diff --git a/CHANGELOG.md b/CHANGELOG.md
index 82d2daa88d8c45e8c39007f69772a2711c49636d..ef266eccedca1b75f8e8a369c1dabf737c1f757a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,9 @@ Differences Between DuMu<sup>x</sup> 3.8 and DuMu<sup>x</sup> 3.7
 
 ### Improvements and Enhancements
 
+- __Pore network__: Added the dual network model proposed in Koch et al (2021) https://doi.org/10.1007/s11242-021-01602-5
+- __Pore network__: Added a model for heat conduction in a solid grain network
+- __Nonisothermal__: Added a specialized local residual for incompressible flows where the pressure work term cancels with the pressure-dependent part of the enthalpy so that only the internal energy remains in the advective heat flux.
 
 ### Immediate interface changes not allowing/requiring a deprecation period:
 
@@ -23,7 +26,7 @@ Differences Between DuMu<sup>x</sup> 3.7 and DuMu<sup>x</sup> 3.6
 
 ### General changes / structure
 
-- __Doxygen__: The theme of the Doxygen documentation page has been updated to a more modern look and the content has been restructured. The installation guide, the property system description and the chapter on examples and tutorials have been moved from the handbook to the Doxygen documentation. A chapter on parallelism has been added. One of the CI pipelines now includes a build of the Doxygen documentation. The result of this build can be downloaded from the job artifacts. 
+- __Doxygen__: The theme of the Doxygen documentation page has been updated to a more modern look and the content has been restructured. The installation guide, the property system description and the chapter on examples and tutorials have been moved from the handbook to the Doxygen documentation. A chapter on parallelism has been added. One of the CI pipelines now includes a build of the Doxygen documentation. The result of this build can be downloaded from the job artifacts.
 
 - __License__: DuMux is now REUSE compliant. Many files are individually licensed, others covered by rules in `.reuse/dep5`.
 
diff --git a/doc/doxygen/groups/models.md b/doc/doxygen/groups/models.md
index 394035f271f3378313e24f749c9295c091fa59a5..b44b106b3e0bdda8a1160e8e76a412e4fb366889 100644
--- a/doc/doxygen/groups/models.md
+++ b/doc/doxygen/groups/models.md
@@ -227,3 +227,8 @@
 @brief Two-phase (immiscible) flow
 @copydoc dumux/porenetwork/2p/model.hh
 @ingroup PoreNetworkModels
+
+@defgroup PNMSolidEnergyModel solidenergy
+@brief Energy equation for the solid (heat equation)
+@copydoc dumux/porenetwork/solidenergy/model.hh
+@ingroup PoreNetworkModels
diff --git a/dumux/flux/porenetwork/grainfourierslaw.hh b/dumux/flux/porenetwork/grainfourierslaw.hh
new file mode 100644
index 0000000000000000000000000000000000000000..6ee48abe3f096f820a0e5175bc706d8851c3dceb
--- /dev/null
+++ b/dumux/flux/porenetwork/grainfourierslaw.hh
@@ -0,0 +1,145 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \brief This file contains the data which is required to calculate
+ *        diffusive heat fluxes with Fourier's law.
+ */
+#ifndef DUMUX_FLUX_PNM_GRAIN_FOURIERS_LAW_HH
+#define DUMUX_FLUX_PNM_GRAIN_FOURIERS_LAW_HH
+
+#include <cmath>
+#include <dumux/common/math.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \brief Specialization of Fourier's Law for the pore-network SOLID model.
+ * \note See Koch et al (2021) https://doi.org/10.1007/s11242-021-01602-5
+ *       and Khan et al (2019) https://doi.org/10.1016/j.compchemeng.2018.12.025 
+ */
+template <class Scalar>
+struct TruncatedPyramidGrainFouriersLaw
+{
+    template<class Problem, class Element, class FVElementGeometry, class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static Scalar flux(const Problem& problem,
+                       const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                       const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
+
+        const Scalar topSideLength = 2.0*fluxVarsCache.throatInscribedRadius();
+
+        // We assume that the distance between pore centroid and throat
+        // centroid (i.e., the height of the pyramid) equals the inscribed pore radius.
+        const Scalar insideHeight = insideVolVars.poreInscribedRadius();
+        const Scalar outsideHeight = outsideVolVars.poreInscribedRadius();
+
+        auto getPyramidBaseLengthFromVolume = [&](const Scalar v, const Scalar h)
+        {
+            const Scalar b = topSideLength;
+            using std::sqrt;
+            return 0.5*sqrt(3.0) * sqrt(-(b*b*h-4.0*v)/h) -0.5*b;
+        };
+
+        // the pyramid base length of the inside pore
+        const Scalar insideBaseSideLength = [&]()
+        {
+            static const bool useAdaptedVolume = getParamFromGroup<bool>(problem.paramGroup(), "GrainFouriersLaw.UseAdaptedVolumeForPyramid", false);
+
+            if (useAdaptedVolume)
+                return getPyramidBaseLengthFromVolume(0.5*insideVolVars.poreVolume(), insideHeight);
+            else
+                return 2.0 * insideVolVars.poreInscribedRadius();
+        }();
+
+        // the pyramid base length of the outside pore
+        const Scalar outsideBaseSideLength = [&]()
+        {
+            static const bool useAdaptedVolume = getParamFromGroup<bool>(problem.paramGroup(), "GrainFouriersLaw.UseAdaptedVolumeForPyramid", false);
+
+            if (useAdaptedVolume)
+                return getPyramidBaseLengthFromVolume(0.5*outsideVolVars.poreVolume(), outsideHeight);
+            else
+                return 2.0 * outsideVolVars.poreInscribedRadius();
+        }();
+
+        auto insideThermalConducitivity = insideVolVars.solidThermalConductivity();
+        auto outsideThermalConducitivity = outsideVolVars.solidThermalConductivity();
+
+        const Scalar gInside = 4.0*insideThermalConducitivity *  0.5*topSideLength * 0.5*insideBaseSideLength / insideHeight;
+        const Scalar gOutside = 4.0*outsideThermalConducitivity *  0.5*topSideLength * 0.5*outsideBaseSideLength / outsideHeight;
+        const Scalar gThroat = Dumux::harmonicMean(insideThermalConducitivity, outsideThermalConducitivity)
+                             * fluxVarsCache.grainContactArea() / fluxVarsCache.throatLength();
+
+        const Scalar g = 1.0 / (1.0/gInside + 1.0/gOutside + 1.0/gThroat);
+
+        // calculate the temperature gradient
+        const Scalar deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+
+        return deltaT * g;
+    }
+};
+
+/*!
+ * \brief Specialization of Fourier's Law for the pore-network SOLID model.
+ * \note See Koch et al (2021) https://doi.org/10.1007/s11242-021-01602-5
+ */
+template <class Scalar>
+struct SphereCapGrainFouriersLaw
+{
+    template<class Problem, class Element, class FVElementGeometry, class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static Scalar flux(const Problem& problem,
+                       const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                       const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
+
+        auto gSphereCap = [&](const auto& scv, const auto& volVars)
+        {
+            const Scalar R = problem.spatialParams.extendedPoreRadius(scv.dofIndex());
+            const Scalar lambda = volVars.solidThermalConductivity();
+            const Scalar rC = volVars.poreRadius();
+            using std::atanh;
+            return (lambda*M_PI*R) / atanh(rC/R);
+        };
+
+        auto insideThermalConducitivity = insideVolVars.solidThermalConductivity();
+        auto outsideThermalConducitivity = outsideVolVars.solidThermalConductivity();
+
+        const Scalar gInside = gSphereCap(insideScv, insideVolVars);
+        const Scalar gOutside = gSphereCap(outsideScv, outsideVolVars);
+        const Scalar gThroat = Dumux::harmonicMean(insideThermalConducitivity, outsideThermalConducitivity)
+                             * fluxVarsCache.grainContactArea() / fluxVarsCache.throatLength();
+
+        const Scalar g = 1.0 / (1.0/gInside + 1.0/gOutside + 1.0/gThroat);
+
+        // calculate the temperature gradient
+        const Scalar deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+
+        return deltaT * g;
+    }
+
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/multidomain/CMakeLists.txt b/dumux/multidomain/CMakeLists.txt
index 32d888d7cb15b5eb809960fbf4ce6af3c02c14a4..a3aaf5b10f1b6416487790f72fd5e0367de0032a 100644
--- a/dumux/multidomain/CMakeLists.txt
+++ b/dumux/multidomain/CMakeLists.txt
@@ -6,6 +6,7 @@ add_subdirectory(embedded)
 add_subdirectory(facet)
 add_subdirectory(freeflow)
 add_subdirectory(io)
+add_subdirectory(dualnetwork)
 
 file(GLOB DUMUX_MULTIDOMAIN_HEADERS *.hh *.inc)
 install(FILES ${DUMUX_MULTIDOMAIN_HEADERS}
diff --git a/dumux/multidomain/dualnetwork/CMakeLists.txt b/dumux/multidomain/dualnetwork/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e95ca099a830d847fa9c01faca258a750f674217
--- /dev/null
+++ b/dumux/multidomain/dualnetwork/CMakeLists.txt
@@ -0,0 +1,6 @@
+# SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+file(GLOB DUMUX_MULTIDOMAIN_DUALNETWORK_HEADERS *.hh *.inc)
+install(FILES ${DUMUX_MULTIDOMAIN_DUALNETWORK_HEADERS}
+        DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/multidomain/dualnetwork)
diff --git a/dumux/multidomain/dualnetwork/couplingmanager.hh b/dumux/multidomain/dualnetwork/couplingmanager.hh
new file mode 100644
index 0000000000000000000000000000000000000000..55dd22d338160141f4fc42bfcff1200785b7722c
--- /dev/null
+++ b/dumux/multidomain/dualnetwork/couplingmanager.hh
@@ -0,0 +1,971 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup DarcyDarcyCoupling
+ * \brief Coupling manager for equal-dimension boundary coupling
+ */
+
+#ifndef DUMUX_MULTIDOMAIN_DUAL_NETWORK_COUPLINGMANAGER_HH
+#define DUMUX_MULTIDOMAIN_DUAL_NETWORK_COUPLINGMANAGER_HH
+
+#include <iostream>
+#include <vector>
+#include <tuple>
+
+#include <dune/common/indices.hh>
+#include <dune/common/exceptions.hh>
+#include <dune/common/reservedvector.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/math.hh>
+#include <dumux/common/enumerate.hh>
+#include <dumux/common/numeqvector.hh>
+#include <dumux/discretization/elementsolution.hh>
+#include <dumux/discretization/method.hh>
+#include <dumux/multidomain/couplingmanager.hh>
+#include "extendedsourcestencil.hh"
+
+#include "couplingmapper.hh"
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \ingroup DarcyDarcyCoupling
+ * \brief Coupling manager for dual network approach for pore network models
+ * \note Concept and algorithms described in Koch et al (2021) https://doi.org/10.1007/s11242-021-01602-5
+ */
+template<class MDTraits>
+class PNMHeatTransferCouplingManager
+: public CouplingManager<MDTraits>
+{
+    using ParentType = CouplingManager<MDTraits>;
+    using ThisType = PNMHeatTransferCouplingManager<MDTraits>;
+
+    using Scalar = typename MDTraits::Scalar;
+    using SolutionVector = typename MDTraits::SolutionVector;
+
+    template<std::size_t i> using SubDomainTypeTag = typename MDTraits::template SubDomain<i>::TypeTag;
+    template<std::size_t i> using Problem = GetPropType<SubDomainTypeTag<i>, Properties::Problem>;
+    template<std::size_t i> using PrimaryVariables = GetPropType<SubDomainTypeTag<i>, Properties::PrimaryVariables>;
+    template<std::size_t i> using NumEqVector = Dumux::NumEqVector<PrimaryVariables<i>>;
+    template<std::size_t i> using GridVolumeVariables = GetPropType<SubDomainTypeTag<i>, Properties::GridVolumeVariables>;
+    template<std::size_t i> using ElementVolumeVariables = typename GridVolumeVariables<i>::LocalView;
+    template<std::size_t i> using ElementFluxVariablesCache = typename GetPropType<SubDomainTypeTag<i>, Properties::GridFluxVariablesCache>::LocalView;
+    template<std::size_t i> using VolumeVariables = typename GridVolumeVariables<i>::VolumeVariables;
+    template<std::size_t i> using GridGeometry = typename MDTraits::template SubDomain<i>::GridGeometry;
+    template<std::size_t i> using FVElementGeometry = typename GridGeometry<i>::LocalView;
+    template<std::size_t i> using SubControlVolumeFace = typename GridGeometry<i>::SubControlVolumeFace;
+    template<std::size_t i> using SubControlVolume = typename GridGeometry<i>::SubControlVolume;
+    template<std::size_t i> using GridView = typename GridGeometry<i>::GridView;
+    template<std::size_t i> using Element = typename GridView<i>::template Codim<0>::Entity;
+    template<std::size_t i> using Indices = typename GetPropType<SubDomainTypeTag<i>, Properties::ModelTraits>::Indices;
+
+    template<std::size_t id> using GridVariables = typename MDTraits::template SubDomain<id>::GridVariables;
+    using GridVariablesTuple = typename MDTraits::template TupleOfSharedPtr<GridVariables>;
+
+    using CouplingMapper = DualNetworkCouplingMapper<Scalar>;
+
+    template<std::size_t i>
+    static constexpr auto domainIdx()
+    { return typename MDTraits::template SubDomain<i>::Index{}; }
+
+    using CouplingStencil = std::vector<std::size_t>;
+
+
+public:
+    static constexpr auto solidDomainIdx = typename MDTraits::template SubDomain<0>::Index();
+    static constexpr auto voidDomainIdx = typename MDTraits::template SubDomain<1>::Index();
+
+private:
+
+    using VoidElementSolution = std::decay_t<decltype(elementSolution(std::declval<Element<voidDomainIdx>>(), std::declval<SolutionVector>()[voidDomainIdx], std::declval<GridGeometry<voidDomainIdx>>()))>;
+    using SolidElementSolution = std::decay_t<decltype(elementSolution(std::declval<Element<solidDomainIdx>>(), std::declval<SolutionVector>()[solidDomainIdx], std::declval<GridGeometry<solidDomainIdx>>()))>;
+
+    struct CouplingContextForOneConnection
+    {
+        std::size_t connectionGlobalId;
+        std::vector<FVElementGeometry<solidDomainIdx>> solidFVGeometry; // only one needed, but FVElementGeometry can't be default constructed
+        VolumeVariables<solidDomainIdx> solidVolVars;
+        std::vector<FVElementGeometry<voidDomainIdx>> voidFVGeometry;
+        std::vector<ElementVolumeVariables<voidDomainIdx>> voidElemVolVars;
+        std::vector<ElementFluxVariablesCache<voidDomainIdx>> voidElemFluxVarsCache;
+    };
+
+    using CouplingContextForOnePore = std::pair<std::size_t, std::vector<CouplingContextForOneConnection>>;
+    using CouplingContextForOneElement = Dune::ReservedVector<CouplingContextForOnePore, 2>;
+
+    struct ElementCouplingContext
+    {
+        std::size_t boundElementIndex() const
+        { return boundElementIndex_; }
+
+        std::size_t boundDomainId() const
+        { return domaindId_; }
+
+        auto& data()
+        { return data_; }
+
+        template<std::size_t i>
+        void bind(Dune::index_constant<i> domainI,
+                  const Element<i>& element,
+                  const ThisType& couplingManager)
+        {
+            // do nothing if context is already bound correctly
+            const auto eIdx = couplingManager.gridGeometry(domainI).elementMapper().index(element);
+            if (domaindId_ == i && boundElementIndex_ == eIdx && initialized_)
+                return;
+
+            // do nothing if the element does not couple at all
+            // (this check is probably more expensive, so we do it after the above one)
+            constexpr auto domainJ = Dune::index_constant<1-i>{};
+            if (couplingManager.couplingStencil(domainI, element, domainJ).empty())
+                return;
+
+            data_.clear();
+
+            // each element has two pores for which we need to bind some connection coupling context
+            for (int localVertexIdx = 0; localVertexIdx < 2; ++localVertexIdx)
+            {
+                const auto vIdx = couplingManager.gridGeometry(domainI).vertexMapper().subIndex(element, localVertexIdx, 1);
+                if (!couplingManager.isCoupledPore(domainI, vIdx))
+                    continue;
+
+                initialized_ = true;
+                domaindId_ = i;
+                boundElementIndex_ = eIdx;
+
+                const auto& connections = [&]
+                {
+                    if constexpr(domainI == solidDomainIdx)
+                        return couplingManager.couplingMapper().solidToVoidConnections(vIdx);
+                    else
+                        return couplingManager.couplingMapper().voidToSolidConnections(vIdx);
+                }();
+                const auto numConnections = std::distance(connections.begin(), connections.end());
+                assert(numConnections == (domainI == solidDomainIdx ? couplingManager.couplingMapper().solidToVoidConnectionIds().at(vIdx).size() : couplingManager.couplingMapper().voidToSolidConnectionIds().at(vIdx).size()));
+
+                data_.push_back(CouplingContextForOnePore{});
+
+                // iterate over all solid/void connections for the given pore
+                data_.back().first = vIdx;
+                data_.back().second.reserve(numConnections);
+                for (const auto& connection : connections)
+                {
+                    CouplingContextForOneConnection context;
+                    context.connectionGlobalId = connection.id;
+
+                    const auto& solidElement = couplingManager.solidGridGeometry_->element(connection.someSolidElementIdx);
+                    auto solidFVGeometry = localView(*couplingManager.solidGridGeometry_);
+                    solidFVGeometry.bindElement(solidElement);
+                    context.solidFVGeometry.push_back(solidFVGeometry);
+
+                    for (const auto& solidScv : scvs(solidFVGeometry))
+                    {
+                        if (solidScv.dofIndex() == connection.solidVertexIdx)
+                            context.solidVolVars = couplingManager.volVars(solidDomainIdx, solidElement, solidScv);
+                    }
+
+                    auto voidFVGeometry = localView(couplingManager.gridGeometry(voidDomainIdx));
+                    auto voidElemVolVars = localView(couplingManager.gridVariables(voidDomainIdx).curGridVolVars());
+                    auto voidElemFluxVarsCache = localView(couplingManager.gridVariables(voidDomainIdx).gridFluxVarsCache());
+
+                    const auto numConvectionVoidElems = connection.convectionVoidElementIdx.size();
+                    context.voidFVGeometry.reserve(numConvectionVoidElems);
+                    context.voidElemVolVars.reserve(numConvectionVoidElems);
+                    context.voidElemFluxVarsCache.reserve(numConvectionVoidElems);
+                    for (const auto voidElemIdx : connection.convectionVoidElementIdx)
+                    {
+                        const auto voidElem = couplingManager.gridGeometry(voidDomainIdx).element(voidElemIdx);
+                        voidFVGeometry.bindElement(voidElem);
+                        voidElemVolVars.bindElement(voidElem, voidFVGeometry, couplingManager.curSol(voidDomainIdx));
+                        voidElemFluxVarsCache.bindElement(voidElem, voidFVGeometry, voidElemVolVars);
+
+                        context.voidFVGeometry.push_back(voidFVGeometry);
+                        context.voidElemVolVars.push_back(voidElemVolVars);
+                        context.voidElemFluxVarsCache.push_back(voidElemFluxVarsCache);
+                    }
+                    data_.back().second.push_back(std::move(context));
+                }
+            }
+        }
+
+        const auto& operator[](const std::size_t dofIdx) const
+        {
+            for (const auto& d : data_)
+            {
+                if (d.first == dofIdx)
+                    return d.second;
+            }
+            DUNE_THROW(Dune::InvalidStateException, "No connection found");
+        }
+
+    private:
+
+        bool initialized_ = false;
+        std::size_t domaindId_;
+        std::size_t boundElementIndex_;
+        mutable Dune::ReservedVector<CouplingContextForOnePore, 2> data_;
+    };
+
+public:
+
+    //! export traits
+    using MultiDomainTraits = MDTraits;
+    //! export stencil types
+    using CouplingStencils = std::unordered_map<std::size_t, CouplingStencil>;
+
+    /*!
+     * \brief Methods to be accessed by main
+     */
+    // \{
+
+    template<class HostGridView, class HostGridData, class VoidGridView, class SolidGridView>
+    void init(std::shared_ptr<Problem<solidDomainIdx>> solidProblem,
+              std::shared_ptr<Problem<voidDomainIdx>> voidProblem,
+              const HostGridView& hostGridView,
+              const HostGridData& hostGridData,
+              const VoidGridView& voidGridView,
+              const SolidGridView& solidGridView,
+              const SolutionVector& curSol)
+    {
+        voidGridGeometry_ = &voidProblem->gridGeometry();
+        solidGridGeometry_ = &solidProblem->gridGeometry();
+        couplingMapper_ = std::make_unique<CouplingMapper>(hostGridView, hostGridData, voidProblem->gridGeometry(), solidProblem->gridGeometry());
+        this->setSubProblems(std::make_tuple(solidProblem, voidProblem));
+        this->updateSolution(curSol);
+
+        const auto& someVoidElement = voidGridGeometry_->element(0);
+        const auto& someSolidElement = solidGridGeometry_->element(0);
+        voidElementSolution_.update(someVoidElement, curSol[voidDomainIdx], *voidGridGeometry_);
+        solidElementSolution_.update(someSolidElement, curSol[solidDomainIdx], *solidGridGeometry_);
+        setupExtendedStencil();
+    }
+
+    // \}
+
+    /*!
+     * \brief Methods to be accessed by the assembly
+     */
+    // \{
+
+    /*!
+     * \brief returns an iterable container of all indices of degrees of freedom of domain j
+     *        that couple with / influence the element residual of the given element of domain i
+     *
+     * \param domainI the domain index of domain i
+     * \param element the coupled element of domain í
+     * \param domainJ the domain index of domain j
+     */
+    const CouplingStencil& couplingStencil(Dune::index_constant<solidDomainIdx> domainI,
+                                           const Element<solidDomainIdx>& element,
+                                           Dune::index_constant<voidDomainIdx> domainJ) const
+    {
+        const auto eIdx = gridGeometry(domainI).elementMapper().index(element);
+        const auto& stencils = couplingMapper().solidToVoidStencils();
+
+        if (stencils.count(eIdx))
+            return stencils.at(eIdx);
+        else
+            return emptyStencil_;
+    }
+
+    // VOID
+    const CouplingStencil& couplingStencil(Dune::index_constant<voidDomainIdx> domainI,
+                                           const Element<voidDomainIdx>& element,
+                                           Dune::index_constant<solidDomainIdx> domainJ) const
+    {
+        const auto eIdx = gridGeometry(domainI).elementMapper().index(element);
+        const auto& stencils = couplingMapper().voidToSolidStencils();
+
+        if (stencils.count(eIdx))
+            return stencils.at(eIdx);
+        else
+            return emptyStencil_;
+    }
+
+    /*!
+     * \brief Returns whether a given solid pore is coupled to the other domain
+     */
+    bool isCoupledPore(Dune::index_constant<solidDomainIdx> domainI, const std::size_t dofIdx) const
+    {
+        return couplingMapper().isCoupledSolidDof()[dofIdx];
+    }
+
+    /*!
