>
 #include <dumux/discretization/method.hh>
 #include <dumux/discretization/cellcentered/tpfa/fvgridgeometry.hh>
+#include <dumux/discretization/cellcentered/mpfa/fvgridgeometry.hh>
+#include <dumux/discretization/cellcentered/mpfa/fvgridgeometrytraits.hh>
+#include <dumux/discretization/cellcentered/mpfa/dualgridindexset.hh>
+#include <dumux/discretization/cellcentered/mpfa/omethod/interactionvolume.hh>
 #include <dumux/multidomain/facet/box/fvgridgeometry.hh>
 #include <dumux/multidomain/facet/gridmanager.hh>
 #include <dumux/multidomain/facet/couplingmapper.hh>
@@ -49,7 +53,25 @@
 #define USEBOXINBULK 0
 #endif
 
-//! Computes the average distance of corners to the center of a geometry.
+#ifndef USEMPFAINBULK // default to tpfa if not specified otherwise
+#define USEMPFAINBULK 0
+#endif
+
+//! Helper class to define the MpfaFVGridGeometry
+template<class GridView>
+struct MpfaGridGeometryTraits
+{
+private:
+    using NITraits = Dumux::NodalIndexSetDefaultTraits< GridView >;
+    using IndexSet = Dumux::CCMpfaDualGridNodalIndexSet< NITraits >;
+    using IVTraits = Dumux::CCMpfaODefaultInteractionVolumeTraits< IndexSet, double >;
+    using IV = Dumux::CCMpfaOInteractionVolume< IVTraits >;
+    using GGTraits = Dumux::CCMpfaFVGridGeometryTraits<GridView, IndexSet, IV, IV>;
+public:
+    using type = Dumux::CCMpfaFVGridGeometry<GridView, GGTraits, /*enableCache*/true>;
+};
+
+//! Computes the average distance of corners to the center of a geometry
 template<class Geometry>
 typename Geometry::ctype averageCornerDistance(const Geometry& geometry)
 {
@@ -76,7 +98,7 @@ void checkScvfEmbedment(const Scvf& scvf, const LowDimGeom& lowDimGeom)
 
 //! Updates a tpfa finite volume grid geometry.
 template< class BulkFVG, class FacetFVG, class GridManager,
-          std::enable_if_t<BulkFVG::discMethod == Dumux::DiscretizationMethod::cctpfa, int> = 0 >
+          std::enable_if_t<BulkFVG::discMethod != Dumux::DiscretizationMethod::box, int> = 0 >
 void updateBulkFvGeometry(BulkFVG& bulkFVG, const FacetFVG& facetFVG, const GridManager& gm)
 {
     bulkFVG.update();
@@ -109,10 +131,17 @@ int main (int argc, char *argv[]) try
     gridManager.init();
 
     // instantiate the grid geometries with caching
+    static_assert(!USEBOXINBULK || !USEMPFAINBULK, "Bulk discretization method not uniquely defined");
+
     using BulkGridView = typename BulkGrid::LeafGridView;
+    using TpfaFVGridGeometry = Dumux::CCTpfaFVGridGeometry<BulkGridView, /*caching*/true>;
+    using MpfaFVGridGeometry = typename MpfaGridGeometryTraits<BulkGridView>::type;
+    using BoxFVGridGeometry = Dumux::BoxFacetCouplingFVGridGeometry<double, BulkGridView, true>;
     using BulkFVGridGeometry = typename std::conditional< USEBOXINBULK,
-                                                          Dumux::BoxFacetCouplingFVGridGeometry<double, BulkGridView, true>,
-                                                          Dumux::CCTpfaFVGridGeometry<BulkGridView, /*caching*/true> >::type;
+                                                          BoxFVGridGeometry,
+                                                          typename std::conditional<USEMPFAINBULK,
+                                                                                    MpfaFVGridGeometry,
+                                                                                    TpfaFVGridGeometry>::type >::type;
     BulkFVGridGeometry bulkFvGeometry( gridManager.grid<0>().leafGridView() );
 