+     * \brief Returns whether a given void pore is coupled to the other domain
+     */
+    bool isCoupledPore(Dune::index_constant<voidDomainIdx> domainI, const std::size_t dofIdx) const
+    {
+        return couplingMapper().isCoupledVoidDof()[dofIdx];
+    }
+
+    //SOLID
+    Scalar conductionSource(Dune::index_constant<solidDomainIdx> domainI,
+                            const Element<solidDomainIdx>& element,
+                            const FVElementGeometry<solidDomainIdx>& fvGeometry,
+                            const ElementVolumeVariables<solidDomainIdx>& elemVolVars,
+                            const SubControlVolume<solidDomainIdx>& scv) const
+    {
+        const auto& solidSol = this->curSol(solidDomainIdx);
+        const auto& voidSol = this->curSol(voidDomainIdx);
+
+        Scalar source = 0.0;
+
+        // iterate over all connection throats
+        for (const auto& connection : couplingMapper().solidToVoidConnections(scv.dofIndex()))
+        {
+            const Scalar t = getConnectionTransmissiblity(solidDomainIdx, connection, elemVolVars, scv);
+            const Scalar deltaT = solidSol[scv.dofIndex()][Indices<solidDomainIdx>::temperatureIdx] - voidSol[connection.voidVertexIdx][Indices<voidDomainIdx>::temperatureIdx];
+            source -= t * deltaT;
+        }
+
+        source /= (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+        return source;
+    }
+
+    template<class Connection, class Context>
+    Scalar convectiveHeatFluxForOneConnection(const Connection& connection, const Context& context) const
+    {
+        const auto& solidSol = this->curSol(solidDomainIdx);
+        const auto& voidSol = this->curSol(voidDomainIdx);
+        const Scalar tSolid = solidSol[connection.solidVertexIdx];
+        Scalar resultConvection = 0.0;
+
+        // iterate over all convection void elements
+        for (const auto& [localConvectionVoidElementIdx, convectionVoidElementIdx] : enumerate(connection.convectionVoidElementIdx))
+        {
+            const auto& voidElement = voidGridGeometry_->element(convectionVoidElementIdx);
+            const auto& voidFVGeometry = context.voidFVGeometry[localConvectionVoidElementIdx];
+            const auto& voidElemVolVars = context.voidElemVolVars[localConvectionVoidElementIdx];
+            const auto& voidElemFluxVarsCache = context.voidElemFluxVarsCache[localConvectionVoidElementIdx];
+
+            const Scalar distance = [&, convectionVoidElementIdx = convectionVoidElementIdx, solidVertexIdx = connection.solidVertexIdx]
+            {
+                const auto& throatCenter = this->problem(voidDomainIdx).spatialParams().throatCenter(convectionVoidElementIdx);
+                for (const auto& solidScv : scvs(context.solidFVGeometry[0]))
+                {
+                    if (solidScv.dofIndex() == solidVertexIdx)
+                        return (solidScv.dofPosition() - throatCenter).two_norm();
+                }
+                DUNE_THROW(Dune::InvalidStateException, "No solid scv found");
+            }();
+
+            using VoidFluxVariables = GetPropType<SubDomainTypeTag<voidDomainIdx>, Properties::FluxVariables>;
+            VoidFluxVariables fluxVars;
+            const auto& scvf = voidFVGeometry.scvf(0);
+            fluxVars.init(this->problem(voidDomainIdx), voidElement, voidFVGeometry, voidElemVolVars, scvf, voidElemFluxVarsCache);
+
+            static constexpr auto phaseIdx = 0;
+            const Scalar flux = fluxVars.advectiveFlux(phaseIdx, [phaseIdx = phaseIdx](const auto& volVars){ return volVars.mobility(phaseIdx);});
+            const Scalar velocity = flux / voidElemFluxVarsCache[scvf].throatCrossSectionalArea(phaseIdx);
+
+            const auto tFluidMean = [&]
+            {
+                Scalar result = 0.0;
+                const auto numScv = voidFVGeometry.numScv();
+                assert(numScv == 2);
+                for (const auto& voidScv : scvs(voidFVGeometry))
+                    result += 1.0/numScv * voidSol[voidScv.dofIndex()][Indices<voidDomainIdx>::temperatureIdx];
+                return result;
+            };
+
+            const auto tFluidUpstream = [&]
+            {
+                const auto upstreamDofIdx = flux > 0.0 ? voidFVGeometry.scv(scvf.insideScvIdx()).dofIndex() : voidFVGeometry.scv(scvf.outsideScvIdx()).dofIndex();
+                return voidSol[upstreamDofIdx][Indices<voidDomainIdx>::temperatureIdx];
+            };
+
+            enum class FluidTemperatureMode {mean, self, upstream};
+            static const auto fluidTemperatureMode = [&]
+            {
+                static const auto mode = getParam<std::string>("Problem.FluidTemperatureMode", "mean");
+                std::cout << "Using FluidTemperatureMode " << mode << std::endl;
+                if (mode == "mean")
+                    return FluidTemperatureMode::mean;
+                else if (mode == "self")
+                    return FluidTemperatureMode::self;
+                else if (mode == "upstream")
+                    return FluidTemperatureMode::upstream;
+                else
+                    DUNE_THROW(Dune::IOError, mode << " is not a valid FluidTemperatureMode");
+            }();
+
+            const Scalar tFluid = [&, voidVertexIdx = connection.voidVertexIdx]
+            {
+                if (fluidTemperatureMode == FluidTemperatureMode::mean)
+                    return tFluidMean();
+                else if (fluidTemperatureMode == FluidTemperatureMode::self)
+                    return voidSol[voidVertexIdx][Indices<voidDomainIdx>::temperatureIdx];
+                else
+                    return tFluidUpstream();
+            }();
+
+            const Scalar nu = 0.5*(voidElemVolVars[0].viscosity(phaseIdx)/voidElemVolVars[0].density(phaseIdx)
+                                 + voidElemVolVars[1].viscosity(phaseIdx)/voidElemVolVars[1].density(phaseIdx));
+            using std::abs;
+            const Scalar Re = abs(velocity) * 2.0*voidElemFluxVarsCache[scvf].throatInscribedRadius() / nu;
+
+            static const Scalar fixedLambda = getParam<Scalar>("Problem.FixedConvectionLambda", -1.0);
+            static const Scalar lambaFactor = getParam<Scalar>("Problem.ConvectionLambaFactor", 0.9);
+            static const Scalar lambaExponent = getParam<Scalar>("Problem.ConvectionLambaExponent", 0.4);
+            using std::pow;
+            const Scalar lambda = fixedLambda > 0.0 ? fixedLambda : 1.0 + lambaFactor*pow(Re, lambaExponent);
+            const Scalar selfA = connection.connectionArea / connection.convectionVoidElementIdx.size();
+
+            const auto neighborA = [&]
+            {
+                // get the area associated to the other void dof
+                for (const auto& voidScv : scvs(voidFVGeometry))
+                {
+                    if (voidScv.dofIndex() != connection.voidVertexIdx)
+                    {
+                        const auto& otherConnections = couplingMapper().voidToSolidConnections(voidScv.dofIndex());
+                        for (const auto& otherConn : otherConnections)
+                        {
+                            if (otherConn.solidVertexIdx == connection.solidVertexIdx)
+                            {
+                                if (otherConn.voidVertexIdx != voidScv.dofIndex())
+                                    DUNE_THROW(Dune::InvalidStateException, "Void dofs don't match");
+
+                                return otherConn.connectionArea/otherConn.convectionVoidElementIdx.size(); //TODO: does this belong to last "if-statement" -> if yes, set brackets?
+                            }
+                        }
+                    }
+                }
+                DUNE_THROW(Dune::InvalidStateException, "No neighbor area found");
+            };
+
+            static const bool useAvgA = getParam<bool>("Problem.UseAverageConvectionArea", false);
+            const Scalar A = useAvgA ? 0.5*(selfA + neighborA()) : selfA;
+
+            const Scalar deltaT = (elementCouplingContext_.boundDomainId() == voidDomainIdx) ? (tSolid - tFluid) : (tFluid - tSolid);
+
+            static const int verbose = getParam<int>("Problem.SourceVerboseForDof", -1);
+            if (verbose >= 0 && (connection.voidVertexIdx == verbose || connection.solidVertexIdx == verbose))
+            {
+                std::cout << "\n" << std::endl;
+                const auto domain = elementCouplingContext_.boundDomainId() == solidDomainIdx ? "solid" : "void";
+                std::cout << "At " << domain << ", dof " << verbose << ", flow elem " << convectionVoidElementIdx << ", globalId " << connection.id << std::endl;
+                std::cout << std::scientific << std::setprecision(15) << "velocity " << velocity << ", Re "  << Re << ", delTaT " << deltaT << ", result " << lambda*A/distance*deltaT << std::endl;
+                std::cout <<  std::scientific << std::setprecision(15) << "A " << A << ", distance " << distance << std::endl;
+                std::cout << std::endl;
+            }
+
+            resultConvection += lambda*A/distance * deltaT;
+        }
+
+        return resultConvection;
+    }
+
+    template<std::size_t i>
+    Scalar convectionSource(Dune::index_constant<i> domainI,
+                            const Element<i>& element,
+                            const FVElementGeometry<i>& fvGeometry,
+                            const ElementVolumeVariables<i>& elemVolVars,
+                            const SubControlVolume<i>& scv) const
+    {
+        bindCouplingContext(domainI, element);
+
+        static const int verbose = getParam<int>("Problem.SourceVerboseForDof", -1);
+        if (scv.dofIndex() == verbose)
+            std::cout << "Start Source at elemn " << fvGeometry.gridGeometry().elementMapper().index(element) << " *******************************" <<  std::endl;
+
+        // iterate over all connection throats
+        const auto& connections = [&]
+        {
+            if constexpr (domainI == solidDomainIdx)
+                return couplingMapper().solidToVoidConnections(scv.dofIndex());
+            else
+                return couplingMapper().voidToSolidConnections(scv.dofIndex());
+        }();
+
+        Scalar source = 0.0;
+        const auto& contextForPore = elementCouplingContext_[scv.dofIndex()];
+
+        for (const auto& [localConnectionIdx, connection] : enumerate(connections))
+            source += convectiveHeatFluxForOneConnection(connection, contextForPore[localConnectionIdx]);
+
+        if (scv.dofIndex() == verbose)
+            std::cout << std::scientific << std::setprecision(15) << "total conv source  " << source << "\n\n ********************" << std::endl;
+
+        source /= (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+
+        return source;
+    }
+
+
+    //VOID
+    Scalar conductionSource(Dune::index_constant<voidDomainIdx> domainI,
+                            const Element<voidDomainIdx>& element,
+                            const FVElementGeometry<voidDomainIdx>& fvGeometry,
+                            const ElementVolumeVariables<voidDomainIdx>& elemVolVars,
+                            const SubControlVolume<voidDomainIdx>& scv) const
+    {
+        const auto& voidSol = this->curSol(voidDomainIdx);
+        const auto& solidSol = this->curSol(solidDomainIdx);
+
+        Scalar source = 0.0;
+
+        // iterate over all connection throats
+        for (const auto& connection : couplingMapper().voidToSolidConnections(scv.dofIndex()))
+        {
+            const Scalar t = getConnectionTransmissiblity(voidDomainIdx, connection, elemVolVars, scv);
+            const Scalar deltaT = voidSol[scv.dofIndex()][Indices<voidDomainIdx>::temperatureIdx] - solidSol[connection.solidVertexIdx][Indices<solidDomainIdx>::temperatureIdx];
+            source -= t * deltaT;
+        }
+
+        source /= (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+        return source;
+    }
+
+    // for void TODO this should not be in the general coupling manager
+    Scalar sourceWithFixedTransmissibility(Dune::index_constant<voidDomainIdx> domainI,
+                                           const Element<voidDomainIdx>& element,
+                                           const FVElementGeometry<voidDomainIdx>& fvGeometry,
+                                           const ElementVolumeVariables<voidDomainIdx>& elemVolVars,
+                                           const SubControlVolume<voidDomainIdx>& scv,
+                                           Dune::index_constant<solidDomainIdx> domainJ) const
+    {
+        const auto& voidSol = this->curSol(voidDomainIdx);
+        const auto& solidSol = this->curSol(solidDomainIdx);
+
+        Scalar source = 0.0;
+
+        // iterate over all connection throats
+        for (const auto& connection : couplingMapper().voidToSolidConnections(scv.dofIndex()))
+        {
+            const Scalar t = this->problem(voidDomainIdx).getInternalReferenceHeatTransmissibilityCoupling();
+            const Scalar deltaT = voidSol[scv.dofIndex()][Indices<voidDomainIdx>::temperatureIdx] - solidSol[connection.solidVertexIdx][Indices<solidDomainIdx>::temperatureIdx];
+            source -= t * deltaT;
+        }
+
+        source /= (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+        return source;
+    }
+
+
+    // for solid TODO this should not be in the general coupling manager
+    Scalar sourceWithFixedTransmissibility(Dune::index_constant<solidDomainIdx> domainI,
+                                           const Element<solidDomainIdx>& element,
+                                           const FVElementGeometry<solidDomainIdx>& fvGeometry,
+                                           const ElementVolumeVariables<solidDomainIdx>& elemVolVars,
+                                           const SubControlVolume<solidDomainIdx>& scv,
+                                           Dune::index_constant<voidDomainIdx> domainJ) const
+    {
+        const auto& voidSol = this->curSol(voidDomainIdx);
+        const auto& solidSol = this->curSol(solidDomainIdx);
+
+        Scalar source = 0.0;
+
+        // iterate over all connection throats
+        for (const auto& connection : couplingMapper().solidToVoidConnections(scv.dofIndex()))
+        {
+            const Scalar t = this->problem(voidDomainIdx).getInternalReferenceHeatTransmissibilityCoupling();
+            const Scalar deltaT = solidSol[scv.dofIndex()][Indices<domainI>::temperatureIdx] - voidSol[connection.voidVertexIdx][Indices<domainJ>::temperatureIdx];
+            source -= t * deltaT;
+        }
+
+        source /= (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+        return source;
+    }
+
+    template<std::size_t i, class Connection>
+    Scalar getConnectionTransmissiblity(Dune::index_constant<i> domainI,
+                                        const Connection& connection,
+                                        const ElementVolumeVariables<i>& elemVolVars,
+                                        const SubControlVolume<i>& scv) const
+    {
+        static constexpr bool isVoid = domainI == voidDomainIdx;
+
+        const auto poreRadiusVoid = [&]
+        {
+            static const bool useExactPoreRadiusVoid = getParam<bool>("Problem.UseExactPoreRadiusVoid", false);
+            if (useExactPoreRadiusVoid)
+            {
+                using std::sqrt;
+                static const Scalar R = getParam<Scalar>("Problem.SphereRadius", 50e-6);
+                static const Scalar overlapFactor = getParam<Scalar>("Problem.OverlapFactor");
+                static const Scalar dx = overlapFactor*R;
+                static const Scalar r = sqrt(3.0) * dx - R;
+                return r;
+            }
+            else
+                return gridGeometry(voidDomainIdx).poreInscribedRadius(connection.voidVertexIdx);
+        }();
+
+        const auto poreRadiusSolid = [&]
+        {
+            static const bool useExactPoreRadiusSolid = getParam<bool>("Problem.UseExactPoreRadiusSolid", false);
+            if (useExactPoreRadiusSolid)
+            {
+                static const Scalar R = getParam<Scalar>("Problem.SphereRadius", 50e-6);
+                return R;
+            }
+            else
+                return this->problem(solidDomainIdx).spatialParams().poreExtendedRadius(connection.solidVertexIdx);
+        }();
+
+        const Scalar fluidThermalConductivity = [&]
+        {
+            if constexpr (isVoid)
+                return elemVolVars[scv].effectiveThermalConductivity();
+            else
+            {
+                const auto& voidElement = voidGridGeometry_->element(connection.someVoidElementIdx);
+                auto voidFVGeometry = localView(*voidGridGeometry_);
+                voidFVGeometry.bindElement(voidElement);
+
+                for (const auto& voidScv : scvs(voidFVGeometry))
+                {
+                    if (voidScv.dofIndex() == connection.voidVertexIdx)
+                        return volVars(voidDomainIdx, voidElement, voidScv).effectiveThermalConductivity();
+                }
+
+                DUNE_THROW(Dune::InvalidStateException, "No scv found");
+            }
+        }();
+
+        const Scalar solidThermalConductivity = [&]
+        {
+            if constexpr (!isVoid)
+                return elemVolVars[scv].effectiveThermalConductivity();
+            else
+            {
+                const auto& solidElement = solidGridGeometry_->element(connection.someSolidElementIdx);
+                auto solidFVGeometry = localView(*solidGridGeometry_);
+                solidFVGeometry.bindElement(solidElement);
+
+                for (const auto& solidScv : scvs(solidFVGeometry))
+                {
+                    if (solidScv.dofIndex() == connection.solidVertexIdx)
+                        return volVars(solidDomainIdx, solidElement, solidScv).effectiveThermalConductivity();
+                }
+
+                DUNE_THROW(Dune::InvalidStateException, "No scv found");
+            }
+        }();
+
+        const Scalar kappa = fluidThermalConductivity / solidThermalConductivity;
+        static const Scalar Nu = getParam<Scalar>("Problem.Nu", 1.0);
+        static const Scalar Bi = getParam<Scalar>("Problem.Bi", 1.0);
+
+        static const bool useExactConnectionLength = getParam<bool>("Problem.UseExactConnectionLength", false);
+        const Scalar length = useExactConnectionLength ? poreRadiusSolid + poreRadiusVoid : connection.connectionLength;
+
+        static const bool useExactConnectionAreaSphere = getParam<bool>("Problem.UseExactConnectionAreaSphere", false);
+        static const Scalar connectionAreaShapeFactor = getParam<Scalar>("Problem.ConnectionAreaShapeFactor", 0.9);
+        const Scalar area = [&]()
+        {
+            if (useExactConnectionAreaSphere)
+            {
+                static const Scalar R = getParam<Scalar>("Problem.SphereRadius", 50e-6);
+                static const Scalar overlapFactor = getParam<Scalar>("Problem.OverlapFactor");
+                static const auto dx = overlapFactor*R;
+                static const auto h = R - dx;
+                static const auto interfacialArea = 4*M_PI*R*R - 6*(2*M_PI*R*h);
+                assert(std::abs(length - std::sqrt(3.0) * dx) < 1e-14); // TODO remove
+                return interfacialArea/8.0*connectionAreaShapeFactor;
+            }
+            else
+                return connection.connectionArea*connectionAreaShapeFactor;
+        }();
+        return area / length * (fluidThermalConductivity*Bi*(poreRadiusSolid + poreRadiusVoid))/(poreRadiusSolid*kappa + poreRadiusVoid*Bi/Nu);
+    }
+
+    // \}
+
+    //! Return the volume variables of domain i for a given element and scv
+    VolumeVariables<solidDomainIdx> volVars(Dune::index_constant<solidDomainIdx> domainI,
+                                            const Element<solidDomainIdx>& element,
+                                            const SubControlVolume<solidDomainIdx>& scv) const
+    {
+        VolumeVariables<solidDomainIdx> volVars;
+        const auto elemSol = elementSolution(element, this->curSol(domainI), gridGeometry(domainI));
+        volVars.update(elemSol, this->problem(domainI), element, scv);
+        return volVars;
+    }
+
+    VolumeVariables<voidDomainIdx> volVars(Dune::index_constant<voidDomainIdx> domainI,
+                                           const Element<voidDomainIdx>& element,
+                                           const SubControlVolume<voidDomainIdx>& scv) const
+    {
+        VolumeVariables<voidDomainIdx> volVars;
+        const auto elemSol = elementSolution(element, this->curSol(domainI), gridGeometry(domainI));
+        volVars.update(elemSol, this->problem(domainI), element, scv);
+        return volVars;
+    }
+
+    template<std::size_t i, std::size_t j, class LocalAssemblerI>
+    decltype(auto) evalCouplingResidual(Dune::index_constant<i> domainI,
+                                        const LocalAssemblerI& localAssemblerI,
+                                        Dune::index_constant<j> domainJ,
+                                        std::size_t dofIdxGlobalJ)
+    {
+        static_assert(i != j, "A domain cannot be coupled to itself!");
+
+        typename LocalAssemblerI::LocalResidual::ElementResidualVector residual;
+
+        const auto& element = localAssemblerI.element();
+        const auto& fvGeometry = localAssemblerI.fvGeometry();
+        const auto& curElemVolVars = localAssemblerI.curElemVolVars();
+
+        residual.resize(fvGeometry.numScv());
+        for (const auto& scv : scvs(fvGeometry))
+        {
+            auto couplingSource = this->problem(domainI).source(element, fvGeometry, curElemVolVars, scv);
+            couplingSource *= -scv.volume()*curElemVolVars[scv].extrusionFactor();
+            residual[scv.indexInElement()] = couplingSource;
+        }
+
+        return residual;
+    }
+
+    //! Bind the coupling context for a low dim element TODO remove Assembler
+    template<std::size_t i, class Assembler = int>
+    void bindCouplingContext(Dune::index_constant<i> domainI, const Element<i>& element, const Assembler& assembler = 0) const
+    { elementCouplingContext_.bind(domainI, element, *this); }
+
+    /*!
+     * \brief Update the coupling context
+     */
+    template<std::size_t i, class LocalAssemblerI, std::size_t j, class PriVars>
+    void updateCouplingContext(Dune::index_constant<i> domainI,
+                               const LocalAssemblerI& localAssemblerI,
+                               Dune::index_constant<j> domainJ,
+                               const std::size_t dofIdxGlobalJ,
+                               const PriVars& priVars,
+                               int pvIdxJ)
+    {
+        this->curSol(domainJ)[dofIdxGlobalJ][pvIdxJ] = priVars[pvIdxJ];
+
+        // each element has two pores for which we need to bind some connection coupling context
+        for (auto& context : elementCouplingContext_.data())
+        {
+            for (auto& connInfo : context.second)
+            {
+                const auto& staticConnectionInfo = couplingMapper().connectionInfo()[connInfo.connectionGlobalId];
+
+                // when the solid dof is deflected, just updated the solid volVars
+                if constexpr (domainJ == solidDomainIdx)
+                {
+                    const auto& solidElement = gridGeometry(domainJ).element(staticConnectionInfo.someSolidElementIdx);
+                    for (const auto& scv : scvs(connInfo.solidFVGeometry.front()))
+                    {
+                        solidElementSolution_[scv.localDofIndex()] = this->curSol(domainJ)[scv.dofIndex()];
+                        if (scv.dofIndex() == dofIdxGlobalJ)
+                            connInfo.solidVolVars.update(solidElementSolution_, this->problem(domainJ), solidElement, scv);
+                    }
+                }
+                else // deflection of void dofs
+                {
+                    assert(staticConnectionInfo.convectionVoidElementIdx.size() == connInfo.voidFVGeometry.size());
+                    for (int voidElemLocalIdx = 0; voidElemLocalIdx < staticConnectionInfo.convectionVoidElementIdx.size(); ++voidElemLocalIdx)
+                    {
+                        const auto eIdx = staticConnectionInfo.convectionVoidElementIdx[voidElemLocalIdx];
+                        const auto& element = gridGeometry(voidDomainIdx).element(eIdx);
+                        const auto& fvGeometry = connInfo.voidFVGeometry[voidElemLocalIdx];
+                        auto& elemVolVars = connInfo.voidElemVolVars[voidElemLocalIdx];
+
+                        for (const auto& scv : scvs(fvGeometry))
+                        {
+                            if (scv.dofIndex() == dofIdxGlobalJ)
+                            {
+                                voidElementSolution_[scv.localDofIndex()] = this->curSol(voidDomainIdx)[scv.dofIndex()];
+                                getVolVarAccess_(domainJ, gridVars_(voidDomainIdx).curGridVolVars(), elemVolVars, scv).update(voidElementSolution_, this->problem(voidDomainIdx), element, scv);
+                            }
+                        }
+
+                        for (const auto& scvf : scvfs(fvGeometry))
+                        {
+                            if constexpr (getPropValue<SubDomainTypeTag<j>, Properties::EnableGridFluxVariablesCache>())
+                                gridVars_(voidDomainIdx).gridFluxVarsCache().cache(eIdx, scvf.index()).update(problem(voidDomainIdx), element, fvGeometry, elemVolVars, scvf);
+                            else
+                                connInfo.voidElemFluxVarsCache[voidElemLocalIdx][scvf].update(this->problem(voidDomainIdx), element, fvGeometry, elemVolVars, scvf);
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    const auto& couplingContext() const
+    { return elementCouplingContext_; }
+
+
+    template<std::size_t i>
+    const auto& gridGeometry(Dune::index_constant<i> domainI) const
+    {
+        if constexpr (i == voidDomainIdx)
+            return *voidGridGeometry_;
+        else
+            return *solidGridGeometry_;
+    }
+
+    const CouplingMapper& couplingMapper() const
+    { return *couplingMapper_; }
+
+    /*!
+     * \brief set the pointers to the grid variables
+     * \param gridVariables A tuple of shared pointers to the grid variables
+     */
+    void setGridVariables(GridVariablesTuple&& gridVariables)
+    { gridVariables_ = gridVariables; }
+
+    /*!
+     * \brief set a pointer to one of the grid variables
+     * \param gridVariables a pointer to the grid variables
+     * \param domainIdx the domain index of the grid variables
+     */
+    template<class  GridVariables, std::size_t i>
+    void setGridVariables(std::shared_ptr<GridVariables> gridVariables, Dune::index_constant<i> domainIdx)
+    { std::get<i>(gridVariables_) = gridVariables; }
+
+    /*!
+     * \brief Return a reference to the grid variables of a sub problem
+     * \param domainIdx The domain index
+     */
+    template<std::size_t i>
+    const GridVariables<i>& gridVariables(Dune::index_constant<i> domainIdx) const
+    {
+        if (std::get<i>(gridVariables_))
+            return *std::get<i>(gridVariables_);
+        else
+            DUNE_THROW(Dune::InvalidStateException, "The gridVariables pointer was not set. Use setGridVariables() before calling this function");
+    }
+
+    /*!
+     * \brief extend the jacobian pattern of the diagonal block of domain i
+     *        by those entries that are not already in the uncoupled pattern
+     * \note Such additional dependencies can arise from the coupling, e.g. if a coupling source
+     *       term depends on a non-local average of a quantity of the same domain
+     */
+    template<std::size_t id, class JacobianPattern>
+    void extendJacobianPattern(Dune::index_constant<id> domainI, JacobianPattern& pattern) const
+    {
+        extendedSourceStencil_.extendJacobianPattern(*this, domainI, pattern);
+    }
+
+    /*!
+     * \brief evaluate additional derivatives of the element residual of a domain with respect
+     *        to dofs in the same domain that are not in the regular stencil (per default this is not the case)
+     * \note Such additional dependencies can arise from the coupling, e.g. if a coupling source
+     *       term depends on a non-local average of a quantity of the same domain
+     * \note This is the same for box and cc
+     */
+    template<std::size_t i, class LocalAssemblerI, class JacobianMatrixDiagBlock, class GridVariables>
+    void evalAdditionalDomainDerivatives(Dune::index_constant<i> domainI,
+                                         const LocalAssemblerI& localAssemblerI,
+                                         const typename LocalAssemblerI::LocalResidual::ElementResidualVector&,
+                                         JacobianMatrixDiagBlock& A,
+                                         GridVariables& gridVariables)
+    {
+        // std::cout << "calling evalAdditionalDomainDerivatives " << std::endl;
+        extendedSourceStencil_.evalAdditionalDomainDerivatives(*this, domainI, localAssemblerI, this->curSol(domainI), A, gridVariables); //TODO: call without curSol, but currently protected .../dumux/dumux/multidomain/couplingmanager.hh
+    }
+
+    //! Return a reference to an empty stencil
+    std::vector<std::size_t>& emptyStencil()
+    { return emptyStencil_; }
+
+
+    //! Return a reference to an empty stencil
+    template<std::size_t i>
+    const std::vector<std::size_t>& emptyStencil(Dune::index_constant<i> domainI) const
+    { return emptyStencil_; }
+
+    template<std::size_t i>
+    const auto& gridView(Dune::index_constant<i> domainI) const
+    {
+        return gridGeometry(domainI).gridView();
+    }
+
+
+    void setupExtendedStencil()
+    {
+        extendedSourceStencil_.clear();
+
+        for (const auto& element : elements(gridView(voidDomainIdx)))
+        {
+            const auto eIdx = gridGeometry(voidDomainIdx).elementMapper().index(element);
+            const auto vIdx0 = gridGeometry(voidDomainIdx).vertexMapper().subIndex(element, 0, 1);
+            const auto vIdx1 = gridGeometry(voidDomainIdx).vertexMapper().subIndex(element, 1, 1);
+
+            for (const auto& is : intersections(gridView(voidDomainIdx), element))
+            {
+                if (is.neighbor())
+                {
+                    const auto& outsideElement = is.outside();
+                    for (int i = 0; i < 2; ++i)
+                    {
+                        const auto outsideVertexIdx = gridGeometry(voidDomainIdx).vertexMapper().subIndex(outsideElement, i, 1);
+                        if (outsideVertexIdx != vIdx0 && outsideVertexIdx != vIdx1)
+                            extendedSourceStencil_.stencil()[eIdx].push_back(outsideVertexIdx);
+                    }
+                }
+            }
+
+            removeDuplicates_(extendedSourceStencil_.stencil()[eIdx]);
+        }
+    }
+
+
+protected:
+
+    template<std::size_t i>
+    VolumeVariables<i>& getVolVarAccess_(Dune::index_constant<i> domainIdx, GridVolumeVariables<i>& gridVolVars, ElementVolumeVariables<i>& elemVolVars, const SubControlVolume<i>& scv)
+    {
+        if constexpr (getPropValue<SubDomainTypeTag<i>, Properties::EnableGridVolumeVariablesCache>())
+            return gridVolVars.volVars(scv);
+        else
+            return elemVolVars[scv];
+    }
+
+    /*!
+     * \brief Return a reference to the grid variables of a sub problem
+     * \param domainIdx The domain index
+     */
+    template<std::size_t i>
+    GridVariables<i>& gridVars_(Dune::index_constant<i> domainIdx)
+    {
+        if (std::get<i>(gridVariables_))
+            return *std::get<i>(gridVariables_);
+        else
+            DUNE_THROW(Dune::InvalidStateException, "The gridVariables pointer was not set. Use setGridVariables() before calling this function");
+    }
+
+    //! Removes duplicate entries from the coupling stencils
+    void removeDuplicates_(std::vector<std::size_t>& stencil)
+    {
+        std::sort(stencil.begin(), stencil.end());
+        stencil.erase(std::unique(stencil.begin(), stencil.end()), stencil.end());
+    }
+
+
+    bool convectiveHeatTransfer_;
+
+    std::vector<std::size_t> emptyStencil_;
+    std::unique_ptr<const CouplingMapper> couplingMapper_;
+    const GridGeometry<voidDomainIdx>* voidGridGeometry_;
+    const GridGeometry<solidDomainIdx>* solidGridGeometry_;
+
+    VoidElementSolution voidElementSolution_;
+    SolidElementSolution solidElementSolution_;
+    mutable ElementCouplingContext elementCouplingContext_;
+
+    /*!
+     * \brief A tuple of std::shared_ptrs to the grid variables of the sub problems
+     */
+    GridVariablesTuple gridVariables_;
+
+    //! the extended source stencil object
+    PoreNetwork::PNMHeatExtendedSourceStencil<ThisType> extendedSourceStencil_;
+};
+
+}; // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/multidomain/dualnetwork/couplingmapper.hh b/dumux/multidomain/dualnetwork/couplingmapper.hh
new file mode 100644
index 0000000000000000000000000000000000000000..32c76259ed424398c9add55d54c9d0ff5d301c6a
--- /dev/null
+++ b/dumux/multidomain/dualnetwork/couplingmapper.hh
@@ -0,0 +1,415 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PoreNetwork
+ * \copydoc Dumux::PoreNetwork::DualNetworkCouplingMapper
+ */
+
+#ifndef DUMUX_DUAL_NETWORK_COUPLINGMAPPER_HH
+#define DUMUX_DUAL_NETWORK_COUPLINGMAPPER_HH
+
+#include <type_traits>
+#include <unordered_map>
+#include <algorithm>
+#include <vector>
+#include <dune/common/iteratorrange.hh>
+
+#include <dune/common/exceptions.hh>
+#include <dumux/common/entitymap.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \ingroup PoreNetwork
+ * \brief Coupling mapper for Stokes and Darcy domains with equal dimension.
+ */
+
+template<class Scalar>
+class DualNetworkCouplingMapper
+{
+    struct HostGridConnectionInfo
+    {
+        std::size_t hostGridElementIndex;
+        std::size_t voidVertexHostIdx;
+        std::size_t solidVertexHostIdx;
+        Scalar connectionArea;
+        Scalar connectionLength;
+        std::vector<std::size_t> voidElementHostIdx;
+        std::vector<std::size_t> solidElementHostIdx;
+        std::vector<std::size_t> coupledVoidVertexHostIdx;
+        std::vector<std::size_t> coupledSolidVertexHostIdx;
+        std::size_t connectionGlobalId;
+    };
+
+    struct SubGridConnectionInfo
+    {
+        std::size_t id; // the global id of the connections
+        std::size_t solidVertexIdx; // the directly coupled solid vertex
+        std::size_t voidVertexIdx; // the directly coupled void vertex
+        std::size_t someSolidElementIdx; // index of one the solid elements adjacent to the solid vertex
+        std::size_t someVoidElementIdx; // index of one the void elements adjacent to the solid vertex
+        std::vector<std::size_t> convectionVoidElementIdx; // all void elements adjacent to the own void vertex coupled to the same solid vertex
+        Scalar connectionArea;
+        Scalar connectionLength;
+    };
+
+    template<class Vector>
+    class ConnectionIterator : public Dune::ForwardIteratorFacade<ConnectionIterator<Vector>, const SubGridConnectionInfo>
+    {
+        using ThisType = ConnectionIterator<Vector>;
+        using Iterator = typename Vector::const_iterator;
+    public:
+        ConnectionIterator(const Iterator& it, const std::vector<SubGridConnectionInfo>& info)
+        : it_(it), InfoPtr_(&info) {}
+
+        ConnectionIterator() : it_(Iterator()), InfoPtr_(nullptr) {}
+
+        //! dereferencing yields a subcontrol volume
+        const SubGridConnectionInfo& dereference() const
+        { return InfoPtr_->at(*it_); }
+        // { return (*InfoPtr_)[*it_]; }
+
+        bool equals(const ThisType& other) const
+        { return it_ == other.it_; }
+
+        void increment()
+        { ++it_; }
+
+    private:
+        Iterator it_;
+        const std::vector<SubGridConnectionInfo>* InfoPtr_;
+    };
+
+public:
+    using Stencil = std::vector<std::size_t>;
+
+    template<class HostGridView, class HostGridData, class VoidGridGeometry, class SolidGridGeometry>
+    DualNetworkCouplingMapper(const HostGridView& hostGridView,
+                              const HostGridData& hostGridData,
+                              const VoidGridGeometry& voidGridGeometry,
+                              const SolidGridGeometry& solidGridGeometry)
+    {
+        fillVertexMap_(hostGridView, voidGridGeometry, voidHostToSubVertexIdxMap_);
+        fillVertexMap_(hostGridView, solidGridGeometry, solidHostToSubVertexIdxMap_);
+        fillElementMap_(hostGridView, voidGridGeometry, voidHostToSubElementIdxMap_);
+        fillElementMap_(hostGridView, solidGridGeometry, solidHostToSubElementIdxMap_);
+
+        isCoupledVoidDof_.resize(voidGridGeometry.gridView().size(1), false);
+        isCoupledSolidDof_.resize(solidGridGeometry.gridView().size(1), false);
+
+        const auto connectionInfo = getConnectionInfo_(hostGridView, hostGridData);
+        connectionInfo_.resize(connectionInfo.size());
+        for (const auto& info : connectionInfo)
+        {
+            auto voidHostToSubVertexIdx = [&](const auto hostIdx)
+            { return voidHostToSubVertexIdxMap_.at(hostIdx); };
+
+            auto solidHostToSubVertexIdx = [&](const auto hostIdx)
+            { return solidHostToSubVertexIdxMap_.at(hostIdx); };
+
+            const auto directlyCoupledVoidDofIdx = voidHostToSubVertexIdx(info.voidVertexHostIdx);
+            const auto directlyCoupledSolidDofIdx = solidHostToSubVertexIdx(info.solidVertexHostIdx);
+
+            auto coupledVoidElementIdxSub = info.voidElementHostIdx;
+            auto coupledSolidElementIdxSub = info.solidElementHostIdx;
+
+            // convert hostgrid indices to subgrid indices
+            std::transform(coupledVoidElementIdxSub.begin(), coupledVoidElementIdxSub.end(),
+                           coupledVoidElementIdxSub.begin(), [&](const auto eIdx){ return voidHostToSubElementIdxMap_.at(eIdx); });
+            std::transform(coupledSolidElementIdxSub.begin(), coupledSolidElementIdxSub.end(),
+                           coupledSolidElementIdxSub.begin(), [&](const auto eIdx){ return solidHostToSubElementIdxMap_.at(eIdx); });
+
+            // initialize an empty vector - will be filled later in a second loop
+            auto convectionVoidElementIdx = std::vector<std::size_t>();
+
+            voidToSolidConnectionIds_[directlyCoupledVoidDofIdx].emplace_back(info.connectionGlobalId);
+            solidToVoidConnectionIds_[directlyCoupledSolidDofIdx].emplace_back(info.connectionGlobalId);
+
+            connectionInfo_[info.connectionGlobalId] = SubGridConnectionInfo{info.connectionGlobalId,
+                                                                             directlyCoupledSolidDofIdx,
+                                                                             directlyCoupledVoidDofIdx,
+                                                                             coupledSolidElementIdxSub[0],
+                                                                             coupledVoidElementIdxSub[0],
+                                                                             convectionVoidElementIdx,
+                                                                             info.connectionArea,
+                                                                             info.connectionLength};
+
+            hostGridElementIndexToGlobalId_[info.hostGridElementIndex] = info.connectionGlobalId;
+
+            isCoupledVoidDof_[directlyCoupledVoidDofIdx] = true;
+            isCoupledSolidDof_[directlyCoupledSolidDofIdx] = true;
+
+            for (const auto eIdxVoidHost : info.voidElementHostIdx)
+            {
+                const auto eIdxSubVoid = voidHostToSubElementIdxMap_.at(eIdxVoidHost);
+                voidToSolidStencils_[eIdxSubVoid].push_back(directlyCoupledSolidDofIdx);
+            }
+
+            for (const auto eIdxSolidHost : info.solidElementHostIdx)
+            {
+                const auto eIdxSubSolid = solidHostToSubElementIdxMap_.at(eIdxSolidHost);
+                solidToVoidStencils_[eIdxSubSolid].push_back(directlyCoupledVoidDofIdx);
+            }
+        }
+
+        for (auto& stencil : voidToSolidStencils_)
+            removeDuplicates_(stencil.second);
+        for (auto& stencil : solidToVoidStencils_)
+            removeDuplicates_(stencil.second);
+
+        // second loop: find void element coupling for convective transport
+        auto voidFVGeometry = localView(voidGridGeometry);
+        for (const auto& voidElement : elements(voidGridGeometry.gridView()))
+        {
+            voidFVGeometry.bindElement(voidElement);
+            std::array<std::size_t, 2> dofIndex;
+            std::array<std::vector<std::size_t>, 2> coupledSolidVertexIdx;
+            for (const auto& scv : scvs(voidFVGeometry))
+                dofIndex[scv.indexInElement()] = scv.dofIndex();
+
+            // check if both void pores couple to the same solid pore
+            if (isCoupledVoidDof_[dofIndex[0]] && isCoupledVoidDof_[dofIndex[1]])
+            {
+                for (auto& conn0 : voidToSolidConnectionIds_[dofIndex[0]])
+                {
+                    for (auto& conn1 : voidToSolidConnectionIds_[dofIndex[1]])
+                    {
+                        const auto globalId0 = conn0;
+                        const auto globalId1 = conn1;
+                        assert(globalId0 != globalId1);
+
+                        if (connectionInfo_[globalId0].solidVertexIdx == connectionInfo_[globalId1].solidVertexIdx)
+                        {
+                            const auto voidElemIdx = voidGridGeometry.elementMapper().index(voidElement);
+                            connectionInfo_[globalId0].convectionVoidElementIdx.push_back(voidElemIdx);
+                            connectionInfo_[globalId1].convectionVoidElementIdx.push_back(voidElemIdx);
+                        }
+                    }
+                }
+            }
+        }
+
+        for (auto& entry : voidToSolidConnectionIds_)
+        {
+            removeDuplicates_(entry.second);
+
+            std::cout << "void dof " << entry.first << " couples to " << entry.second.size() << " solid dofs: " << std::endl;
+            for (auto& conn : entry.second)
+            {
+                const auto& info = connectionInfo_[conn];
+                assert(entry.first == info.voidVertexIdx);
+                std::cout << "solid vertex " << info.solidVertexIdx << " with elems ";
+                for (const auto e : info.convectionVoidElementIdx)
+                    std::cout << e << " ";
+                std:: cout << "||" << std::endl;
+            }
+
+            std::cout << std::endl;
+        }
+
+        for (auto& entry : solidToVoidConnectionIds_)
+        {
+            removeDuplicates_(entry.second);
+
+            std::cout << "solid dof " << entry.first << " couples to " << entry.second.size() << " void dofs: " << std::endl;
+            for (auto& conn : entry.second)
+            {
+                const auto& info = connectionInfo_[conn];
+                assert(entry.first == info.solidVertexIdx);
+                std::cout << "void vertex " << info.voidVertexIdx << " with elems ";
+                for (const auto e : info.convectionVoidElementIdx)
+                    std::cout << e << " ";
+                std:: cout << "||" << std::endl;
+            }
+
+            std::cout << std::endl;
+        }
+
+        // TODO maybe delete hostToSub maps? or make public?