     using FacetGridView = typename FacetGrid::LeafGridView;
@@ -148,10 +177,16 @@ int main (int argc, char *argv[]) try
         // check both the map from the bulk facet as well as from the hierarchy mapper
         const auto& bulkFacetMap = i == 0 ? bulkFacetMapper.couplingMap(bulkDomainId, facetDomainId)
                                           : hierarchyMapper.couplingMap(bulkDomainId, facetDomainId);
-        if (bulkFacetMap.size() != 56)
-            DUNE_THROW(Dune::InvalidStateException, "BulkFacetMap has " << bulkFacetMap.size() << " instead of 56 entries");
+
+        const std::size_t expectedNoEntries = USEMPFAINBULK ? 263 : 56;
+        if (bulkFacetMap.size() != expectedNoEntries)
+            DUNE_THROW(Dune::InvalidStateException, "BulkFacetMap has " << bulkFacetMap.size() << " instead of " << expectedNoEntries << " entries");
         else
-            std::cout << "Found 56 entries in bulk-facet map" << std::endl;
+            std::cout << "Found " << expectedNoEntries << " entries in bulk-facet map" << std::endl;
+
+        // The rest is too cumbersome to test for mpfa
+        if (USEMPFAINBULK)
+            continue;
 
         std::size_t singleCouplings = 0;
         std::size_t doubleCouplings = 0;
@@ -214,11 +249,15 @@ int main (int argc, char *argv[]) try
         {
             const auto lowDimGeom = facetFvGeometry.element(entry.first).geometry();
 
-            const auto cStencilSize = entry.second.couplingStencil.size();
-            const std::vector<unsigned int> possibleStencilSizes = USEBOXINBULK ? std::vector<unsigned int>{6, 7, 8}
-                                                                                : std::vector<unsigned int>{2};
-            if ( !std::count(possibleStencilSizes.begin(), possibleStencilSizes.end(), cStencilSize) )
-                DUNE_THROW(Dune::InvalidStateException, "Coupling stencil size of " << cStencilSize << " is invalid");
+            // stencil sizes are too cumbersome to test for mpfa
+            if (!USEMPFAINBULK)
+            {
+                const auto cStencilSize = entry.second.couplingStencil.size();
+                const std::vector<unsigned int> possibleStencilSizes = USEBOXINBULK ? std::vector<unsigned int>{6, 7, 8}
+                                                                                    : std::vector<unsigned int>{2};
+                if ( !std::count(possibleStencilSizes.begin(), possibleStencilSizes.end(), cStencilSize) )
+                    DUNE_THROW(Dune::InvalidStateException, "Coupling stencil size of " << cStencilSize << " is invalid");
+            }
 
             for (const auto& embedment : entry.second.embedments)
             {
diff --git a/test/multidomain/facet/test_facetcouplingmapper_boundary.cc b/test/multidomain/facet/test_facetcouplingmapper_boundary.cc
index 16c8aed12e9a4b56b07b9e9ee00f5e9316ef3703..5f42fea4712f1f0896bb024692a89db670d1cc1b 100644
--- a/test/multidomain/facet/test_facetcouplingmapper_boundary.cc
+++ b/test/multidomain/facet/test_facetcouplingmapper_boundary.cc
@@ -19,7 +19,7 @@
 /*!
  * \file
  * \ingroup FacetTests
- * \brief Tests the grid creator class for models using facet coupling.
+ * \brief Tests the coupling mapper class for models using facet coupling.
  */
 
 #include <config.h>
diff --git a/test/multidomain/facet/test_gridmanager.cc b/test/multidomain/facet/test_gridmanager.cc
index c5b91dbab4a61ff01cd6675ed030b1ca43f7ec5e..8a14d9725c81aeca4a06c7a934ed047ea96b9971 100644
--- a/test/multidomain/facet/test_gridmanager.cc
+++ b/test/multidomain/facet/test_gridmanager.cc
@@ -19,7 +19,7 @@
 /*!
  * \file
  * \ingroup FacetTests
- * \brief Tests the grid creator class for models using facet coupling.
+ * \brief Tests the grid manager class for models using facet coupling.
  */
 
 #include <config.h>
diff --git a/test/multidomain/facet/test_vertexmapper.cc b/test/multidomain/facet/test_vertexmapper.cc
index 1c155597feb009b378a8b3737e577ef44ff12b91..7a0c07b05ddbb65fbeb446e05fc33ac225590253 100644
--- a/test/multidomain/facet/test_vertexmapper.cc
+++ b/test/multidomain/facet/test_vertexmapper.cc
@@ -19,7 +19,7 @@
 /*!
  * \file
  * \ingroup FacetTests
- * \brief Tests the grid creator class for models using facet coupling.
+ * \brief Tests the vertex mapper class for models using facet coupling.
  */
 
 #include <config.h>
diff --git a/test/multidomain/facet/tracer_tracer/CMakeLists.txt b/test/multidomain/facet/tracer_tracer/CMakeLists.txt
index 7a47170bd1f5c02f9a8372c1201dcd928ae29279..cfdb893ce248f652f8e69856eab6b8bcc52f623a 100644
--- a/test/multidomain/facet/tracer_tracer/CMakeLists.txt
+++ b/test/multidomain/facet/tracer_tracer/CMakeLists.txt
@@ -21,6 +21,27 @@ dune_add_test(NAME test_md_facet_tracertracer_tpfa
                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_tracertracer_tpfa params.input \
                                                               -Vtk.OutputName test_md_facet_tracertracer_tpfa")
 
+dune_add_test(NAME test_md_facet_tracertracer_mpfa
+              LABELS multidomain
+              SOURCES main.cc
+              COMPILE_DEFINITIONS ONEPBULKTYPETAG=OnePBulkMpfa
+              COMPILE_DEFINITIONS ONEPLOWDIMTYPETAG=OnePLowDimMpfa
+              COMPILE_DEFINITIONS TRACERBULKTYPETAG=TracerBulkMpfa
+              COMPILE_DEFINITIONS TRACERLOWDIMTYPETAG=TracerLowDimMpfa
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_tracertracer_mpfa_onep_bulk-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_tracertracer_mpfa_onep_bulk-00000.vtu
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_tracertracer_mpfa_onep_lowdim-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_tracertracer_mpfa_onep_lowdim-00000.vtp
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_tracertracer_mpfa_tracer_bulk-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_tracertracer_mpfa_tracer_bulk-00010.vtu
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_tracertracer_mpfa_tracer_lowdim-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_tracertracer_mpfa_tracer_lowdim-00010.vtp
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_tracertracer_mpfa params.input \
+                                                              -Vtk.OutputName test_md_facet_tracertracer_mpfa")
+
 dune_add_test(NAME test_md_facet_tracertracer_box
               LABELS multidomain
               SOURCES main.cc
diff --git a/test/multidomain/facet/tracer_tracer/main.cc b/test/multidomain/facet/tracer_tracer/main.cc
index 7763851b360ba71e3c1b7b72f4c67529aca4f6e0..9523a4f844093986f2914b76c2f74beb1cbf71f8 100644
--- a/test/multidomain/facet/tracer_tracer/main.cc
+++ b/test/multidomain/facet/tracer_tracer/main.cc
@@ -97,6 +97,18 @@ struct CouplingManager<TypeTag, TTag::TracerBulkTpfa> { using type = typename Tp
 template<class TypeTag>
 struct CouplingManager<TypeTag, TTag::TracerLowDimTpfa> { using type = typename TpfaTracerTraits::CouplingManager; };
 