+    }
+
+    const auto& voidToSolidStencils() const
+    { return voidToSolidStencils_; }
+
+    const auto& solidToVoidStencils() const
+    { return solidToVoidStencils_; }
+
+    const std::vector<bool>& isCoupledVoidDof() const
+    { return isCoupledVoidDof_; }
+
+    const std::vector<bool>& isCoupledSolidDof() const
+    { return isCoupledSolidDof_; }
+
+    //! Returns an iterator allowing for (const auto& conn : voidToSolidConnections(dofIdx)) {...}
+    auto voidToSolidConnections(const std::size_t dofIdx) const
+    {
+        const auto& ids = voidToSolidConnectionIds().at(dofIdx);
+        using Iterator = ConnectionIterator<std::vector<std::size_t>>;
+        return Dune::IteratorRange<Iterator>(Iterator(ids.cbegin(), connectionInfo()),
+                                             Iterator(ids.cend(), connectionInfo()));
+    }
+
+    auto solidToVoidConnections(const std::size_t dofIdx) const
+    {
+        const auto& ids = solidToVoidConnectionIds().at(dofIdx);
+        using Iterator = ConnectionIterator<std::vector<std::size_t>>;
+        return Dune::IteratorRange<Iterator>(Iterator(ids.cbegin(), connectionInfo()),
+                                             Iterator(ids.cend(), connectionInfo()));
+    }
+
+    const auto& voidToSolidConnectionIds() const
+    { return voidToSolidConnectionIds_; }
+
+    const auto& solidToVoidConnectionIds() const
+    { return solidToVoidConnectionIds_; }
+
+    const auto& connectionInfo() const
+    { return connectionInfo_; }
+
+    const auto& voidHostToSubVertexIdxMap() const
+    { return voidHostToSubVertexIdxMap_; }
+
+    const auto& solidHostToSubVertexIdxMap() const
+    { return solidHostToSubVertexIdxMap_; }
+
+    const auto& voidHostToSubElementIdxMap() const
+    { return voidHostToSubElementIdxMap_; }
+
+    const auto& solidHostToSubElementIdxMap() const
+    { return solidHostToSubElementIdxMap_; }
+
+    const auto& hostGridElementIndexToGlobalId() const
+    { return hostGridElementIndexToGlobalId_; }
+
+private:
+
+    template<class HostGridView, class HostGridData>
+    std::vector<HostGridConnectionInfo> getConnectionInfo_(const HostGridView& hostGridView,
+                                                           const HostGridData& hostGridData)
+    {
+        std::vector<HostGridConnectionInfo> connectionInfo;
+        std::size_t connectionGlobalId = 0;
+
+        for (const auto& element : elements(hostGridView))
+        {
+            if (hostGridData.getParameter(element, "ThroatDomainType") == 2) // interconnection throat
+            {
+                const auto& vertex0 = element.template subEntity<1>(0);
+                const auto& vertex1 = element.template subEntity<1>(1);
+
+                HostGridConnectionInfo info;
+                info.hostGridElementIndex = hostGridView.indexSet().index(element);
+                info.connectionGlobalId = connectionGlobalId++;
+                info.voidVertexHostIdx = hostGridView.indexSet().index(vertex0);
+                info.solidVertexHostIdx = hostGridView.indexSet().index(vertex1);
+
+                if (hostGridData.getParameter(vertex0, "PoreDomainType") == 1)
+                {
+                    assert(hostGridData.getParameter(vertex1, "PoreDomainType") == 0);
+                    using std::swap;
+                    swap(info.voidVertexHostIdx, info.solidVertexHostIdx);
+                }
+
+                info.connectionArea = hostGridData.getParameter(element, "ThroatCrossSectionalArea");
+                info.connectionLength = element.geometry().volume();
+
+                for (const auto& intersection : intersections(hostGridView, element))
+                {
+                    if (!intersection.neighbor())
+                        continue;
+
+                    const auto& outsideElement = intersection.outside();
+
+                    // skip other interconnection throats
+                    if (hostGridData.getParameter(outsideElement, "ThroatDomainType") == 2)
+                        continue;
+
+                    const auto outsideElementIdx = hostGridView.indexSet().index(outsideElement);
+
+                    if (hostGridData.getParameter(outsideElement, "ThroatDomainType") == 0)
+                        info.voidElementHostIdx.push_back(outsideElementIdx);
+                    else
+                        info.solidElementHostIdx.push_back(outsideElementIdx);
+
+                    std::array outsideDomainType = {-1, -1};
+                    for (int localVIdx = 0; localVIdx < 2; ++localVIdx)
+                    {
+                        const auto& outsideVertex = outsideElement.template subEntity<1>(localVIdx);
+                        const auto outsideVertexIdx = hostGridView.indexSet().index(outsideVertex);
+                        outsideDomainType[localVIdx] = hostGridData.getParameter(outsideVertex, "PoreDomainType");
+
+                        if (localVIdx == 1 && (outsideDomainType[1] != outsideDomainType[0]))
+                            DUNE_THROW(Dune::IOError, "Pore with hostIdx " << hostGridView.indexSet().index(outsideElement.template subEntity<1>(0))
+                                                       << " has domain type " << outsideDomainType[0]
+                                                       << ", but pore with hostIdx " << outsideVertexIdx
+                                                       << " has domain type " << outsideDomainType[1] << ". Check your grid file");
+
+                        if (outsideDomainType[localVIdx] == 0)
+                            info.coupledVoidVertexHostIdx.push_back(outsideVertexIdx);
+                        else
+                            info.coupledSolidVertexHostIdx.push_back(outsideVertexIdx);
+                    }
+                }
+
+                connectionInfo.emplace_back(std::move(info));
+            }
+        }
+
+        return connectionInfo;
+    }
+
+    template<class HostGridView, class SubGridGeometry, class Map>
+    void fillVertexMap_(const HostGridView& hostGridView, const SubGridGeometry& subGridGeometry, Map& map)
+    {
+        for (const auto& vertex : vertices(subGridGeometry.gridView()))
+        {
+            const auto vIdxSub = subGridGeometry.vertexMapper().index(vertex);
+            const auto vIdxHost = hostGridView.indexSet().index(vertex.impl().hostEntity());
+            map[vIdxHost] = vIdxSub;
+        }
+    }
+
+    template<class HostGridView, class SubGridGeometry, class Map>
+    void fillElementMap_(const HostGridView& hostGridView, const SubGridGeometry& subGridGeometry, Map& map)
+    {
+        for (const auto& element : elements(subGridGeometry.gridView()))
+        {
+            const auto eIdxSub = subGridGeometry.elementMapper().index(element);
+            const auto eIdxHost = hostGridView.indexSet().index(element.impl().hostEntity());
+            map[eIdxHost] = eIdxSub;
+        }
+    }
+
+    //! Removes duplicate entries from the coupling stencils
+    void removeDuplicates_(std::vector<std::size_t>& stencil)
+    {
+        std::sort(stencil.begin(), stencil.end());
+        stencil.erase(std::unique(stencil.begin(), stencil.end()), stencil.end());
+    }
+
+    std::unordered_map<std::size_t, std::size_t> voidHostToSubVertexIdxMap_;
+    std::unordered_map<std::size_t, std::size_t> solidHostToSubVertexIdxMap_;
+    std::unordered_map<std::size_t, std::size_t> voidHostToSubElementIdxMap_;
+    std::unordered_map<std::size_t, std::size_t> solidHostToSubElementIdxMap_;
+
+    std::vector<bool> isCoupledVoidDof_;
+    std::vector<bool> isCoupledSolidDof_;
+
+    std::unordered_map<std::size_t, Stencil> voidToSolidStencils_;
+    std::unordered_map<std::size_t, Stencil> solidToVoidStencils_;
+
+    std::unordered_map<std::size_t, std::vector<std::size_t>> voidToSolidConnectionIds_;
+    std::unordered_map<std::size_t, std::vector<std::size_t>> solidToVoidConnectionIds_;
+
+    std::vector<SubGridConnectionInfo> connectionInfo_;
+    std::unordered_map<std::size_t, std::size_t> hostGridElementIndexToGlobalId_;
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/multidomain/dualnetwork/extendedsourcestencil.hh b/dumux/multidomain/dualnetwork/extendedsourcestencil.hh
new file mode 100644
index 0000000000000000000000000000000000000000..2463bd23a44b3a69e22d29ef8f4a77ddbb3e27f8
--- /dev/null
+++ b/dumux/multidomain/dualnetwork/extendedsourcestencil.hh
@@ -0,0 +1,180 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PoreNetwork
+ * \brief Extended source stencil helper class for coupling managers
+ */
+
+#ifndef DUMUX_DUAL_NETWORK_EXTENDEDSOURCESTENCIL_HH
+#define DUMUX_DUAL_NETWORK_EXTENDEDSOURCESTENCIL_HH
+
+#include <vector>
+
+#include <dune/common/indices.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/numericdifferentiation.hh>
+#include <dumux/discretization/method.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \ingroup PoreNetwork
+ * \brief A class managing an extended source stencil
+ * \tparam CouplingManager the coupling manager type
+ */
+template<class CouplingManager>
+class PNMHeatExtendedSourceStencil
+{
+    using MDTraits = typename CouplingManager::MultiDomainTraits;
+    using Scalar = typename MDTraits::Scalar;
+
+    template<std::size_t id> using SubDomainTypeTag = typename MDTraits::template SubDomain<id>::TypeTag;
+    template<std::size_t id> using GridGeometry = GetPropType<SubDomainTypeTag<id>, Properties::GridGeometry>;
+    template<std::size_t id> using GridView = typename GridGeometry<id>::GridView;
+    template<std::size_t id> using Element = typename GridView<id>::template Codim<0>::Entity;
+
+    static constexpr auto solidDomainIdx = CouplingManager::solidDomainIdx;
+    static constexpr auto voidDomainIdx = CouplingManager::voidDomainIdx;
+
+    template<std::size_t id>
+    static constexpr bool isBox()
+    { return GridGeometry<id>::discMethod == DiscretizationMethods::box; }
+public:
+    /*!
+     * \brief extend the jacobian pattern of the diagonal block of domain i
+     *        by those entries that are not already in the uncoupled pattern
+     * \note Such additional dependencies can arise from the coupling, e.g. if a coupling source
+     *       term depends on a non-local average of a quantity of the same domain
+     */
+    template<std::size_t id, class JacobianPattern>
+    void extendJacobianPattern(const CouplingManager& couplingManager, Dune::index_constant<id> domainI, JacobianPattern& pattern) const
+    {
+        // add additional dof dependencies
+        for (const auto& element : elements(couplingManager.gridView(domainI)))
+        {
+            const auto& dofs = extendedSourceStencil_(couplingManager, domainI, element);
+            if constexpr (isBox<domainI>())
+            {
+                for (int i = 0; i < element.subEntities(GridView<domainI>::dimension); ++i)
+                    for (const auto globalJ : dofs)
+                        pattern.add(couplingManager.problem(domainI).gridGeometry().vertexMapper().subIndex(element, i, GridView<domainI>::dimension), globalJ);
+            }
+            else
+            {
+                const auto globalI = couplingManager.problem(domainI).gridGeometry().elementMapper().index(element);
+                for (const auto globalJ : dofs)
+                    pattern.add(globalI, globalJ);
+            }
+        }
+    }
+
+    /*!
+     * \brief evaluate additional derivatives of the element residual of a domain with respect
+     *        to dofs in the same domain that are not in the regular stencil (per default this is not the case)
+     * \note Such additional dependencies can arise from the coupling, e.g. if a coupling source
+     *       term depends on a non-local average of a quantity of the same domain
+     * \note This is the same for box and cc
+     */
+    template<std::size_t i, class LocalAssemblerI, class SolutionVector, class JacobianMatrixDiagBlock, class GridVariables> //TODO edit function s.t. curSol from couplingmanager is used like in dumux/dumux/multidomain/embedded/extendedsourcestencil.hh (commit 3257876)
+    void evalAdditionalDomainDerivatives(CouplingManager& couplingManager,
+                                         Dune::index_constant<i> domainI,
+                                         const LocalAssemblerI& localAssemblerI,
+                                         const SolutionVector& curSol,
+                                         JacobianMatrixDiagBlock& A,
+                                         GridVariables& gridVariables) const
+    {
+        // const auto& curSolI = couplingManager.curSol(domainI); //TODO:curSol declared protected in .../dumux/dumux/multidomain/couplingmanager.hh
+        const auto& curSolI = curSol;
+        constexpr auto numEq = std::decay_t<decltype(curSolI[0])>::size();
+        const auto& elementI = localAssemblerI.element();
+
+        // only do something if we have an extended stencil
+        if (extendedSourceStencil_(couplingManager, domainI, elementI).empty())
+            return;
+
+        // compute the undeflected residual (source only!)
+        const auto origResidual = localAssemblerI.evalLocalSourceResidual(elementI);
+
+        // compute derivate for all additional dofs in the circle stencil
+        for (const auto dofIndex : extendedSourceStencil_(couplingManager, domainI, elementI))
+        {
+            // std::cout << "deflecting " << dofIndex << std::endl;
+            auto partialDerivs = origResidual;
+            const auto origPriVars = curSolI[dofIndex];
+
+            // calculate derivatives w.r.t to the privars at the dof at hand
+            for (int pvIdx = 0; pvIdx < numEq; pvIdx++)
+            {
+                // reset partial derivatives
+                partialDerivs = 0.0;
+
+                auto evalResiduals = [&](Scalar priVar)
+                {
+                    // update the coupling context (solution vector and recompute element residual)
+                    auto priVars = origPriVars;
+                    priVars[pvIdx] = priVar;
+                    couplingManager.updateCouplingContext(domainI, localAssemblerI, domainI, dofIndex, priVars, pvIdx);
+                    return localAssemblerI.evalLocalSourceResidual(elementI);
+                };
+
+                // derive the residuals numerically
+                static const int numDiffMethod = getParam<int>("Assembly.NumericDifferenceMethod");
+                NumericDifferentiation::partialDerivative(evalResiduals, curSolI[dofIndex][pvIdx],
+                                                          partialDerivs, origResidual, numDiffMethod); //TODO: maybe change like in dumux/dumux/md/embedded/extendedsourcestencil.hh line 142
+
+                // update the global stiffness matrix with the current partial derivatives
+                for (const auto& scvJ : scvs(localAssemblerI.fvGeometry()))
+                {
+                    for (int eqIdx = 0; eqIdx < numEq; eqIdx++)
+                    {
+                        // 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'.
+                        // std::cout << "Adding " << partialDerivs[scvJ.indexInElement()][eqIdx] << ", pvIdx " << pvIdx <<  std::endl;
+                        A[scvJ.dofIndex()][dofIndex][eqIdx][pvIdx] += partialDerivs[scvJ.indexInElement()][eqIdx];
+                    }
+                }
+
+                // restore the original coupling context
+                couplingManager.updateCouplingContext(domainI, localAssemblerI, domainI, dofIndex, origPriVars, pvIdx);
+            }
+        }
+    }
+
+    //! clear the internal data
+    void clear() { sourceStencils_.clear(); }
+
+    //! return a reference to the stencil
+    auto& stencil()
+    { return sourceStencils_; }
+
+private:
+    //! the extended source stencil due to the source average (always empty for lowdim, but may be filled for bulk)
+    template<std::size_t id>
+    const auto& extendedSourceStencil_(const CouplingManager& couplingManager, Dune::index_constant<id> domainId, const Element<id>& element) const
+    {
+        if constexpr (domainId == voidDomainIdx)
+        {
+            const auto voidElementIdx = couplingManager.problem(voidDomainIdx).gridGeometry().elementMapper().index(element);
+            if (sourceStencils_.count(voidElementIdx))
+                return sourceStencils_.at(voidElementIdx);
+        }
+
+        return couplingManager.emptyStencil(domainId);
+    }
+
+    //! the additional stencil for the kernel evaluations / circle averages
+    std::unordered_map<std::size_t, std::vector<std::size_t>> sourceStencils_;
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/porenetwork/CMakeLists.txt b/dumux/porenetwork/CMakeLists.txt
index 3b6b5dc9e5d59dd0c13d1605324633bdd2c653b1..328dbdfddcf607efe2f65547ce9ae314c4d91a8e 100644
--- a/dumux/porenetwork/CMakeLists.txt
+++ b/dumux/porenetwork/CMakeLists.txt
@@ -6,6 +6,7 @@ add_subdirectory(1pnc)
 add_subdirectory(2p)
 add_subdirectory(common)
 add_subdirectory(util)
+add_subdirectory(solidenergy)
 
 file(GLOB DUMUX_PORENETWORK_HEADERS *.hh *.inc)
 install(FILES ${DUMUX_PORENETWORK_HEADERS}
diff --git a/dumux/porenetwork/solidenergy/CMakeLists.txt b/dumux/porenetwork/solidenergy/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c437a45f7a80c9ab1b53b34587498643e443b333
--- /dev/null
+++ b/dumux/porenetwork/solidenergy/CMakeLists.txt
@@ -0,0 +1,6 @@
+# SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+file(GLOB DUMUX_PORENETWORK_SOLIDENERGY_HEADERS *.hh *.inc)
+install(FILES ${DUMUX_PORENETWORK_SOLIDENERGY_HEADERS}
+        DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/porenetwork/solidenergy)
diff --git a/dumux/porenetwork/solidenergy/fluxvariablescache.hh b/dumux/porenetwork/solidenergy/fluxvariablescache.hh
new file mode 100644
index 0000000000000000000000000000000000000000..5bf204bb3e3f6c05c95640f6ebba3f919cfa1e83
--- /dev/null
+++ b/dumux/porenetwork/solidenergy/fluxvariablescache.hh
@@ -0,0 +1,54 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PNMSolidEnergyModel
+ * \brief Flux variables cache for PNM solid-energy model
+ */
+#ifndef DUMUX_PNM_SOLID_ENERGY_FLUXVARIABLESCACHE_HH
+#define DUMUX_PNM_SOLID_ENERGY_FLUXVARIABLESCACHE_HH
+
+namespace Dumux::PoreNetwork {
+
+template<class Scalar>
+class SolidEnergyFluxVariablesCache
+{
+public:
+    //! whether the cache needs an update when the solution changes
+    static bool constexpr isSolDependent = false;
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class SubControlVolumeFace>
+    void update(const Problem& problem,
+                const Element& element,
+                const FVElementGeometry& fvGeometry,
+                const ElementVolumeVariables& elemVolVars,
+                const SubControlVolumeFace& scvf)
+    {
+        grainContactArea_ = problem.spatialParams().throatCrossSectionalArea(element, elemVolVars);
+        throatLength_ = problem.spatialParams().throatLength(element, elemVolVars);
+        throatInscribedRadius_ = problem.spatialParams().throatInscribedRadius(element, elemVolVars);
+    }
+
+    Scalar grainContactArea() const
+    { return grainContactArea_; }
+
+    Scalar throatLength() const
+    { return throatLength_; }
+
+    Scalar throatInscribedRadius() const
+    { return throatInscribedRadius_; }
+
+private:
+    Scalar grainContactArea_;
+    Scalar throatLength_;
+    Scalar throatInscribedRadius_;
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/porenetwork/solidenergy/iofields.hh b/dumux/porenetwork/solidenergy/iofields.hh
new file mode 100644
index 0000000000000000000000000000000000000000..92d6d516cacdcf41808f334a2eada8d0004e3588
--- /dev/null
+++ b/dumux/porenetwork/solidenergy/iofields.hh
@@ -0,0 +1,43 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PNMSolidEnergyModel
+ * \copydoc Dumux::PoreNetwork::SolidEnergyIOFields
+ */
+#ifndef DUMUX_PNM_SOLID_ENERGY_IO_FIELDS_HH
+#define DUMUX_PNM_SOLID_ENERGY_IO_FIELDS_HH
+
+#include <dumux/porenetwork/common/iofields.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \ingroup PNMSolidEnergyModel
+ * \brief Adds output fields specific to the PNM solid-energy model
+ */
+class SolidEnergyIOFields
+{
+public:
+
+    template <class OutputModule>
+    static void initOutputModule(OutputModule& out)
+    {
+        CommonIOFields::initOutputModule(out);
+        out.addVolumeVariable( [](const auto& v){ return v.temperature(); }, IOName::temperature());
+    }
+
+    template <class ModelTraits, class FluidSystem = void, class SolidSystem = void>
+    static std::string primaryVariableName(int pvIdx, int state = 0)
+    {
+        return IOName::temperature();
+    }
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/porenetwork/solidenergy/model.hh b/dumux/porenetwork/solidenergy/model.hh
new file mode 100644
index 0000000000000000000000000000000000000000..a278bd2c367bb2eea5d1e859ea19617b7fe1d5aa
--- /dev/null
+++ b/dumux/porenetwork/solidenergy/model.hh
@@ -0,0 +1,98 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PNMSolidEnergyModel
+ * \brief The energy balance equation for a porous solid in pore-networks based on PorousMediumFlow-SolidEnergy
+ */
+
+#ifndef DUMUX_PNM_SOLID_ENERGY_MODEL_HH
+#define DUMUX_PNM_SOLID_ENERGY_MODEL_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/porenetwork/properties.hh>
+
+#include <dumux/porousmediumflow/solidenergy/model.hh>
+#include <dumux/flux/porenetwork/grainfourierslaw.hh>
+
+#include "spatialparams.hh"
+#include "volumevariables.hh"
+#include "fluxvariablescache.hh"
+#include "iofields.hh"
+
+/*!
+ * \ingroup PNMSolidEnergyModel
+ * \brief The energy balance equation for a porous solid
+ *
+ * The energy balance is described by the following equation:
+ \f[
+   \frac{ \partial n c_p \varrho T}{\partial t}
+   - \text{div} \left\lbrace \lambda_\text{pm} \textbf{grad} T \right\rbrace = q,
+ \f]
+ * where \f$n\f$ is the volume fraction of the conducting material, \f$c_p\f$ its specific heat capacity,
+ * \f$\varrho\f$ its density, \f$T\f$ the temperature, and \f$\lambda\f$ the heat conductivity of the porous solid.
+*/
+
+///////////////////////////////////////////////////////////////////////////
+// properties for the solid-energy model
+///////////////////////////////////////////////////////////////////////////
+namespace Dumux::Properties {
+
+//////////////////////////////////////////////////////////////////
+// Type tags
+//////////////////////////////////////////////////////////////////
+
+//! The type tags for the implicit solid-energy problems
+// Create new type tags
+namespace TTag {
+struct PNMSolidEnergy{ using InheritsFrom = std::tuple<PoreNetworkModel, SolidEnergy>; };
+}
+
+//! Set the volume variables property
+template<class TypeTag>
+struct VolumeVariables<TypeTag, TTag::PNMSolidEnergy>
+{
+private:
+    using PV = GetPropType<TypeTag, Properties::PrimaryVariables>;
+    using SSY = GetPropType<TypeTag, Properties::SolidSystem>;
+    using SST = GetPropType<TypeTag, Properties::SolidState>;
+    using MT = GetPropType<TypeTag, Properties::ModelTraits>;
+
+    using Traits = SolidEnergyVolumeVariablesTraits<PV, SSY, SST, MT>;
+public:
+    using type = PoreNetwork::SolidEnergyVolumeVariables<Traits>;
+};
+
+template<class TypeTag>
+struct HeatConductionType<TypeTag, TTag::PNMSolidEnergy>
+{ using type = PoreNetwork::TruncatedPyramidGrainFouriersLaw<GetPropType<TypeTag, Properties::Scalar>>; };
+
+//! The spatial parameters to be employed.
+//! Use PNMOnePSpatialParams by default.
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::PNMSolidEnergy>
+{
+private:
+    using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    using type = PoreNetwork::SolidEnergySpatialParams<FVGridGeometry, Scalar>;
+};
+
+//! The flux variables cache
+template<class TypeTag>
+struct FluxVariablesCache<TypeTag, TTag::PNMSolidEnergy>
+{ using type = PoreNetwork::SolidEnergyFluxVariablesCache<GetPropType<TypeTag, Properties::Scalar>>; };
+
+//! Set the vtk output fields specific to this model
+template<class TypeTag>
+struct IOFields<TypeTag, TTag::PNMSolidEnergy>
+{ using type = PoreNetwork::SolidEnergyIOFields; };
+
+} // namespace Dumux::Properties
+
+#endif
diff --git a/dumux/porenetwork/solidenergy/spatialparams.hh b/dumux/porenetwork/solidenergy/spatialparams.hh
new file mode 100644
index 0000000000000000000000000000000000000000..562aece0c9640a5d0f6193300b1d3ffaecfec47f
--- /dev/null
+++ b/dumux/porenetwork/solidenergy/spatialparams.hh
@@ -0,0 +1,56 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PNMSolidEnergyModel
+ * \ingroup SpatialParameters
+ * \brief The spatial parameters for solid-energy models in pore networks.
+ */
+#ifndef DUMUX_PNM_SOLID_ENERGY_SPATIAL_PARAMS_HH
+#define DUMUX_PNM_SOLID_ENERGY_SPATIAL_PARAMS_HH
+
+#include <dumux/porenetwork/common/spatialparams.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \ingroup PNMSolidEnergyModel
+ * \ingroup SpatialParameters
+ * \brief The base class for spatial parameters for pore network solid models.
+ */
+template<class FVGridGeometry, class Scalar>
+class SolidEnergySpatialParams
+: public PoreNetwork::SpatialParams<FVGridGeometry, Scalar,
+                                        SolidEnergySpatialParams<FVGridGeometry, Scalar>>
+{
+    using ParentType = PoreNetwork::SpatialParams<
+        FVGridGeometry, Scalar, SolidEnergySpatialParams<FVGridGeometry, Scalar>
+    >;
+
+    using GridView = typename FVGridGeometry::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+    using FVElementGeometry = typename FVGridGeometry::LocalView;
+    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
+
+public:
+    using PermeabilityType = Scalar;
+    using ParentType::ParentType;
+
+    /*!
+     * \brief Define the porosity \f$\mathrm{[-]}\f$.
+     *
+     * \param globalPos The global position
+     */
+    Scalar porosityAtPos(const GlobalPosition& globalPos) const
+    { return 0.0; }
+
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/porenetwork/solidenergy/volumevariables.hh b/dumux/porenetwork/solidenergy/volumevariables.hh
new file mode 100644
index 0000000000000000000000000000000000000000..3bbc63249135119dc669f9f9ce882e8768ac5598
--- /dev/null
+++ b/dumux/porenetwork/solidenergy/volumevariables.hh
@@ -0,0 +1,71 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup PNMSolidEnergyModel
+ * \brief Quantities required by the solid-energy fully implicit model defined on a vertex.
+ */
+
+#ifndef DUMUX_PNM_SOLID_ENERGY_VOLUME_VARIABLES_HH
+#define DUMUX_PNM_SOLID_ENERGY_VOLUME_VARIABLES_HH
+
+#include <dumux/porousmediumflow/solidenergy/volumevariables.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \ingroup PNMSolidEnergyModel
+ * \brief Contains the quantities which are constant within a
+ *        finite volume in the solid-energy model.
+ *
+ * \tparam Traits Class encapsulating types to be used by the vol vars
+ */
+template<class Traits>
+class SolidEnergyVolumeVariables : public Dumux::SolidEnergyVolumeVariables<Traits>
+{
+    using ParentType = Dumux::SolidEnergyVolumeVariables<Traits>;
+
+    using Scalar = typename Traits::PrimaryVariables::value_type;
+public:
+
+    /*!
+     * \brief Updates all quantities for a given control volume.