+// set cm property for the mpfa test
+using MpfaTraits = TestTraits<Properties::TTag::OnePBulkMpfa, Properties::TTag::OnePLowDimMpfa>;
+using MpfaTracerTraits = TestTraits<Properties::TTag::TracerBulkMpfa, Properties::TTag::TracerLowDimMpfa>;
+template<class TypeTag>
+struct CouplingManager<TypeTag, TTag::OnePBulkMpfa> { using type = typename MpfaTraits::CouplingManager; };
+template<class TypeTag>
+struct CouplingManager<TypeTag, TTag::OnePLowDimMpfa> { using type = typename MpfaTraits::CouplingManager; };
+template<class TypeTag>
+struct CouplingManager<TypeTag, TTag::TracerBulkMpfa> { using type = typename MpfaTracerTraits::CouplingManager; };
+template<class TypeTag>
+struct CouplingManager<TypeTag, TTag::TracerLowDimMpfa> { using type = typename MpfaTracerTraits::CouplingManager; };
+
 } // end namespace Properties
 } // end namespace Dumux
 
diff --git a/test/multidomain/facet/tracer_tracer/problem_1p_bulk.hh b/test/multidomain/facet/tracer_tracer/problem_1p_bulk.hh
index af08f05f68346cc0e2bf170c6b7c56d4556f0ca2..b46b0ad6c15994f81ed69bcf4c5b710868337f35 100644
--- a/test/multidomain/facet/tracer_tracer/problem_1p_bulk.hh
+++ b/test/multidomain/facet/tracer_tracer/problem_1p_bulk.hh
@@ -33,6 +33,7 @@
 
 #include <dumux/multidomain/facet/box/properties.hh>
 #include <dumux/multidomain/facet/cellcentered/tpfa/properties.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/properties.hh>
 
 #include <dumux/porousmediumflow/problem.hh>
 #include <dumux/porousmediumflow/1p/model.hh>
@@ -49,6 +50,7 @@ namespace Properties {
 namespace TTag {
 struct OnePBulk { using InheritsFrom = std::tuple<OneP>; };
 struct OnePBulkTpfa { using InheritsFrom = std::tuple<CCTpfaFacetCouplingModel, OnePBulk>; };
+struct OnePBulkMpfa { using InheritsFrom = std::tuple<CCMpfaFacetCouplingModel, OnePBulk>; };
 struct OnePBulkBox { using InheritsFrom = std::tuple<BoxFacetCouplingModel, OnePBulk>; };
 } // end namespace TTag
 
diff --git a/test/multidomain/facet/tracer_tracer/problem_1p_lowdim.hh b/test/multidomain/facet/tracer_tracer/problem_1p_lowdim.hh
index 4c4854d4f982fc75f572556e61abad55fc7cb4c5..8794e7c11130f9d9a33fc8f5e7ff77f3c173c33b 100644
--- a/test/multidomain/facet/tracer_tracer/problem_1p_lowdim.hh
+++ b/test/multidomain/facet/tracer_tracer/problem_1p_lowdim.hh
@@ -49,6 +49,7 @@ namespace Properties {
 namespace TTag {
 struct OnePLowDim { using InheritsFrom = std::tuple<OneP>; };
 struct OnePLowDimTpfa { using InheritsFrom = std::tuple<OnePLowDim, CCTpfaModel>; };
+struct OnePLowDimMpfa { using InheritsFrom = std::tuple<OnePLowDim, CCTpfaModel>; };
 struct OnePLowDimBox { using InheritsFrom = std::tuple<OnePLowDim, BoxModel>; };
 } // end namespace TTag
 
diff --git a/test/multidomain/facet/tracer_tracer/problem_tracer_bulk.hh b/test/multidomain/facet/tracer_tracer/problem_tracer_bulk.hh
index d073fe1b53a2533e3579ec57ff48fc0991ec9c0d..414f6bbed0a98e7c5226c27184b02decabbe64b4 100644
--- a/test/multidomain/facet/tracer_tracer/problem_tracer_bulk.hh
+++ b/test/multidomain/facet/tracer_tracer/problem_tracer_bulk.hh
@@ -29,6 +29,7 @@
 