+     *
+     * \param elemSol A vector containing all primary variables connected to the element
+     * \param problem The object specifying the problem which ought to
+     *                be simulatedgit
+     * \param element An element which contains part of the control volume
+     * \param scv The sub-control volume
+     */
+    template<class ElemSol, class Problem, class Element, class Scv>
+    void update(const ElemSol& elemSol,
+                const Problem& problem,
+                const Element& element,
+                const Scv& scv)
+    {
+        ParentType::update(elemSol, problem, element, scv);
+
+        poreInscribedRadius_ = problem.spatialParams().poreInscribedRadius(element, scv, elemSol);
+        poreVolume_ = problem.gridGeometry().poreVolume(scv.dofIndex());
+    }
+
+    Scalar poreInscribedRadius() const
+    { return poreInscribedRadius_; }
+
+
+    Scalar poreVolume() const
+    { return poreVolume_; }
+
+protected:
+
+    Scalar poreInscribedRadius_;
+    Scalar poreVolume_;
+};
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/dumux/porousmediumflow/nonisothermal/localresidual_incompressible.hh b/dumux/porousmediumflow/nonisothermal/localresidual_incompressible.hh
new file mode 100644
index 0000000000000000000000000000000000000000..850d4b474cca2d3a90b878b23898a728b8d324a9
--- /dev/null
+++ b/dumux/porousmediumflow/nonisothermal/localresidual_incompressible.hh
@@ -0,0 +1,96 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \ingroup NIModel
+ * \brief Element-wise calculation of the local residual for non-isothermal
+ *        fully implicit models.
+ */
+
+#ifndef DUMUX_ENERGY_LOCAL_RESIDUAL_INCOMPRESSIBLE_HH
+#define DUMUX_ENERGY_LOCAL_RESIDUAL_INCOMPRESSIBLE_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/numeqvector.hh>
+#include "localresidual.hh"
+
+namespace Dumux {
+
+// forward declaration
+template<class TypeTag, bool enableEneryBalance>
+class EnergyLocalResidualIncompressibleImplementation;
+
+template<class TypeTag>
+using EnergyLocalResidualIncompressible = EnergyLocalResidualIncompressibleImplementation<TypeTag, GetPropType<TypeTag, Properties::ModelTraits>::enableEnergyBalance()>;
+
+/*!
+ * \ingroup NIModel
+ * \brief Element-wise calculation of the energy residual for non-isothermal problems.
+ */
+template<class TypeTag>
+class EnergyLocalResidualIncompressibleImplementation<TypeTag, false>: public EnergyLocalResidualImplementation<TypeTag, false>
+{}; //energy balance not enabled
+
+/*!
+ * \ingroup NIModel
+ * \brief TODO docme!
+ */
+template<class TypeTag>
+class EnergyLocalResidualIncompressibleImplementation<TypeTag, true>: public EnergyLocalResidualImplementation<TypeTag, true>
+{
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>;
+    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
+    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
+    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+    using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
+    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
+    using Indices = typename ModelTraits::Indices;
+
+    static constexpr int numPhases = ModelTraits::numFluidPhases();
+    enum { energyEqIdx = Indices::energyEqIdx };
+
+public:
+    /*!
+     * \brief The advective phase energy fluxes for incompressible flow.
+     *
+     * Using specific internal energy $u$ instead of specific enthalpy \f$h\f$ for incompressible flow in convective flux
+     * to account for otherwise neglected pressure work term (\f$\nabla p \cdot v\f$).
+     *
+     * Compressible formulation in EnergyLocalResidual (neglecting pressure work term (\f$\nabla p \cdot v\f$))
+     * is
+     \f{align*}{
+     \frac{\partial}{\partial t} (\rho u) &= -\nabla \cdot (\rho v h) + \nabla \cdot (\lambda \nabla T)
+     \f}
+     *
+     * Incompressible energy formulation is
+     \f{align*}{
+     \frac{\partial}{\partial t} (\rho u) = -\nabla \cdot (\rho v u) + \nabla \cdot (\lambda \nabla T)
+     \f}
+     *
+     * \param flux The flux
+     * \param fluxVars The flux variables.
+     * \param phaseIdx The phase index
+     */
+    static void heatConvectionFlux(NumEqVector& flux,
+                                   FluxVariables& fluxVars,
+                                   int phaseIdx)
+    {
+        // internal energy used instead of enthalpy for incompressible flow
+        auto upwindTerm = [phaseIdx](const auto& volVars)
+        { return volVars.density(phaseIdx)*volVars.mobility(phaseIdx)*volVars.internalEnergy(phaseIdx); };
+
+        flux[energyEqIdx] += fluxVars.advectiveFlux(phaseIdx, upwindTerm);
+    }
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/CMakeLists.txt b/test/multidomain/CMakeLists.txt
index 02e190d442f316c347adc706ecf5d85f37f9d034..d1cbb4783c2cf009de39399c535a200e5d93574f 100644
--- a/test/multidomain/CMakeLists.txt
+++ b/test/multidomain/CMakeLists.txt
@@ -5,3 +5,4 @@ add_subdirectory(embedded)
 add_subdirectory(poromechanics)
 add_subdirectory(boundary)
 add_subdirectory(facet)
+add_subdirectory(dualnetwork)
diff --git a/test/multidomain/dualnetwork/CMakeLists.txt b/test/multidomain/dualnetwork/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fbeae0cf0e78bbb0b651d3620eb1935614b9cdd5
--- /dev/null
+++ b/test/multidomain/dualnetwork/CMakeLists.txt
@@ -0,0 +1,17 @@
+# SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+dune_symlink_to_source_files(FILES grids "params.input")
+
+dumux_add_test(NAME test_md_dualnetwork_heat_1p_solid
+              LABELS multidomain dualnetwork 1p
+              SOURCES main.cc
+              CMAKE_GUARD "( dune-subgrid_FOUND AND dune-foamgrid_FOUND AND HAVE_UMFPACK )"
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_md_dualnetwork_heat_solid-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_dualnetwork_heat_solid-00001.vtp
+                                ${CMAKE_SOURCE_DIR}/test/references/test_md_dualnetwork_heat_void-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_md_dualnetwork_heat_void-00001.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_dualnetwork_heat_1p_solid params.input
+                                    -Vtk.OutputName test_md_dualnetwork_heat")
diff --git a/test/multidomain/dualnetwork/fourierslaw.hh b/test/multidomain/dualnetwork/fourierslaw.hh
new file mode 100644
index 0000000000000000000000000000000000000000..f01f6a331871a68d49a5c54f78fd19383ebbee4e
--- /dev/null
+++ b/test/multidomain/dualnetwork/fourierslaw.hh
@@ -0,0 +1,450 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \brief This file contains the data which is required to calculate
+ *        diffusive heat fluxes with Fourier's law.
+ */
+#ifndef DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_FLUID_FOURIERS_LAW_HH
+#define DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_FLUID_FOURIERS_LAW_HH
+
+#include <dumux/common/math.hh>
+
+namespace Dumux::PoreNetwork {
+
+template<bool isFluid>
+struct FluidOrGrainPyramidFouriersLaw
+{
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto flux(const Problem& problem,
+                     const Element& element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                     const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+        return transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache) * deltaT;
+    }
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto transmissibility(const Problem& problem,
+                                 const Element& element,
+                                 const FVElementGeometry& fvGeometry,
+                                 const ElementVolumeVariables& elemVolVars,
+                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                                 const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        using Scalar = typename ElementVolumeVariables::VolumeVariables::PrimaryVariables::value_type;
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
+
+        const auto getConductivity = [&](const auto& volVars)
+        {
+            if constexpr (isFluid)
+                return volVars.fluidThermalConductivity(0);
+            else
+                return volVars.solidThermalConductivity();
+        };
+
+        const auto insideThermalConducitivity = getConductivity(insideVolVars);
+        const auto outsideThermalConducitivity = getConductivity(outsideVolVars);
+
+        const auto eIdx = fvGeometry.gridGeometry().elementMapper().index(element);
+        const auto throatCenter = problem.spatialParams().throatCenter(eIdx);
+        const auto distanceInside = (insideScv.dofPosition() - throatCenter).two_norm();
+        const auto distanceOutside = (outsideScv.dofPosition() - throatCenter).two_norm();
+
+        const auto throatArea = [&]()
+        {
+            static const Scalar givenArea = getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.ThroatArea", 0.0);
+            if (givenArea > 0.0)
+                return givenArea;
+
+            if constexpr (isFluid)
+                return fluxVarsCache.throatCrossSectionalArea(0);
+            else
+                return fluxVarsCache.grainContactArea();
+        }();
+
+
+        const Scalar pyramidFrustumTopArea = [&]()
+        {
+            static const bool realArea = getParamFromGroup<bool>(problem.paramGroup(), "Problem.UseRealThroatAreaInPyramid", true);
+            if (realArea)
+                return throatArea;
+            else
+            {
+                // use inscribed throat diameter as square side length
+                const Scalar baseLength = fluxVarsCache.throatInscribedRadius() * 2.0;
+                return baseLength*baseLength;
+            }
+        }();
+
+        const auto getPyramidFrustumBaseArea = [&](const auto& volVars, const Scalar distance)
+        {
+            static const Scalar givenArea = getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.PoreArea", 0.0);
+            if (givenArea > 0.0)
+                return givenArea;
+
+            static const bool realVolume = getParamFromGroup<bool>(problem.paramGroup(), "Problem.UseVolumeEqualPyramid", true);
+            if (realVolume)
+            {
+                using std::sqrt;
+                const Scalar vol = 0.5 * volVars.poreVolume();
+                const Scalar baseLenTop = sqrt(pyramidFrustumTopArea);
+                const Scalar height = distance;
+                // see https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus
+                const Scalar baseLenBot = 0.5*sqrt(3.0) * sqrt(-(baseLenTop*baseLenTop*height-4.0*vol)/height) -0.5*baseLenTop;
+                return baseLenBot*baseLenBot;
+            }
+            else
+                return volVars.poreVolume() / (2.0*distance);
+        };
+
+        using std::sqrt;
+        const auto baseAreaInside = getPyramidFrustumBaseArea(insideVolVars, distanceInside);
+        const auto baseAreaOutside = getPyramidFrustumBaseArea(outsideVolVars, distanceOutside);
+        const auto topArea = pyramidFrustumTopArea;
+        const auto insideTransmissibility = insideThermalConducitivity * sqrt(baseAreaInside*topArea) / distanceInside;
+        const auto outsideTransmissibility = outsideThermalConducitivity * sqrt(baseAreaOutside*topArea) / distanceOutside;
+
+        return 1.0 / (1.0/insideTransmissibility + 1.0/outsideTransmissibility);
+    }
+};
+
+template<bool isFluid>
+struct FixedFactorFouriersLaw
+{
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto flux(const Problem& problem,
+                     const Element& element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                     const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+        return transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache) * deltaT;
+    }
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto transmissibility(const Problem& problem,
+                                 const Element& element,
+                                 const FVElementGeometry& fvGeometry,
+                                 const ElementVolumeVariables& elemVolVars,
+                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                                 const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        using Scalar = typename ElementVolumeVariables::VolumeVariables::PrimaryVariables::value_type;
+
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+
+        const auto getConductivity = [&](const auto& volVars)
+        {
+            if constexpr (isFluid)
+                return volVars.fluidThermalConductivity(0);
+            else
+                return volVars.solidThermalConductivity();
+        };
+
+        const auto insideThermalConducitivity = getConductivity(insideVolVars);
+        const auto outsideThermalConducitivity = getConductivity(outsideVolVars);
+
+        const auto eIdx = fvGeometry.gridGeometry().elementMapper().index(element);
+        const auto throatCenter = problem.spatialParams().throatCenter(eIdx);
+        const auto distanceInside = (insideScv.dofPosition() - throatCenter).two_norm();
+        const auto distanceOutside = (outsideScv.dofPosition() - throatCenter).two_norm();
+
+        static const Scalar fixedFactor = getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.FixedFourierFactor");
+        const auto insideTransmissibility = insideThermalConducitivity*4*distanceInside*fixedFactor;
+        const auto outsideTransmissibility = outsideThermalConducitivity*4*distanceOutside*fixedFactor;
+
+        return 1.0 / (1.0/insideTransmissibility + 1.0/outsideTransmissibility);
+    }
+};
+
+template<bool isFluid>
+struct FancyFactorFouriersLaw
+{
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto flux(const Problem& problem,
+                     const Element& element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                     const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+        return transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache) * deltaT;
+    }
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto transmissibility(const Problem& problem,
+                                 const Element& element,
+                                 const FVElementGeometry& fvGeometry,
+                                 const ElementVolumeVariables& elemVolVars,
+                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                                 const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        using Scalar = typename ElementVolumeVariables::VolumeVariables::PrimaryVariables::value_type;
+
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+
+        const auto getConductivity = [&](const auto& volVars)
+        {
+            if constexpr (isFluid)
+                return volVars.fluidThermalConductivity(0);
+            else
+                return volVars.solidThermalConductivity();
+        };
+
+        const auto insideThermalConducitivity = getConductivity(insideVolVars);
+        const auto outsideThermalConducitivity = getConductivity(outsideVolVars);
+
+        const auto eIdx = fvGeometry.gridGeometry().elementMapper().index(element);
+
+        const auto distance = [&](const auto& scv)
+        {
+            static const bool useThroatCenter =  getParamFromGroup<bool>(problem.paramGroup(), "Problem.UseThroatCenter", true);
+            if (useThroatCenter)
+            {
+                const auto throatCenter = problem.spatialParams().throatCenter(eIdx);
+                return (scv.dofPosition() - throatCenter).two_norm();
+            }
+            else
+            {
+                static const Scalar R = getParam<Scalar>("Problem.SphereRadius", 50e-6);
+                static const Scalar overlapFactor = getParam<Scalar>("Problem.OverlapFactor");
+                static const auto dx = overlapFactor*R;
+                return dx;
+            }
+        };
+
+        const Scalar distanceInside = distance(insideScv);
+        const Scalar distanceOutside = distance(outsideScv);
+
+        assert(distanceInside > 0.0);
+        assert(distanceOutside > 0.0);
+
+        static const Scalar liquidThermalConductivity = getParam<Scalar>("2.Component.LiquidThermalConductivity");
+        static const Scalar solidThermalConductivity = getParam<Scalar>("1.Component.SolidThermalConductivity");
+        static const Scalar kappa = liquidThermalConductivity / solidThermalConductivity;
+        static const Scalar kappaFactor = isFluid ? kappa : 1.0/kappa;
+
+        const Scalar ApInside = insideVolVars.poreVolume()/(2.0*distanceInside);
+        const Scalar ApOutside = outsideVolVars.poreVolume()/(2.0*distanceOutside);
+
+        Scalar effectiveAreaInside = 0.0;
+        Scalar effectiveAreaOutside = 0.0;
+        Scalar At = 0.0;
+
+        const auto effectiveArea = [kappaFactor = kappaFactor](const Scalar At, const Scalar Cinf, const Scalar C0)
+        {
+            return At*(Cinf + ((C0 - Cinf)*(Cinf - 1.0))/((Cinf - 1.0) + kappaFactor*(1.0 - C0)));
+        };
+
+        static const Scalar useExactThroatAreaSphere = getParam<bool>("Problem.UseExactThroatAreaSphere", false);
+        if (useExactThroatAreaSphere)
+        {
+            static const Scalar R = getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.SphereRadius", 50e-6);
+            const auto As = [](Scalar x, Scalar dx, Scalar R) { return M_PI*(R - x)*(R + x); };
+            const auto Asq = [](Scalar x, Scalar dx, Scalar R) { return 4*dx*dx; };
+            const auto Asemicirc = [](Scalar x, Scalar dx, Scalar R) {
+                const auto r = std::sqrt((R - x)*(R + x));
+                return (r*r)*std::acos(dx/r) - dx*std::sqrt(r*r - dx*dx);
+            };
+            const auto A1s = [&](Scalar x, Scalar dx, Scalar R) { return As(x, dx, R) - 4*Asemicirc(x, dx, R); };
+            const auto A2s = [&](Scalar x, Scalar dx, Scalar R) { return As(x, dx, R); };
+            const auto A1f = [&](Scalar x, Scalar dx, Scalar R) { return Asq(x, dx, R) - A1s(x, dx, R); };
+            // const auto A2f = [&](Scalar x, Scalar dx, Scalar R) { return Asq(x, dx, R) - A2s(x, dx, R); }; // TODO unused?
+
+            At = isFluid ? A1f(0, distanceInside, R) : A2s(distanceInside, distanceInside, R);
+            const Scalar C0 = isFluid ? 0.1 : 0.45;
+            const Scalar Cinf = isFluid ? ApInside/At : ApInside/At*1.45;
+            effectiveAreaInside = effectiveArea(At, Cinf, C0);
+            effectiveAreaOutside = effectiveAreaInside;
+            assert(std::isnormal(effectiveAreaInside));
+        }
+        else
+        {
+            At = [&]
+            {
+                if constexpr (isFluid)
+                    return elemFluxVarsCache[scvf].throatCrossSectionalArea(0);
+                else
+                    return elemFluxVarsCache[scvf].grainContactArea();
+            }();
+
+            static const Scalar C0 = isFluid ? getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.C0Fluid")
+                                   : getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.C0Solid");
+            static const Scalar CinfFactor = isFluid ? getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.CInfFactorFluid")
+                                           : getParamFromGroup<Scalar>(problem.paramGroup(), "Problem.CInfFactorSolid");
+            using std::max;
+            const Scalar CinfInside = max(ApInside/At*CinfFactor, 1.0);
+            const Scalar CinfOutside = max(ApOutside/At*CinfFactor, 1.0);
+            effectiveAreaInside = effectiveArea(At, CinfInside, C0);
+            effectiveAreaOutside = effectiveArea(At, CinfOutside, C0);
+        }
+
+        assert(std::isnormal(effectiveAreaInside));
+        assert(effectiveAreaInside > 0.0);
+        assert(std::isnormal(effectiveAreaOutside));
+        assert(effectiveAreaOutside > 0.0);
+
+        const Scalar tInside = std::sqrt(effectiveAreaInside*At)/distanceInside;
+        const Scalar tOutside = std::sqrt(effectiveAreaOutside*At)/distanceOutside;
+
+        const auto insideTransmissibility = insideThermalConducitivity*tInside;
+        const auto outsideTransmissibility = outsideThermalConducitivity*tOutside;
+        const auto result = 1.0 / (1.0/insideTransmissibility + 1.0/outsideTransmissibility);
+
+        if (!std::isnormal(result))
+            DUNE_THROW(Dune::InvalidStateException, "Error in heat conductivity. Check your grid and your factors.");
+
+        return result;
+    }
+};
+
+template<class BaseLaw>
+struct ScalingFouriersLaw
+{
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto flux(const Problem& problem,
+                     const Element& element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                     const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        using Scalar = typename ElementVolumeVariables::VolumeVariables::PrimaryVariables::value_type;
+        const auto deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+
+        static const bool useScaling = getParamFromGroup<bool>(problem.paramGroup(), "Problem.UseFourierScaling", true);
+        if (!useScaling)
+            return transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache) * deltaT;
+
+
+        Scalar factor = 1.0;
+        const auto& bBoxMin = problem.gridGeometry().bBoxMin();
+        const auto& bBoxMax = problem.gridGeometry().bBoxMax();
+        const auto throatCenter = element.geometry().center();
+
+        for (int i = 0; i < throatCenter.size(); ++i)
+        {
+            constexpr Scalar eps = 1e-8; // TODO
+            if (throatCenter[i] < bBoxMin[i] + eps || throatCenter[i] > bBoxMax[i] - eps)
+                factor *= 0.5;
+        }
+
+        static const Scalar baseTransmissibility = problem.getInternalReferenceHeatTransmissibility();
+        return baseTransmissibility * factor * deltaT;
+    }
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto transmissibility(const Problem& problem,
+                                 const Element& element,
+                                 const FVElementGeometry& fvGeometry,
+                                 const ElementVolumeVariables& elemVolVars,
+                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                                 const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        return BaseLaw::transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
+    }
+};
+
+template<bool isFluid>
+struct FlexibleFouriersLaw
+{
+    enum class Mode {pyramid, fixedFactor, fancyFactor, tpfa};
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto flux(const Problem& problem,
+                     const Element& element,
+                     const FVElementGeometry& fvGeometry,
+                     const ElementVolumeVariables& elemVolVars,
+                     const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                     const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = elemVolVars[outsideScv];
+        const auto deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
+        return transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache) * deltaT;
+    }
+
+    template<class Problem, class Element, class FVElementGeometry,
+             class ElementVolumeVariables, class ElementFluxVariablesCache>
+    static auto transmissibility(const Problem& problem,
+                                 const Element& element,
+                                 const FVElementGeometry& fvGeometry,
+                                 const ElementVolumeVariables& elemVolVars,
+                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
+                                 const ElementFluxVariablesCache& elemFluxVarsCache)
+    {
+        static const Mode mode = [&]()
+        {
+            const auto m = getParamFromGroup<std::string>(problem.paramGroup(), "Problem.ThroatConductionType");
+            if (m == "Pyramid")
+                return Mode::pyramid;
+            else if (m == "FancyFactor")
+                return Mode::fancyFactor;
+            else if (m == "FixedFactor")
+                return Mode::fixedFactor;
+            else
+                return Mode::tpfa;
+        }();
+
+        if (mode == Mode::pyramid)
+            return FluidOrGrainPyramidFouriersLaw<isFluid>::transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
+        else if (mode == Mode::fixedFactor)
+            return FixedFactorFouriersLaw<isFluid>::transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
+        else if (mode == Mode::fancyFactor)
+            return FancyFactorFouriersLaw<isFluid>::transmissibility(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
+        else return 0.0; // TODO implement TPFA
+    }
+};
+
+
+} // end namespace Dumux::PoreNetwork
+
+#endif
diff --git a/test/multidomain/dualnetwork/grids/Berea_center_cropped_200_200_dual.dgf b/test/multidomain/dualnetwork/grids/Berea_center_cropped_200_200_dual.dgf
new file mode 100644
index 0000000000000000000000000000000000000000..77c9b8e3b6b99068cb7cc37654c4c044ee202308
--- /dev/null
+++ b/test/multidomain/dualnetwork/grids/Berea_center_cropped_200_200_dual.dgf
@@ -0,0 +1,7917 @@
+DGF
+% SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+% SPDX-License-Identifier: CC-BY-4.0
+% Vertex parameters: PoreInscribedRadius PoreExtendedRadius PoreVolume PoreLabel PoreDomainType
+% Element parameters: ThroatInscribedRadius ThroatLength ThroatCrossSectionalArea ThroatShapeFactor ThroatCenterX ThroatCenterY ThroatCenterZ ThroatLabel ThroatDomainType
+Vertex
+parameters 5
+0.0001881917232142857 0.00034896884598214286 0.00021423666741071426 1.1406094216772177e-05 6.803074543952941e-05 3.4205122251999993e-13 -1.0 0.0
+0.000311925710553814 0.0010358762661093696 0.0001842786955764542 3.0420603129166368e-05 6.301662207126617e-05 8.768116605847499e-13 3.0 0.0
+0.00045785103983794734 0.00036100855418636055 0.00018263135972316003 2.4154800110906098e-05 7.502064745426178e-05 9.046033224144998e-13 -1.0 0.0
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+1048 1052 2.6725e-05 1e-09 3.513990075e-09 0.06074074074074075 0.0009995149999999999 0.00045432499999999994 0.00013362499999999998 -1.0 1.0
+1051 1085 1.6034999999999998e-05 3.525664007540729e-05 9.7134685e-10 0.0625 0.00033673499999999995 5.345e-05 0.0005558799999999999 4.0 1.0
+1051 1115 3.585534927129745e-05 1e-09 6.3137545249999994e-09 0.0625 0.00044363499999999995 1.6034999999999998e-05 0.0006039849999999999 4.0 1.0
+1056 1058 2.6725e-05 3.0172091198161282e-05 7.3422394249999995e-09 0.019099286563614745 0.00073761 0.000475705 0.00043294499999999996 -1.0 1.0
+1056 1074 2.20379990363121e-05 7.055796305860522e-05 4.742458149999999e-09 0.0369792826910225 0.00078037 0.000550535 0.00042225499999999996 -1.0 1.0
+1059 1070 3.162144758939743e-05 1e-09 6.742289899999999e-09 0.03344671201814059 0.00058795 0.00047035999999999996 0.000903305 -1.0 1.0
+1061 1075 3.422469955682754e-05 6.127583032761627e-06 5.428114749999999e-09 0.04638671875 0.000828475 0.00022449 0.001010205 6.0 1.0
+1061 1108 1.690237429857254e-05 2.351343540252602e-05 1.3141751499999998e-09 0.05867346938775509 0.0007001949999999999 0.00013896999999999998 0.0009620999999999999 6.0 1.0
+1062 1092 2.3298315777778623e-05 4.6490093187916595e-05 2.028400775e-09 0.0625 0.0010262399999999999 0.0007536449999999999 0.0008926149999999999 6.0 1.0
+1062 1095 5.7567411046028133e-05 3.938263035183545e-05 1.3941684199999999e-08 0.0625 0.000903305 0.000689505 0.00103693 6.0 1.0
+1064 1110 1.7727359982728957e-05 1e-09 2.9140405499999998e-09 0.03631185475258099 0.0008658899999999999 9.086499999999999e-05 0.000272595 4.0 1.0
+1066 1075 5.2912801442146295e-05 1e-09 1.4827323974999998e-08 0.04707482993197279 0.000860545 0.00029932 0.00098348 6.0 1.0
+1066 1095 2.507027276754379e-05 0.00011683996982100556 7.313670399999999e-09 0.030914140804250693 0.00083382 0.00045966999999999997 0.00093003 6.0 1.0
+1066 1104 1.690237429857254e-05 4.5760981470852516e-05 6.570875749999999e-10 0.0625 0.001031585 0.000261905 0.0007750249999999999 2.0 1.0
+1066 1111 1.1951783515214919e-05 9.987404654041472e-05 8.285017249999999e-10 0.04640000000000001 0.00099417 0.000144315 0.0007910599999999999 4.0 1.0
+1069 1095 1.690237429857254e-05 0.00011306096383405336 2.0569697999999997e-09 0.035555555555555556 0.0007215749999999999 0.0007001949999999999 0.001063655 6.0 1.0
+1069 1102 5.731874001026153e-05 1e-09 1.5170152274999998e-08 0.0625 0.000475705 0.0006574349999999999 0.0009620999999999999 6.0 1.0
+1075 1096 3.7415e-05 1e-09 7.02798015e-09 0.0625 0.0009139949999999999 0.00024587 0.001063655 6.0 1.0
+1078 1091 3.380474859714508e-05 1e-09 8.485000424999998e-09 0.021330077563918415 4.276e-05 0.00075899 0.000550535 1.0 1.0
+1082 1103 1.511794272303581e-05 1e-09 1.1141919749999999e-09 0.043333333333333335 0.00078037 1.6034999999999998e-05 7.483e-05 5.0 1.0
+1088 1090 7.030249889373778e-05 1e-09 2.3226617324999998e-08 0.061474480151228736 0.00013896999999999998 5.8794999999999995e-05 0.000518465 4.0 1.0
+1090 1107 3.817093517541885e-05 1e-09 6.3137545249999994e-09 0.057492195629552545 0.00019241999999999998 0.00018707499999999998 0.00059864 1.0 1.0
+1106 1109 2.3903567030429837e-05 3.27420166785989e-05 9.99915875e-10 0.0625 3.2069999999999996e-05 0.00041156499999999997 0.00012827999999999998 5.0 1.0
+
+#
+BOUNDARYDOMAIN
+default 1
+#
diff --git a/test/multidomain/dualnetwork/main.cc b/test/multidomain/dualnetwork/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..923673c6ce17d0828ca0ae25dbdd052808f607d8
--- /dev/null
+++ b/test/multidomain/dualnetwork/main.cc
@@ -0,0 +1,669 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ *
+ * \brief test for the pore network model
+ */
+#include <config.h>
+
+#include <iostream>
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/timer.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/initialize.hh>
+
+#include <dumux/linear/istlsolvers.hh>
+#include <dumux/linear/linearsolvertraits.hh>
+#include <dumux/linear/linearalgebratraits.hh>
+
+#include <dumux/io/grid/gridmanager_sub.hh>
+
+#include <dumux/io/grid/porenetwork/gridmanager.hh>
+#include <dumux/io/grid/porenetwork/subgriddata.hh>
+
+#include <dumux/multidomain/fvassembler.hh>
+#include <dumux/multidomain/newtonsolver.hh>
+
+#include <dumux/porenetwork/common/pnmvtkoutputmodule.hh>
+#include <dumux/porenetwork/common/boundaryflux.hh>
+
+#include "properties.hh"
+
+int main(int argc, char** argv)
+{
+    using namespace Dumux;
+
+    // initialize MPI, finalize is done automatically on exit
+    Dumux::initialize(argc, argv);
+    const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+    // print dumux start message
+    if (mpiHelper.rank() == 0)
+        DumuxMessage::print(/*firstCall=*/true);
+
+    ////////////////////////////////////////////////////////////
+    // parse the command line arguments and input file
+    ////////////////////////////////////////////////////////////
+
+    // parse command line arguments
+    Parameters::init(argc, argv);
+
+    //////////////////////////////////////////////////////////////////////
+    // try to create a grid (from the given grid file or the input file)
+    /////////////////////////////////////////////////////////////////////
+
+    using HostGridManager = PoreNetwork::GridManager<3>;
+    HostGridManager hostGridManager;
+    hostGridManager.init();
+    const auto hostGridView = hostGridManager.grid().leafGridView();
+    const auto hostGridData = hostGridManager.getGridData();
+
+    using SubGrid = Dune::SubGrid<1, typename HostGridManager::Grid>;
+    using SubGridManager = GridManager<SubGrid>;
+
+    auto elementSelectorVoid = [&](const auto& element)
+    {
+        return hostGridData->getParameter(element, "ThroatDomainType") == 0;
+    };
+
+    auto elementSelectorSolid = [&](const auto& element)
+    {
+        return hostGridData->getParameter(element, "ThroatDomainType") == 1;
+    };
+
+    // for debugging only
+    auto elementSelectorCoupling = [&](const auto& element)
+    {
+        return hostGridData->getParameter(element, "ThroatDomainType") == 2;
+    };
+
+    auto& hostGrid = hostGridManager.grid();
+    SubGridManager subgridManagerVoid; subgridManagerVoid.init(hostGrid, elementSelectorVoid);
+    SubGridManager subgridManagerSolid; subgridManagerSolid.init(hostGridManager.grid(), elementSelectorSolid);
+    SubGridManager subgridManagerCoupling; subgridManagerCoupling.init(hostGridManager.grid(), elementSelectorCoupling);
+    const auto voidGridView = subgridManagerVoid.grid().leafGridView();
+    const auto solidGridView = subgridManagerSolid.grid().leafGridView();
+    const auto couplingGridView = subgridManagerCoupling.grid().leafGridView(); // for debugging only
+
+    std::cout << "Void grid has " << voidGridView.size(0) << " elements" << std::endl;
+    std::cout << "Solid grid has " << solidGridView.size(0) << " elements" << std::endl;
+
+    using SubGridData = PoreNetwork::SubGridData<HostGridManager::Grid, SubGridManager::Grid>;
+    auto voidGridData = std::make_shared<SubGridData>(subgridManagerVoid.grid(), hostGridData);
+    auto solidGridData = std::make_shared<SubGridData>(subgridManagerSolid.grid(), hostGridData);
+
+    using SolidTypeTag = Properties::TTag::PNMSolidModel;
+    using VoidTypeTag = Properties::TTag::PNMVoidModel;
+
+    // create the finite volume grid geometry
+    using VoidGridGeometry = GetPropType<VoidTypeTag, Properties::GridGeometry>;
+    auto voidGridGeometry = std::make_shared<VoidGridGeometry>(voidGridView, *voidGridData);
+    voidGridGeometry->update(voidGridView,*voidGridData);
+
+    using SolidGridGeometry = GetPropType<SolidTypeTag, Properties::GridGeometry>;
+    auto solidGridGeometry = std::make_shared<SolidGridGeometry>(solidGridView,*solidGridData);
+    solidGridGeometry->update(solidGridView,*solidGridData);
+
+    // the spatial parameters
+    using VoidSpatialParams = GetPropType<VoidTypeTag, Properties::SpatialParams>;
+    auto voidSpatialParams = std::make_shared<VoidSpatialParams>(voidGridGeometry, *voidGridData);
+
+    using SolidSpatialParams = GetPropType<SolidTypeTag, Properties::SpatialParams>;
+    auto solidSpatialParams = std::make_shared<SolidSpatialParams>(solidGridGeometry, *solidGridData);
+
+    // the coupling manager
+    using Traits = MultiDomainTraits<SolidTypeTag, VoidTypeTag>;
+    using CouplingManager = PoreNetwork::PNMHeatTransferCouplingManager<Traits>;
+    auto couplingManager = std::make_shared<CouplingManager>();
+    using SolutionVector = typename Traits::SolutionVector;
+    SolutionVector sol;
+
+    // the problem (boundary conditions)
+    using VoidProblem = GetPropType<VoidTypeTag, Properties::Problem>;
+    auto voidProblem = std::make_shared<VoidProblem>(voidGridGeometry, voidSpatialParams, couplingManager);
+    sol[CouplingManager::voidDomainIdx].resize(voidProblem->gridGeometry().numDofs());
+    voidProblem->applyInitialSolution(sol[CouplingManager::voidDomainIdx]);
+
+    using SolidProblem = GetPropType<SolidTypeTag, Properties::Problem>;
+    auto solidProblem = std::make_shared<SolidProblem>(solidGridGeometry, solidSpatialParams, couplingManager);
+    sol[CouplingManager::solidDomainIdx].resize(solidProblem->gridGeometry().numDofs());
+    solidProblem->applyInitialSolution(sol[CouplingManager::solidDomainIdx]);
+
+    auto solOld = sol;
+
+    // initialize the coupling manager
+    couplingManager->init(solidProblem, voidProblem,
+                          hostGridView, *hostGridData,
+                          voidGridView, solidGridView, sol);
+
+    // the grid variables
+    using VoidGridVariables = GetPropType<VoidTypeTag, Properties::GridVariables>;
+    auto voidGridVariables = std::make_shared<VoidGridVariables>(voidProblem, voidGridGeometry);
+    voidGridVariables->init(sol[CouplingManager::voidDomainIdx]);
+
+    using SolidGridVariables = GetPropType<SolidTypeTag, Properties::GridVariables>;
+    auto solidGridVariables = std::make_shared<SolidGridVariables>(solidProblem, solidGridGeometry);
+    solidGridVariables->init(sol[CouplingManager::solidDomainIdx]);
+
+    // initialize the vtk output modules
+    using Scalar = typename Traits::Scalar;
+    using VoidVtkWriter = PoreNetwork::VtkOutputModule<
+        VoidGridVariables, GetPropType<VoidTypeTag, Properties::FluxVariables>, decltype(sol[CouplingManager::voidDomainIdx])
+    >;
+    VoidVtkWriter voidVtkWriter(*voidGridVariables, sol[CouplingManager::voidDomainIdx],  voidProblem->name());
+    GetPropType<VoidTypeTag, Properties::IOFields>::initOutputModule(voidVtkWriter);
+    using SolidVtkWriter = PoreNetwork::VtkOutputModule<
+        SolidGridVariables, GetPropType<SolidTypeTag, Properties::FluxVariables>, decltype(sol[CouplingManager::solidDomainIdx])
+    >;
+    SolidVtkWriter solidVtkWriter(*solidGridVariables, sol[CouplingManager::solidDomainIdx],  solidProblem->name());
+    GetPropType<SolidTypeTag, Properties::IOFields>::initOutputModule(solidVtkWriter);
+
+    // get some time loop parameters
+    using Scalar = typename Traits::Scalar;
+    const auto tEnd = getParam<Scalar>("TimeLoop.TEnd", 1.0);
+    const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize", 1.0);
+    auto dt = getParam<Scalar>("TimeLoop.DtInitial", 1.0);
+
+    // instantiate time loop
+    auto timeLoop = std::make_shared<TimeLoop<Scalar>>(0, dt, tEnd);
+    timeLoop->setMaxTimeStepSize(maxDt);
+
+    static const bool isStationary = getParam<bool>("Problem.IsStationary", true);
+
+    // the assembler
+    using Assembler = MultiDomainFVAssembler<Traits, CouplingManager, DiffMethod::numeric>;
+    auto assembler = isStationary ? std::make_shared<Assembler>(std::make_tuple(solidProblem, voidProblem),
+                                                                std::make_tuple(solidGridGeometry,
+                                                                                voidGridGeometry),
+                                                                std::make_tuple(solidGridVariables,
+                                                                                voidGridVariables),
+                                                                couplingManager)
+                                  : std::make_shared<Assembler>(std::make_tuple(solidProblem, voidProblem),
+                                                                std::make_tuple(solidGridGeometry,
+                                                                                voidGridGeometry),
+                                                                std::make_tuple(solidGridVariables,
+                                                                                voidGridVariables),
+                                                                couplingManager,
+                                                                timeLoop, solOld);
+
+    // the linear solver
+    using LinearSolver = UMFPackIstlSolver<SeqLinearSolverTraits,
+                                               LinearAlgebraTraitsFromAssembler<Assembler>>;
+    auto linearSolver = std::make_shared<LinearSolver>();
+
+    // pass gridvars to void problem
+    voidProblem->setGridVariables(voidGridVariables);
+
+    // pass gridVars to coupling manager
+    couplingManager->setGridVariables(std::make_tuple(solidGridVariables, voidGridVariables));
+
+    // add dof indices and corresponding host grid vertex indices
+    std::vector<std::size_t> voidDofIdx(voidGridView.size(1));
+    std::vector<std::size_t> voidHostGridVertexIdx(voidGridView.size(1));
+    std::vector<Scalar> voidConductionSource(voidGridView.size(1));
+    std::vector<Scalar> voidConvectionSource(voidGridView.size(1));
+    for (const auto& v : vertices(voidGridView))
+    {
+        const auto vIdx = voidGridView.indexSet().index(v);
+        voidDofIdx[vIdx] = vIdx;
+        voidHostGridVertexIdx[vIdx] = hostGridView.indexSet().index(v.impl().hostEntity());
+    }
+
+    auto voidFVGeometry = localView(*voidGridGeometry);
+    auto voidElemVolVars = localView(voidGridVariables->curGridVolVars());
+    for (const auto& element : elements(voidGridView))
+    {
+        voidFVGeometry.bind(element);
+        voidElemVolVars.bind(element, voidFVGeometry, sol[CouplingManager::voidDomainIdx]);
+        couplingManager->bindCouplingContext(CouplingManager::voidDomainIdx, element);
+
+        for (const auto& scv : scvs(voidFVGeometry))
+        {
+            if (couplingManager->isCoupledPore(CouplingManager::voidDomainIdx, scv.dofIndex()))
+            {
+                voidConductionSource[scv.dofIndex()] += couplingManager->conductionSource(CouplingManager::voidDomainIdx, element,
+                                                                                          voidFVGeometry, voidElemVolVars, scv)
+                                                                                          * scv.volume();
+
+                voidConvectionSource[scv.dofIndex()] += couplingManager->convectionSource(CouplingManager::voidDomainIdx, element,
+                                                                                          voidFVGeometry, voidElemVolVars, scv)
+                                                                                          * scv.volume();
+            }
+        }
+    }
+
+    voidVtkWriter.addField(voidDofIdx, "dofIdx", Vtk::FieldType::vertex);
+    voidVtkWriter.addField(voidHostGridVertexIdx, "hostGridVertexIdx", Vtk::FieldType::vertex);
+    voidVtkWriter.addField(voidConductionSource, "conductionSource", Vtk::FieldType::vertex);
+    voidVtkWriter.addField(voidConvectionSource, "convectionSource", Vtk::FieldType::vertex);
+    voidVtkWriter.addField(voidGridGeometry->poreVolume(), "poreVolume", Vtk::FieldType::vertex);
+    voidVtkWriter.addField(voidGridGeometry->throatCrossSectionalArea(), "throatArea", Vtk::FieldType::element);
+
+    std::vector<std::size_t> solidDofIdx(solidGridView.size(1));
+    std::vector<std::size_t> solidHostGridVertexIdx(solidGridView.size(1));
+    std::vector<Scalar> solidConductionSource(solidGridView.size(1));
+    std::vector<Scalar> solidConvectionSource(solidGridView.size(1));
+    for (const auto& v : vertices(solidGridView))
+    {
+        const auto vIdx = solidGridView.indexSet().index(v);
+        solidDofIdx[vIdx] = vIdx;
+        solidHostGridVertexIdx[vIdx] = hostGridView.indexSet().index(v.impl().hostEntity());
+    }
+
+    auto solidFVGeometry = localView(*solidGridGeometry);
+    auto solidElemVolVars = localView(solidGridVariables->curGridVolVars());
+    for (const auto& element : elements(solidGridView))
+    {
+        solidFVGeometry.bind(element);
+        solidElemVolVars.bind(element, solidFVGeometry, sol[CouplingManager::solidDomainIdx]);
+        couplingManager->bindCouplingContext(CouplingManager::solidDomainIdx, element);
+
+        for (const auto& scv : scvs(solidFVGeometry))
+        {
+            if (couplingManager->isCoupledPore(CouplingManager::solidDomainIdx, scv.dofIndex()))
+            {
+                solidConductionSource[scv.dofIndex()] += couplingManager->conductionSource(CouplingManager::solidDomainIdx, element,
+                                                                                           solidFVGeometry, solidElemVolVars, scv)
+                                                                                           * scv.volume();
+
+                solidConvectionSource[scv.dofIndex()] += couplingManager->convectionSource(CouplingManager::solidDomainIdx, element,