 #include <dumux/multidomain/facet/box/properties.hh>
 #include <dumux/multidomain/facet/cellcentered/tpfa/properties.hh>
+#include <dumux/multidomain/facet/cellcentered/mpfa/properties.hh>
 
 #include <dumux/porousmediumflow/tracer/model.hh>
 #include <dumux/porousmediumflow/problem.hh>
@@ -51,6 +52,7 @@ struct TracerTestBulk { using InheritsFrom = std::tuple<Tracer>; };
 
 // define the type tags
 struct TracerBulkTpfa { using InheritsFrom = std::tuple<CCTpfaFacetCouplingModel, TracerTestBulk>; };
+struct TracerBulkMpfa { using InheritsFrom = std::tuple<CCMpfaFacetCouplingModel, TracerTestBulk>; };
 struct TracerBulkBox { using InheritsFrom = std::tuple<BoxFacetCouplingModel, TracerTestBulk>; };
 } // end namespace TTag
 
@@ -110,6 +112,7 @@ class TracerBulkProblem : public PorousMediumFlowProblem<TypeTag>
     using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
     using GridView = GetPropType<TypeTag, Properties::GridView>;
     using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+    using SubControlVolumeFace = typename FVGridGeometry::SubControlVolumeFace;
     using FVElementGeometry = typename FVGridGeometry::LocalView;
     using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
     using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
@@ -157,6 +160,14 @@ public:
         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;
+    }
+
     /*!
      * \brief Evaluates the initial value for a control volume.
      *
diff --git a/test/multidomain/facet/tracer_tracer/problem_tracer_lowdim.hh b/test/multidomain/facet/tracer_tracer/problem_tracer_lowdim.hh
index 84f490fe0c398c354cd5826786260895637fb1c5..0517e652ae44193f406087e2e6ee79d025ae6bf7 100644
--- a/test/multidomain/facet/tracer_tracer/problem_tracer_lowdim.hh
+++ b/test/multidomain/facet/tracer_tracer/problem_tracer_lowdim.hh
@@ -51,6 +51,7 @@ struct TracerTestLowDim { using InheritsFrom = std::tuple<Tracer>; };
 
 // define the type tags for both bulk and lowdim type tag here
 struct TracerLowDimTpfa { using InheritsFrom = std::tuple<TracerTestLowDim, CCTpfaModel>; };
+struct TracerLowDimMpfa { using InheritsFrom = std::tuple<TracerTestLowDim, CCTpfaModel>; };
 struct TracerLowDimBox { using InheritsFrom = std::tuple<TracerTestLowDim, BoxModel>; };
 } // end namespace TTag
 
diff --git a/test/references/test_md_facet_tracertracer_mpfa_onep_bulk-reference.vtu b/test/references/test_md_facet_tracertracer_mpfa_onep_bulk-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..d68ad7f420788188edf38182d8a3b34be71e316c
--- /dev/null
+++ b/test/references/test_md_facet_tracertracer_mpfa_onep_bulk-reference.vtu
@@ -0,0 +1,1401 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+  <UnstructuredGrid>
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diff --git a/test/references/test_md_facet_tracertracer_mpfa_onep_lowdim-reference.vtp b/test/references/test_md_facet_tracertracer_mpfa_onep_lowdim-reference.vtp
new file mode 100644
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new file mode 100644
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--- /dev/null
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diff --git a/test/references/test_md_facet_tracertracer_mpfa_tracer_lowdim-reference.vtp b/test/references/test_md_facet_tracertracer_mpfa_tracer_lowdim-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..40527b5bc3742206f2954d7b6bd9c0052bf78608
--- /dev/null
+++ b/test/references/test_md_facet_tracertracer_mpfa_tracer_lowdim-reference.vtp
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