+                                                                                           solidFVGeometry, solidElemVolVars, scv)
+                                                                                           * scv.volume();
+            }
+        }
+    }
+
+    solidVtkWriter.addField(solidDofIdx, "dofIdx", Vtk::FieldType::vertex);
+    solidVtkWriter.addField(solidHostGridVertexIdx, "hostGridVertexIdx", Vtk::FieldType::vertex);
+    solidVtkWriter.addField(solidConductionSource, "conductionSource", Vtk::FieldType::vertex);
+    solidVtkWriter.addField(solidConvectionSource, "convectionSource", Vtk::FieldType::vertex);
+
+    voidVtkWriter.write(0);
+    solidVtkWriter.write(0);
+
+    // for debugging
+    Dune::VTKWriter<std::decay_t<decltype(couplingGridView)>> couplingWriter(couplingGridView);
+    std::vector<std::size_t> couplingDebugVertexIndices(couplingGridView.size(1));
+    std::vector<std::size_t> couplingDebugConnectionIds(couplingGridView.size(0));
+    std::vector<std::size_t> connectionIdToDebugElemIdx(couplingGridView.size(0));
+    std::vector<Scalar> connectionArea(couplingGridView.size(0));
+    std::vector<Scalar> connectionLength(couplingGridView.size(0));
+    for (const auto& v : vertices(couplingGridView))
+        couplingDebugVertexIndices[couplingGridView.indexSet().index(v)] = hostGridView.indexSet().index(v.impl().hostEntity());
+
+    for (const auto& e : elements(couplingGridView))
+    {
+        const auto hostGridElementIdx = hostGridView.indexSet().index(e.impl().hostEntity());
+        const auto id = couplingManager->couplingMapper().hostGridElementIndexToGlobalId().at(hostGridElementIdx);
+        const auto debugElemIdx = couplingGridView.indexSet().index(e);
+        couplingDebugConnectionIds[debugElemIdx] = id;
+        connectionIdToDebugElemIdx[id] = debugElemIdx;
+
+        connectionArea[debugElemIdx] = couplingManager->couplingMapper().connectionInfo()[id].connectionArea;
+        connectionLength[debugElemIdx] = couplingManager->couplingMapper().connectionInfo()[id].connectionLength;
+    }
+    couplingWriter.addVertexData(couplingDebugVertexIndices, "hostGridVertexIdx");
+    couplingWriter.addCellData(connectionArea, "connectionArea");
+    couplingWriter.addCellData(connectionLength, "connectionLength");
+    couplingWriter.addCellData(couplingDebugConnectionIds, "connectionId");
+
+
+    std::fill(voidConductionSource.begin(), voidConductionSource.end(), 0.0);
+    std::fill(voidConvectionSource.begin(), voidConvectionSource.end(), 0.0);
+    std::fill(solidConductionSource.begin(), solidConductionSource.end(), 0.0);
+    std::fill(solidConvectionSource.begin(), solidConvectionSource.end(), 0.0);
+
+    // the non-linear solver
+    using NewtonSolver = MultiDomainNewtonSolver<Assembler, LinearSolver, CouplingManager>;
+    NewtonSolver nonLinearSolver(assembler, linearSolver, couplingManager);
+
+    const auto voidBoundaryFlux = PoreNetwork::BoundaryFlux(
+        *voidGridVariables, assembler->localResidual(CouplingManager::voidDomainIdx), sol[CouplingManager::voidDomainIdx]
+    );
+    const auto solidBoundaryFlux = PoreNetwork::BoundaryFlux(
+        *solidGridVariables, assembler->localResidual(CouplingManager::solidDomainIdx), sol[CouplingManager::solidDomainIdx]
+    );
+
+    if (isStationary)
+    {
+        // solve the non-linear system without time step control
+        nonLinearSolver.solve(sol);
+
+        if (couplingGridView.size(0) != couplingManager->couplingMapper().connectionInfo().size())
+            DUNE_THROW(Dune::InvalidStateException, "Wrong number of connections");
+
+        std::vector<Scalar> solidConnectionFlux(couplingGridView.size(0), 0.0);
+        std::vector<Scalar> voidConnectionFlux(couplingGridView.size(0), 0.0);
+        std::vector<Scalar> tVoidMinusTSolid(couplingGridView.size(0), 0.0);
+        std::vector<bool> solidConnectionVisited(couplingGridView.size(0), false);
+        std::vector<bool> voidConnectionVisited(couplingGridView.size(0), false);
+
+        Scalar totalSolidInletHeatFlux = 0.0;
+
+        couplingWriter.addCellData(voidConnectionFlux, "connectionFluxVoid");
+        couplingWriter.addCellData(solidConnectionFlux, "connectionFluxSolid");
+        couplingWriter.addCellData(tVoidMinusTSolid, "tVoidMinusTSolid");
+
+        for (const auto& element : elements(solidGridView))
+        {
+            solidFVGeometry.bind(element);
+            solidElemVolVars.bind(element, solidFVGeometry, sol[CouplingManager::solidDomainIdx]);
+            couplingManager->bindCouplingContext(CouplingManager::solidDomainIdx, element);
+
+            for (const auto& scv : scvs(solidFVGeometry))
+            {
+                totalSolidInletHeatFlux += solidProblem->robinInletHeatFlux(element, solidFVGeometry, solidElemVolVars, scv) * scv.volume();
+                if (couplingManager->isCoupledPore(CouplingManager::solidDomainIdx, scv.dofIndex()))
+                {
+                    // iterate over all connection throats
+                    const auto& connections = couplingManager->couplingMapper().solidToVoidConnections(scv.dofIndex());
+                    const auto& contextForPore = couplingManager->couplingContext()[scv.dofIndex()];
+
+                    for (const auto& [localConnectionIdx, connection] : enumerate(connections))
+                    {
+                        if (!solidConnectionVisited[connection.id])
+                        {
+                            solidConnectionVisited[connection.id] = true;
+                            const auto& context = contextForPore[localConnectionIdx];
+                            const Scalar tVoid = sol[CouplingManager::voidDomainIdx][connection.voidVertexIdx][1];
+                            const Scalar tSolid = sol[CouplingManager::solidDomainIdx][connection.solidVertexIdx][0];
+
+                            tVoidMinusTSolid[connection.id] = tVoid - tSolid;
+
+                            if (voidProblem->sourceMode() == decltype(voidProblem->sourceMode())::convection)
+                                solidConnectionFlux[connection.id] = couplingManager->convectiveHeatFluxForOneConnection(connection, context);
+                            else
+                            {
+                                const Scalar t = couplingManager->getConnectionTransmissiblity(CouplingManager::solidDomainIdx, connection, solidElemVolVars, scv);
+                                const Scalar deltaT = tSolid - tVoid;
+                                solidConnectionFlux[connection.id] = -t * deltaT;
+                            }
+                        }
+                    }
+
+                    solidConductionSource[scv.dofIndex()] +=
+                        couplingManager->conductionSource(CouplingManager::solidDomainIdx, element, solidFVGeometry, solidElemVolVars, scv)*scv.volume();
+
+                    solidConvectionSource[scv.dofIndex()] +=
+                        couplingManager->convectionSource(CouplingManager::solidDomainIdx, element, solidFVGeometry, solidElemVolVars, scv)*scv.volume();
+                }
+            }
+        }
+
+        std::vector<Scalar> voidEnergyOutflowFlux(voidGridGeometry->numDofs(), 0.0);
+
+        for (const auto& element : elements(voidGridView))
+        {
+            voidFVGeometry.bind(element);
+            voidElemVolVars.bind(element, voidFVGeometry, sol[CouplingManager::voidDomainIdx]);
+            couplingManager->bindCouplingContext(CouplingManager::voidDomainIdx, element);
+
+            for (const auto& scv : scvs(voidFVGeometry))
+            {
+                if (couplingManager->isCoupledPore(CouplingManager::voidDomainIdx, scv.dofIndex()))
+                {
+                    // iterate over all connection throats
+                    const auto& connections = couplingManager->couplingMapper().voidToSolidConnections(scv.dofIndex());
+                    const auto& contextForPore = couplingManager->couplingContext()[scv.dofIndex()];
+
+                    for (const auto& [localConnectionIdx, connection] : enumerate(connections))
+                    {
+                        if (!voidConnectionVisited[connection.id])
+                        {
+                            voidConnectionVisited[connection.id] = true;
+                            const auto& context = contextForPore[localConnectionIdx];
+
+                            if (voidProblem->sourceMode() == decltype(voidProblem->sourceMode())::convection)
+                                voidConnectionFlux[connection.id] = couplingManager->convectiveHeatFluxForOneConnection(connection, context);
+                            else
+                            {
+                                const Scalar t = couplingManager->getConnectionTransmissiblity(CouplingManager::voidDomainIdx, connection, voidElemVolVars, scv);
+                                const Scalar deltaT = sol[CouplingManager::solidDomainIdx][connection.solidVertexIdx][0] - sol[CouplingManager::voidDomainIdx][connection.voidVertexIdx][1];
+                                voidConnectionFlux[connection.id] = t * deltaT;
+                            }
+                        }
+                    }
+
+                    voidConductionSource[scv.dofIndex()] += couplingManager->conductionSource(CouplingManager::voidDomainIdx, element,
+                                                                                              voidFVGeometry, voidElemVolVars, scv)
+                                                                                              * scv.volume();
+
+                    voidConvectionSource[scv.dofIndex()] += couplingManager->convectionSource(CouplingManager::voidDomainIdx, element,
+                                                                                              voidFVGeometry, voidElemVolVars, scv)
+                                                                                              * scv.volume();
+                }
+
+                if (voidProblem->onOutletBoundary(scv))
+                    voidEnergyOutflowFlux[scv.dofIndex()] += voidProblem->heatOutFlowCondition(element, voidFVGeometry, voidElemVolVars, scv) * scv.volume();
+            }
+        }
+
+        // write vtk output
+        voidVtkWriter.write(1);
+        solidVtkWriter.write(1);
+        couplingWriter.write("coupling");
+
+        static const bool fluxVerbose = getParam<bool>("Problem.BoundaryFluxVerbose", false);
+
+        voidProblem->setOutletToDirichletForOutput(sol[CouplingManager::voidDomainIdx]);
+        solidProblem->setInletToDirichletForOutput(sol[CouplingManager::solidDomainIdx]);
+
+        const auto voidInletFlux = voidBoundaryFlux.getFlux(std::vector<int>{voidProblem->inletPoreLabel()}, fluxVerbose);
+        const auto voidOutletFlux = voidBoundaryFlux.getFlux(std::vector<int>{voidProblem->outletPoreLabel()}, fluxVerbose);
+        const auto voidHeaterFlux = voidBoundaryFlux.getFlux(std::vector<int>{voidProblem->heaterPoreLabel()}, fluxVerbose);
+        const auto solidInletFlux = solidBoundaryFlux.getFlux(std::vector<int>{voidProblem->inletPoreLabel()}, fluxVerbose);
+        const auto solidOutletFlux = solidBoundaryFlux.getFlux(std::vector<int>{voidProblem->outletPoreLabel()}, fluxVerbose);
+        const auto solidHeaterFlux = solidBoundaryFlux.getFlux(std::vector<int>{voidProblem->heaterPoreLabel()}, fluxVerbose);
+        using std::abs;
+
+        std::cout << "\n\n ***** Boundary fluxes \n\n" << std::endl;
+        std::cout << "Void inlet flux (total - mass/heat): " << voidInletFlux << std::endl;
+        std::cout << "Void outlet flux (total - mass/heat): " << voidOutletFlux << std::endl;
+        std::cout << "Delta heat flux abs(outlet) - abs(inlet): " << abs(voidOutletFlux.totalFlux[1]) - abs(voidInletFlux.totalFlux[1]) << "\n\n" << std::endl;
+
+        std::cout << "Void heater flux (total - mass/heat): " << voidHeaterFlux << "\n\n" << std::endl;
+
+        std::cout << "Solid inlet flux (total - heat): " << solidInletFlux << std::endl;
+        std::cout << "Solid outlet flux (total - heat): " << solidOutletFlux << std::endl;
+        std::cout << "Solid inlet Robin flux: " << totalSolidInletHeatFlux << std::endl;
+        std::cout << "Delta heat flux abs(outlet) - abs(inlet): " << abs(solidOutletFlux.totalFlux[1]) - abs(solidInletFlux.totalFlux[1]) << "\n\n" << std::endl;
+
+        std::cout << "Solid heater flux (total - heat): " << solidHeaterFlux << "\n\n" << std::endl;
+
+        Scalar totalConvectiveHeatFluxIn = 0.0;
+        Scalar totalConvectiveHeatFluxOut = 0.0;
+        Scalar voidConductionInletHeatFlux = 0.0;
+        std::vector<bool> visited(voidGridGeometry->numDofs(), false);
+
+        for (const auto& element : elements(voidGridView))
+        {
+            voidFVGeometry.bind(element);
+            voidElemVolVars.bind(element, voidFVGeometry, sol[CouplingManager::voidDomainIdx]);
+            couplingManager->bindCouplingContext(CouplingManager::voidDomainIdx, element);
+
+            for (const auto& scv : scvs(voidFVGeometry))
+            {
+                const auto dofIdx = scv.dofIndex();
+
+                if (voidInletFlux.fluxPerPore.count(dofIdx))
+                    voidConductionInletHeatFlux += voidProblem->robinInletConductiveHeatFlux(element, voidFVGeometry, voidElemVolVars, scv) * scv.volume();
+
+                if (visited[dofIdx])
+                    continue;
+                else
+                    visited[dofIdx] = true;
+
+                if (voidInletFlux.fluxPerPore.count(dofIdx))
+                {
+                    const Scalar tIn = getParamFromGroup<Scalar>(voidProblem->paramGroup(), "Problem.InletTemperature");
+                    const Scalar enthalypy = std::decay_t<decltype(voidElemVolVars)>::VolumeVariables::FluidSystem::enthalpy(tIn, voidElemVolVars[scv].pressure(0));
+                    totalConvectiveHeatFluxIn += voidInletFlux.fluxPerPore.at(dofIdx)[0] * enthalypy;
+                }
+                if (voidOutletFlux.fluxPerPore.count(dofIdx))
+                    totalConvectiveHeatFluxOut += voidOutletFlux.fluxPerPore.at(dofIdx)[0] * voidElemVolVars[scv].enthalpy(0);
+            }
+        }
+
+
+        const Scalar sumCouplingVoid = std::accumulate(voidConnectionFlux.cbegin(), voidConnectionFlux.cend(), 0.0);
+        const Scalar sumCouplingSolid = std::accumulate(solidConnectionFlux.cbegin(), solidConnectionFlux.cend(), 0.0);
+
+        std::cout << "Sum of all void coupling heat fluxes: " << sumCouplingVoid << std::endl;
+        std::cout << "Sum of all solid coupling heat fluxes: " << sumCouplingSolid << "\n\n" << std::endl;
+
+        std::cout << "abs(Q_total,out,void) - abs(Q_total,in,void)- abs(Q_total,heater,void): " << abs(voidOutletFlux.totalFlux[1]) - abs(voidInletFlux.totalFlux[1]) -abs(voidHeaterFlux.totalFlux[1]) << std::endl;
+        std::cout << "abs(Q_conv,out,void) - abs(Q_conv,in,void)- abs(Q_total,heater,void): " << abs(totalConvectiveHeatFluxOut) - abs(totalConvectiveHeatFluxIn) - abs(voidHeaterFlux.totalFlux[1]) << std::endl;
+
+
+        std::cout << "Total sum void " << voidInletFlux[1] + voidOutletFlux[1] + voidHeaterFlux[1] - sumCouplingVoid << std::endl;
+
+        std::cout << "\n\n ***Exchange *** " << std::endl;
+        std::cout << "sumCouplingVoid: " << sumCouplingVoid << std::endl;
+        std::cout << "solidInletFlux: " << solidInletFlux << std::endl;
+        std::cout << "voidHeaterFlux: " << voidHeaterFlux[1] << std::endl;
+        std::cout << "Total exchange flux (sumCouplingVoid + solidInletFlux - voidHeaterFlux) " << sumCouplingVoid + solidInletFlux[1] - voidHeaterFlux[1] << std::endl;
+
+        std::cout << "\n\n *** Void convection *** " << std::endl;
+        std::cout << "Void inlet convective heat flux (\u1E41 * h): " << totalConvectiveHeatFluxIn << std::endl;
+        std::cout << "Void outlet convective heat flux (\u1E41 * h): " << totalConvectiveHeatFluxOut << std::endl;
+        const Scalar sumConvection = totalConvectiveHeatFluxIn + totalConvectiveHeatFluxOut;
+        std::cout << "abs((\u1E41 * h)_out) - abs((\u1E41 * h)_in): " << abs(totalConvectiveHeatFluxOut) - abs(totalConvectiveHeatFluxIn) << "\n\n" << std::endl;
+
+        std::cout << "\n\n ***Inlet conduction ***" << std::endl;
+        std::cout << "Void inlet conductive heat flux: " << -voidConductionInletHeatFlux << std::endl; // negative sign because value is used in source term
+        std::cout << "Solid inlet Robin flux: " << -totalSolidInletHeatFlux << std::endl; // negative sign because value is used in source term
+        const Scalar sumInletCond = -voidConductionInletHeatFlux - totalSolidInletHeatFlux;
+        std::cout << "Sum " << std::abs(voidConductionInletHeatFlux) + std::abs(totalSolidInletHeatFlux) << std::endl;
+
+        std::cout << "\n\n ***Heater conduction ***" << std::endl;
+        std::cout << "Solid heater flux: " << solidHeaterFlux << std::endl;
+        std::cout << "Void heater flux: " << voidHeaterFlux.totalFlux[1] << std::endl;
+        const Scalar sumHeaterFlux = solidHeaterFlux[0] + voidHeaterFlux[1];
+        std::cout << "Sum :" << solidHeaterFlux[0] + voidHeaterFlux[1] << std::endl;
+
+        std::cout << "\n\n ***Sum of sums  *** " << std::endl;
+        std::cout << sumConvection + sumInletCond + sumHeaterFlux << std::endl;
+
+        Dune::VTKWriter fluxVtkWriter(voidGridGeometry->gridView());
+        std::vector<Scalar> voidMassFlux(voidGridGeometry->numDofs());
+        std::vector<Scalar> voidHeatFlux(voidGridGeometry->numDofs());
+        std::vector<bool> isConsidered(voidGridGeometry->numDofs(), false);
+        fluxVtkWriter.addVertexData(isConsidered, "isConsidered");
+        fluxVtkWriter.addVertexData(voidMassFlux, "voidMassFlux");
+        fluxVtkWriter.addVertexData(voidHeatFlux, "voidHeatFlux");
+        fluxVtkWriter.addVertexData(voidEnergyOutflowFlux, "voidEnergyOutflowFlux");
+
+        for (const auto& [dofIdx, value] : voidInletFlux.fluxPerPore)
+        {
+            isConsidered[dofIdx] = true;
+            voidMassFlux[dofIdx] = value[0];
+            voidHeatFlux[dofIdx] = value[1];
+        }
+        fluxVtkWriter.write("inlet_flux");
+
+        std::fill(isConsidered.begin(), isConsidered.end(), false);
+        std::fill(voidMassFlux.begin(), voidMassFlux.end(), 0.0);
+        std::fill(voidHeatFlux.begin(), voidHeatFlux.end(), 0.0);
+        for (const auto& [dofIdx, value] : voidOutletFlux.fluxPerPore)
+        {
+            isConsidered[dofIdx] = true;
+            voidMassFlux[dofIdx] = value[0];
+            voidHeatFlux[dofIdx] = value[1];
+        }
+        fluxVtkWriter.write("outlet_flux");
+    }
+    else
+    {
+        // time loop
+        timeLoop->start(); do
+        {
+            // solve the non-linear system with time step control
+            nonLinearSolver.solve(sol, *timeLoop);
+
+            // make the new solution the old solution
+            solOld = sol;
+            voidGridVariables->advanceTimeStep();
+            solidGridVariables->advanceTimeStep();
+
+            // advance to the time loop to the next step
+            timeLoop->advanceTimeStep();
+
+            for (const auto& element : elements(voidGridView))
+            {
+                voidFVGeometry.bind(element);
+                voidElemVolVars.bind(element, voidFVGeometry, sol[CouplingManager::voidDomainIdx]);
+                couplingManager->bindCouplingContext(CouplingManager::voidDomainIdx, element);
+
+                for (const auto& scv : scvs(voidFVGeometry))
+                {
+                    if (couplingManager->isCoupledPore(CouplingManager::voidDomainIdx, scv.dofIndex()))
+                    {
+                        voidConductionSource[scv.dofIndex()] += couplingManager->conductionSource(CouplingManager::voidDomainIdx, element,
+                                                                                                  voidFVGeometry, voidElemVolVars, scv)
+                                                                                                  * scv.volume();
+
+                        voidConvectionSource[scv.dofIndex()] += couplingManager->convectionSource(CouplingManager::voidDomainIdx, element,
+                                                                                                  voidFVGeometry, voidElemVolVars, scv)
+                                                                                                  * scv.volume();
+                    }
+                }
+            }
+
+            for (const auto& element : elements(solidGridView))
+            {
+                solidFVGeometry.bind(element);
+                solidElemVolVars.bind(element, solidFVGeometry, sol[CouplingManager::solidDomainIdx]);
+                couplingManager->bindCouplingContext(CouplingManager::solidDomainIdx, element);
+
+                for (const auto& scv : scvs(solidFVGeometry))
+                {
+                    if (couplingManager->isCoupledPore(CouplingManager::solidDomainIdx, scv.dofIndex()))
+                    {
+                        solidConductionSource[scv.dofIndex()] += couplingManager->conductionSource(CouplingManager::solidDomainIdx, element,
+                                                                                                   solidFVGeometry, solidElemVolVars, scv)
+                                                                                                   * scv.volume();
+
+                        solidConvectionSource[scv.dofIndex()] += couplingManager->convectionSource(CouplingManager::solidDomainIdx, element,
+                                                                                                   solidFVGeometry, solidElemVolVars, scv)
+                                                                                                   * scv.volume();
+                    }
+                }
+            }
+
+            // write vtk output
+            voidVtkWriter.write(timeLoop->time());
+            solidVtkWriter.write(timeLoop->time());
+
+            // report statistics of this time step
+            timeLoop->reportTimeStep();
+
+            // set new dt as suggested by newton solver
+            timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+
+        } while (!timeLoop->finished());
+
+        timeLoop->finalize(voidGridView.comm());
+        timeLoop->finalize(solidGridView.comm());
+    }
+
+    ////////////////////////////////////////////////////////////
+    // finalize, print dumux message to say goodbye
+    ////////////////////////////////////////////////////////////
+
+    // print dumux end message
+    if (mpiHelper.rank() == 0)
+    {
+        Parameters::print();
+        DumuxMessage::print(/*firstCall=*/false);
+    }
+
+    return 0;
+}
diff --git a/test/multidomain/dualnetwork/params.input b/test/multidomain/dualnetwork/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..05d9edd9a75a1909552551bf6f34865f328697b9
--- /dev/null
+++ b/test/multidomain/dualnetwork/params.input
@@ -0,0 +1,76 @@
+[TimeLoop]
+TEnd = 10
+DtInitial = 1e-5
+
+[Grid]
+PoreGeometry = Sphere
+File = grids/Berea_center_cropped_200_200_dual.dgf
+
+[Problem]
+IsStationary = true
+EnableGravity = false
+InitialTemperature = 300
+EnableHeating = true
+PaddingThickness = 5.345e-06
+
+InletIndex = 5 # for z dir
+OutletIndex = 6
+HeaterIndex = 1
+
+Nu = 1
+Bi = 1
+C0Fluid = 0.1
+C0Solid = 0.45
+CInfFactorFluid = 1
+CInfFactorSolid = 0.50
+ConnectionAreaShapeFactor = 0.55
+
+SourceMode = convection
+FluidTemperatureMode = self
+UseAverageConvectionArea = true
+ConvectionLambaFactor = 0.3 # set to 0.9 for metal
+
+[Void.Problem]
+Name = void
+InitialPressure = 0
+InletPressure = 1e4
+OutletPressure = 0
+InletTemperature = 300
+OutletTemperature = 300
+BottomTemperature = 400
+ThroatConductionType = FancyFactor
+UseRobinInlet = true
+RobinShapeFactor = 1.0
+# EnableCoupling = false
+
+[Solid.Problem]
+Name = solid
+InletTemperature = 300
+BottomTemperature = 400
+ThroatConductionType = FancyFactor
+UseRobinInlet = true
+RobinShapeFactor = 1.0
+# EnableCoupling = false
+
+[Vtk]
+OutputName = test
+AddVelocity = true
+
+[1.Component]
+SolidHeatCapacity = 790 # granite
+SolidDensity = 2700
+SolidThermalConductivity = 2.600038292
+
+# SolidHeatCapacity = 900 # metal
+# SolidDensity = 2700
+# SolidThermalConductivity = 205.0120773
+
+[2.Component]
+LiquidDensity = 1e3 # water
+LiquidKinematicViscosity = 1e-6
+LiquidThermalConductivity = 0.679
+LiquidHeatCapacity = 4.2e3
+ReferenceTemperature = 0.0
+
+[Flux]
+UpwindWeight = 1.0
diff --git a/test/multidomain/dualnetwork/problem_solid.hh b/test/multidomain/dualnetwork/problem_solid.hh
new file mode 100644
index 0000000000000000000000000000000000000000..4dd666c7278658c78ed4def802ded081795d1f19
--- /dev/null
+++ b/test/multidomain/dualnetwork/problem_solid.hh
@@ -0,0 +1,222 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+#ifndef DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_PROBLEM_SOLID_HH
+#define DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_PROBLEM_SOLID_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/common/boundarytypes.hh>
+#include <dumux/common/numeqvector.hh>
+
+namespace Dumux {
+
+/*!
+ * \brief Heat problem with multiple solid spheres
+ */
+template <class TypeTag>
+class SolidSubProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using GridView = typename GridGeometry::GridView;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+    using NumEqVector = Dumux::NumEqVector<PrimaryVariables>;
+    using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+    using FVElementGeometry = typename GridGeometry::LocalView;
+    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
+
+    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+    using CouplingManager = GetPropType<TypeTag, Properties::CouplingManager>;
+
+    enum class SourceMode {conduction, convection, max};
+
+public:
+    template<class SpatialParams>
+    SolidSubProblem(std::shared_ptr<const GridGeometry> gridGeometry,
+                    std::shared_ptr<SpatialParams> spatialParams,
+                    std::shared_ptr<const CouplingManager> couplingManager)
+    : ParentType(gridGeometry, spatialParams,  "Solid"), couplingManager_(couplingManager)
+    {
+        problemName_  =  getParam<std::string>("Vtk.OutputName") + "_" + getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
+        initialTemperature_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InitialTemperature");
+        temperatureBottom_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.BottomTemperature");
+        temperatureIn_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InletTemperature");
+        enableCoupling_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.EnableCoupling", true);
+        heatingOn_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.EnableHeating", true);
+        useRobinInlet_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.UseRobinInlet", true);
+
+        inletIndex_ = getParamFromGroup<int>(this->paramGroup(), "Problem.InletIndex");
+        heaterIndex_ = getParamFromGroup<int>(this->paramGroup(), "Problem.HeaterIndex");
+
+        const auto mode = getParamFromGroup<std::string>(this->paramGroup(), "Problem.SourceMode", "max");
+        if (mode == "conduction")
+            sourceMode_ = SourceMode::conduction;
+        else if (mode == "convection")
+            sourceMode_ = SourceMode::convection;
+        else
+            sourceMode_ = SourceMode::max;
+    }
+
+    const std::string& name() const
+    { return problemName_; }
+
+    BoundaryTypes boundaryTypes(const Element &element, const SubControlVolume& scv) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+
+        if ((!useRobinInlet_ && onInletBoundary_(scv)) || (onHeaterBoundary_(scv) && heatingOn_))
+            values.setAllDirichlet();
+
+        return values;
+    }
+
+    template<class ElementVolumeVariables>
+    NumEqVector source(const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const SubControlVolume& scv) const
+    {
+        NumEqVector value = 0.0;
+
+        if (enableCoupling_ && couplingManager_->isCoupledPore(CouplingManager::solidDomainIdx, scv.dofIndex()))
+        {
+            if (sourceMode_ == SourceMode::conduction)
+            {
+                value[Indices::energyEqIdx] = couplingManager_->conductionSource(CouplingManager::solidDomainIdx,
+                                                                                 element, fvGeometry, elemVolVars, scv);
+            }
+            else if (sourceMode_ == SourceMode::convection)
+            {
+                value[Indices::energyEqIdx] = couplingManager_->convectionSource(CouplingManager::solidDomainIdx,
+                                                                                 element, fvGeometry, elemVolVars, scv);
+            }
+            else
+            {
+                const Scalar condSource = couplingManager_->conductionSource(CouplingManager::solidDomainIdx,
+                                                                             element, fvGeometry, elemVolVars, scv);
+                const Scalar convSource = couplingManager_->convectionSource(CouplingManager::solidDomainIdx,
+                                                                             element, fvGeometry, elemVolVars, scv);
+
+                using std::abs;
+                if (abs(condSource) > abs(convSource))
+                    value[Indices::energyEqIdx] = condSource;
+                else
+                    value[Indices::energyEqIdx] = convSource;
+            }
+        }
+
+        value[Indices::energyEqIdx] += robinInletHeatFlux(element, fvGeometry, elemVolVars, scv);
+
+        return value;
+    }
+
+    template<class ElementVolumeVariables>
+    Scalar robinInletHeatFlux(const Element& element,
+                              const FVElementGeometry& fvGeometry,
+                              const ElementVolumeVariables& elemVolVars,
+                              const SubControlVolume& scv) const
+    {
+        Scalar flux = 0.0;
+
+        if (useRobinInlet_ && onInletBoundary_(scv))
+        {
+            const Scalar r = this->spatialParams().poreExtendedRadius(scv.dofIndex());
+            const auto& volVars = elemVolVars[scv];
+            static const Scalar lambdaSolid = getParam<Scalar>("1.Component.SolidThermalConductivity");
+            static const Scalar lambdaFluid = getParam<Scalar>("2.Component.LiquidThermalConductivity");
+            static const Scalar dPadding = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.PaddingThickness");
+            static const Scalar robinShapeFactor = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.RobinShapeFactor", 1.0);
+
+            const Scalar lambdaHarmonic = (r + dPadding)/(r/lambdaSolid + dPadding/lambdaFluid);
+            const Scalar A = M_PI * r*r * robinShapeFactor;
+
+            flux = (temperatureIn_ - volVars.temperature())
+                   * A * lambdaHarmonic / (r + dPadding) / (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+        }
+
+        return flux;
+    }
+
+    PrimaryVariables dirichlet(const Element& element, const SubControlVolume& scv) const
+    {
+        auto values = initialAtPos(scv.dofPosition());
+
+        if (onInletBoundary_(scv))
+        {
+            values = temperatureIn_;
+
+            if (!dirichletValuesForOutput_.empty())
+                values = dirichletValuesForOutput_[scv.dofIndex()];
+        }
+        else if (onHeaterBoundary_(scv))
+            values = temperatureBottom_;
+
+        return values;
+    }
+
+    template<class ElementVolumeVariables, class ElementFluxVariablesCache>
+    NumEqVector neumann(const Element& element,
+                        const FVElementGeometry& fvGeometry,
+                        const ElementVolumeVariables& elemVolVars,
+                        const ElementFluxVariablesCache& elemFluxVarsCache,
+                        const SubControlVolumeFace& scvf) const
+    {
+        return NumEqVector(0.0);
+    }
+
+    PrimaryVariables initialAtPos(const GlobalPosition& pos) const
+    {
+        PrimaryVariables values(initialTemperature_);
+        return values;
+    }
+
+    template<class Sol>
+    void setInletToDirichletForOutput(const Sol& sol)
+    {
+        useRobinInlet_ = false;
+        dirichletValuesForOutput_.resize(sol.size());
+
+        for (const auto& vertex : vertices(this->gridGeometry().gridView()))
+        {
+            const auto vIdx = this->gridGeometry().vertexMapper().index(vertex);
+            dirichletValuesForOutput_[vIdx] = sol[vIdx][Indices::temperatureIdx];
+        }
+    }
+
+private:
+
+    bool onInletBoundary_(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == inletIndex_; }
+
+    bool onHeaterBoundary_(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == heaterIndex_; }
+
+    std::shared_ptr<const CouplingManager> couplingManager_;
+
+    std::string problemName_;
+    Scalar initialTemperature_;
+    Scalar temperatureIn_;
+    Scalar temperatureBottom_;
+    bool heatingOn_;
+    bool enableCoupling_;
+    int inletIndex_;
+    int heaterIndex_;
+    SourceMode sourceMode_;
+    bool useRobinInlet_;
+    std::vector<Scalar> dirichletValuesForOutput_;
+};
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/dualnetwork/problem_void.hh b/test/multidomain/dualnetwork/problem_void.hh
new file mode 100644
index 0000000000000000000000000000000000000000..95a049f5dba418ef026a194dcf477f6fe5fd9bc8
--- /dev/null
+++ b/test/multidomain/dualnetwork/problem_void.hh
@@ -0,0 +1,373 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \brief A test problem for the one-phase pore network model.
+ */
+#ifndef DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_PROBLEM_VOID_HH
+#define DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_PROBLEM_VOID_HH
+
+#include <dumux/porousmediumflow/problem.hh>
+#include <dumux/porenetwork/1p/model.hh>
+
+#include <dumux/common/boundarytypes.hh>
+#include <dumux/common/numeqvector.hh>
+
+namespace Dumux {
+
+template <class TypeTag>
+class VoidSubProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+    using NumEqVector = Dumux::NumEqVector<PrimaryVariables>;
+    using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using GridView = typename GridGeometry::GridView;
+    using FVElementGeometry = typename GridGeometry::LocalView;
+    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+    using Labels = GetPropType<TypeTag, Properties::Labels>;
+    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+
+    using Element = typename GridView::template Codim<0>::Entity;
+    using Vertex = typename GridView::template Codim<GridView::dimension>::Entity;
+
+    using CouplingManager = GetPropType<TypeTag, Properties::CouplingManager>;
+
+    enum class SourceMode {conduction, convection, max};
+
+public:
+    template<class SpatialParams>
+    VoidSubProblem(std::shared_ptr<const GridGeometry> gridGeometry,
+                   std::shared_ptr<SpatialParams> spatialParams,
+                   std::shared_ptr<const CouplingManager> couplingManager)
+    : ParentType(gridGeometry, spatialParams, "Void"), couplingManager_(couplingManager)
+    {
+        problemName_ = getParam<std::string>("Vtk.OutputName") + "_" + getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
+        pressureIn_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InletPressure");
+        pressureOut_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.OutletPressure");
+        temperatureInitial_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InitialTemperature");
+        pressureInitial_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InitialPressure");
+        temperatureIn_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InletTemperature");
+        temperatureBottom_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.BottomTemperature");
+        enableCoupling_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.EnableCoupling", true);
+        heatingOn_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.EnableHeating", true);
+        fixedOutletTemperature_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.FixedOutletTemperature", false);
+        useRobinInlet_ = getParamFromGroup<bool>(this->paramGroup(), "Problem.UseRobinInlet", true);
+
+        if (fixedOutletTemperature_)
+            temperatureOut_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.OutletTemperature");
+
+        inletIndex_ = getParamFromGroup<int>(this->paramGroup(), "Problem.InletIndex");
+        outletIndex_ = getParamFromGroup<int>(this->paramGroup(), "Problem.OutletIndex");
+        heaterIndex_ = getParamFromGroup<int>(this->paramGroup(), "Problem.HeaterIndex");
+
+        const auto mode = getParamFromGroup<std::string>(this->paramGroup(), "Problem.SourceMode", "max");
+        if (mode == "conduction")
+            sourceMode_ = SourceMode::conduction;
+        else if (mode == "convection")
+            sourceMode_ = SourceMode::convection;
+        else
+            sourceMode_ = SourceMode::max;
+    }
+
+    const std::string& name() const
+    { return problemName_; }
+
+    void setGridVariables(std::shared_ptr<GridVariables> gridVars)
+    {
+        gridVars_ = gridVars;
+    }
+
+    BoundaryTypes boundaryTypes(const Element& element, const SubControlVolume& scv) const
+    {
+        BoundaryTypes bcTypes;
+        if (onInletBoundary_(scv))
+        {
+            bcTypes.setDirichlet(Indices::pressureIdx);
+            if (!useRobinInlet_)
+                bcTypes.setDirichlet(Indices::temperatureIdx);
+            else
+                bcTypes.setNeumann(Indices::energyEqIdx);
+        }
+        else if (onOutletBoundary(scv))
+        {
+            // bcTypes.setAllNeumann();
+            bcTypes.setDirichlet(Indices::pressureIdx);
+            if (fixedOutletTemperature_)
+                bcTypes.setDirichlet(Indices::temperatureIdx);
+            else
+                bcTypes.setNeumann(Indices::energyEqIdx);
+        }
+        else if (onHeaterBoundary_(scv) && heatingOn_)
+        {
+            bcTypes.setDirichlet(Indices::temperatureIdx);
+            bcTypes.setNeumann(Indices::conti0EqIdx);
+        }
+        else // neuman for the remaining boundaries
+            bcTypes.setAllNeumann();
+
+        // treat insular pores connected only to the solid phase
+        const auto poreLabel = this->gridGeometry().poreLabel(scv.dofIndex());
+        if (poreLabel == 22)
+            bcTypes.setDirichlet(Indices::pressureIdx);
+
+        return bcTypes;
+    }
+
+    PrimaryVariables dirichlet(const Element& element,
+                               const SubControlVolume& scv) const
+    {
+        PrimaryVariables values(0.0);
+        if (onInletBoundary_(scv))
+        {
+            values[Indices::pressureIdx] = pressureIn_;
+            values[Indices::temperatureIdx] = temperatureIn_;
+
+            if (!dirichletValuesForOutput_.empty())
+                values[Indices::temperatureIdx] = dirichletValuesForOutput_[scv.dofIndex()];
+        }
+        else if (onHeaterBoundary_(scv))
+            values[Indices::temperatureIdx] = temperatureBottom_;
+        else
+        {
+            values[Indices::pressureIdx] = pressureOut_;
+            values[Indices::temperatureIdx] = temperatureOut_;
+
+            if (!dirichletValuesForOutput_.empty())
+                values[Indices::temperatureIdx] = dirichletValuesForOutput_[scv.dofIndex()];
+        }
+
+        return values;
+    }
+
+
+    template<class ElementVolumeVariables>
+    NumEqVector source(const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const SubControlVolume& scv) const
+    {
+        NumEqVector value(0.0);
+
+        if (enableCoupling_ && couplingManager_->isCoupledPore(CouplingManager::voidDomainIdx, scv.dofIndex()))
+        {
+            if (sourceMode_ == SourceMode::conduction)
+            {
+                value[Indices::energyEqIdx] = couplingManager_->conductionSource(
+                    CouplingManager::voidDomainIdx, element, fvGeometry, elemVolVars, scv
+                );
+            }
+            else if (sourceMode_ == SourceMode::convection)
+            {
+                value[Indices::energyEqIdx] = couplingManager_->convectionSource(
+                    CouplingManager::voidDomainIdx, element, fvGeometry, elemVolVars, scv
+                );
+            }
+            else
+            {
+                const Scalar condSource = couplingManager_->conductionSource(
+                    CouplingManager::voidDomainIdx, element, fvGeometry, elemVolVars, scv
+                );
+                const Scalar convSource = couplingManager_->convectionSource(
+                    CouplingManager::voidDomainIdx, element, fvGeometry, elemVolVars, scv
+                );
+                using std::abs;
+                if (abs(condSource) > abs(convSource))
+                    value[Indices::energyEqIdx] = condSource;
+                else
+                    value[Indices::energyEqIdx] = convSource;
+            }
+         }
+
+        value[Indices::energyEqIdx] += robinInletHeatFlux(element, fvGeometry, elemVolVars, scv);
+
+        // outflow condition for heat
+        if (onOutletBoundary(scv) && !fixedOutletTemperature_)
+            value[Indices::energyEqIdx] += heatOutFlowCondition(element, fvGeometry, elemVolVars, scv);
+
+        return value;
+    }
+
+
+    template<class ElementVolumeVariables>
+    Scalar heatOutFlowCondition(const Element& element,
+                                const FVElementGeometry& fvGeometry,
+                                const ElementVolumeVariables& elemVolVars,
+                                const SubControlVolume& scv) const
+    {
+        Scalar value = 0.0;
+        using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
+        auto elemFluxVarsCache = localView(gridVars_->gridFluxVarsCache());
+        elemFluxVarsCache.bindElement(element, fvGeometry, elemVolVars);
+
+        for (auto&& scvf : scvfs(fvGeometry))
+        {
+            FluxVariables fluxVars;
+            fluxVars.init(*this, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
+            const Scalar flux = fluxVars.advectiveFlux(0,
+                [&](const auto& volVars)
+                {
+                    return elemVolVars[scv].mobility(0)
+                            * elemVolVars[scv].density(0)
+                            * elemVolVars[scv].enthalpy(0);
+                }
+            );
+
+            const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+
+            if (insideScv.dofIndex() == scv.dofIndex())
+                value += flux / scv.volume();
+            else
+                value -= flux / scv.volume();
+        }
+        return value;
+    }
+
+    template<class ElementVolumeVariables>
+    Scalar robinInletHeatFlux(const Element& element,
+                            const FVElementGeometry& fvGeometry,
+                            const ElementVolumeVariables& elemVolVars,
+                            const SubControlVolume& scv) const
+    {
+        Scalar flux = 0.0;
+
+        if (useRobinInlet_ && onInletBoundary_(scv))
+        {
+            flux += robinInletAdvectiveHeatFlux(element, fvGeometry, elemVolVars, scv);
+            flux += robinInletConductiveHeatFlux(element, fvGeometry, elemVolVars, scv);
+        }
+
+        return flux;
+    }
+
+    template<class ElementVolumeVariables>
+    Scalar robinInletAdvectiveHeatFlux(const Element& element,
+                                    const FVElementGeometry& fvGeometry,
+                                    const ElementVolumeVariables& elemVolVars,
+                                    const SubControlVolume& scv) const
+    {
+        using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
+        auto elemFluxVarsCache = localView(gridVars_->gridFluxVarsCache());
+        elemFluxVarsCache.bindElement(element, fvGeometry, elemVolVars);
+        const auto& volVars = elemVolVars[scv];
+
+        for (auto&& scvf : scvfs(fvGeometry))
+        {
+            FluxVariables fluxVars;
+            fluxVars.init(*this, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
+            const Scalar enthalypy = ElementVolumeVariables::VolumeVariables::FluidSystem::enthalpy(
+                temperatureIn_, volVars.pressure(0)
+            );
+
+            const Scalar result = fluxVars.advectiveFlux(0,
+                [&](const auto& v)
+                {
+                    return volVars.mobility(0)
+                            * volVars.density(0)*enthalypy;
+                }
+            );
+            const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+
+            if (insideScv.dofIndex() == scv.dofIndex())
+                return result / scv.volume();
+            else
+                return  -result / scv.volume();
+        }
+
+        DUNE_THROW(Dune::InvalidStateException, "Flux failed");
+    }
+
+    template<class ElementVolumeVariables>
+    Scalar robinInletConductiveHeatFlux(const Element& element,
+                                        const FVElementGeometry& fvGeometry,
+                                        const ElementVolumeVariables& elemVolVars,
+                                        const SubControlVolume& scv) const
+    {
+        const auto& volVars = elemVolVars[scv];
+        const Scalar r = volVars.poreInscribedRadius();
+        static const Scalar lambdaFluid = getParam<Scalar>("2.Component.LiquidThermalConductivity");
+        static const Scalar dPadding = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.PaddingThickness");
+        static const Scalar robinShapeFactor = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.RobinShapeFactor", 1.0);
+        const Scalar A = M_PI * r*r * robinShapeFactor;
+
+        return (temperatureIn_ - volVars.temperature())
+            * A * lambdaFluid / (r + dPadding) / (scv.volume() * fvGeometry.gridGeometry().coordinationNumber()[scv.dofIndex()]);
+    }
+
+    PrimaryVariables initial(const Vertex& vertex) const
+    {
+        PrimaryVariables values(0.0);
+        values[Indices::pressureIdx] = pressureInitial_;
+        values[Indices::temperatureIdx] = temperatureInitial_;
+        return values;
+    }
+
+    int outletPoreLabel() const
+    { return outletIndex_; }
+
+    int inletPoreLabel() const
+    { return inletIndex_; }
+
+    int heaterPoreLabel() const
+    { return heaterIndex_; }
+
+    template<class Sol>
+    void setOutletToDirichletForOutput(const Sol& sol)
+    {
+        fixedOutletTemperature_ = true;
+        useRobinInlet_ = false;
+        dirichletValuesForOutput_.resize(sol.size());
+
+        for (const auto& vertex : vertices(this->gridGeometry().gridView()))
+        {
+            const auto vIdx = this->gridGeometry().vertexMapper().index(vertex);
+            dirichletValuesForOutput_[vIdx] = sol[vIdx][Indices::temperatureIdx];
+        }
+    }
+
+    bool onOutletBoundary(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == outletIndex_; }
+
+    auto sourceMode() const
+    { return sourceMode_; }
+
+private:
+
+    bool onInletBoundary_(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == inletIndex_; }
+
+    bool onHeaterBoundary_(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == heaterIndex_; }
+
+    std::shared_ptr<const CouplingManager> couplingManager_;
+    std::shared_ptr<GridVariables> gridVars_;
+
+    std::string problemName_;
+    Scalar pressureIn_;
+    Scalar pressureOut_;
+    Scalar temperatureInitial_;
+    Scalar pressureInitial_;
+    Scalar temperatureIn_;
+    Scalar temperatureOut_;
+    Scalar temperatureBottom_;
+    bool enableCoupling_;
+    bool heatingOn_;
+    bool fixedOutletTemperature_;
+    int inletIndex_;
+    int outletIndex_;
+    int heaterIndex_;
+    SourceMode sourceMode_;
+    std::vector<Scalar> dirichletValuesForOutput_;
+    bool useRobinInlet_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/multidomain/dualnetwork/properties.hh b/test/multidomain/dualnetwork/properties.hh
new file mode 100644
index 0000000000000000000000000000000000000000..88fb59dab5d0835f780461da6a0de3a96307f716
--- /dev/null
+++ b/test/multidomain/dualnetwork/properties.hh
@@ -0,0 +1,160 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \brief Heat problem with multiple solid spheres
+ */
+#ifndef DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_PROPERTIES_HH
+#define DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_PROPERTIES_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/io/grid/gridmanager_sub.hh>
+
+#include <dumux/porenetwork/solidenergy/model.hh>
+#include <dumux/material/components/constant.hh>
+
+#include "problem_solid.hh"
+#include "spatialparams.hh"
+#include "fourierslaw.hh"
+
+namespace Dumux::Properties {
+
+// Create new type tags
+namespace TTag {
+struct PNMSolidModel { using InheritsFrom = std::tuple<PNMSolidEnergy>; };
+} // end namespace TTag
+
+// Set the problem property
+template<class TypeTag>
+struct Problem<TypeTag, TTag::PNMSolidModel>
+{ using type = Dumux::SolidSubProblem<TypeTag>; };
+
+// Set the grid type
+template<class TypeTag>
+struct Grid<TypeTag, TTag::PNMSolidModel>
+{ using type = Dune::SubGrid<1, Dune::FoamGrid<1, 3>>; };
+
+//! The spatial parameters to be employed.
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::PNMSolidModel>
+{
+private:
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    using type = PoreNetwork::SolidSpatialParams<GridGeometry, Scalar>;
+};
+
+// per default the solid system is inert with one constant component
+template<class TypeTag>
+struct SolidSystem<TypeTag, TTag::PNMSolidModel>
+{
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using InertComponent = Components::Constant<1, Scalar>;
+    using type = SolidSystems::InertSolidPhase<Scalar, InertComponent>;
+};
+
+template<class TypeTag>
+struct HeatConductionType<TypeTag, TTag::PNMSolidModel>
+{ using type = PoreNetwork::FlexibleFouriersLaw<false>; };
+
+} // end namespace Dumux::Properties
+
+#include <dumux/porenetwork/1p/model.hh>
+#include <dumux/material/fluidsystems/1pliquid.hh>
+#include <dumux/porousmediumflow/1p/incompressiblelocalresidual.hh>
+#include <dumux/porousmediumflow/nonisothermal/localresidual_incompressible.hh> //local residual for incompressible nonisothermal flow
+
+#include "problem_void.hh"
+
+namespace Dumux::Properties {
+
+// Create new type tags
+namespace TTag {
+struct PNMVoidModel { using InheritsFrom = std::tuple<PNMOnePNI>; };
+} // end namespace TTag
+
+// Set the problem property
+template<class TypeTag>
+struct Problem<TypeTag, TTag::PNMVoidModel>
+{ using type = Dumux::VoidSubProblem<TypeTag>; };
+
+// the fluid system
+template<class TypeTag>
+struct FluidSystem<TypeTag, TTag::PNMVoidModel>
+{
+    using Scalar = GetPropType<TypeTag, Scalar>;
+    using type = FluidSystems::OnePLiquid<Scalar, Dumux::Components::Constant<2, Scalar>> ;
+};
+
+// Set the grid type
+template<class TypeTag>
+struct Grid<TypeTag, TTag::PNMVoidModel>
+{ using type = Dune::SubGrid<1, Dune::FoamGrid<1, 3>>; };
+
+//! The advection type
+template<class TypeTag>
+struct AdvectionType<TypeTag, TTag::PNMVoidModel>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using TransmissibilityLaw = PoreNetwork::TransmissibilityPatzekSilin<Scalar, false/*considerPoreBodyResistance*/>;
+public:
+    using type = PoreNetwork::CreepingFlow<Scalar, TransmissibilityLaw>;
+};
+
+template<class TypeTag>
+struct HeatConductionType<TypeTag, TTag::PNMVoidModel>
+{ using type = PoreNetwork::FlexibleFouriersLaw<true>; };
+
+// use the incompressible local residual (provides analytic jacobian)
+template<class TypeTag>
+struct LocalResidual<TypeTag, TTag::PNMVoidModel>
+{ using type = OnePIncompressibleLocalResidual<TypeTag>; };
+
+template<class TypeTag>
+struct EnergyLocalResidual<TypeTag, TTag::PNMVoidModel>
+{
+    using type = Dumux::EnergyLocalResidualIncompressible<TypeTag> ; //use local residual for incompressible nonisothermal flow as in Dumux term of pressure work gets neglected
+};
+
+//! The spatial parameters to be employed.
+//! Use PNMOnePSpatialParams by default.
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::PNMVoidModel>
+{
+private:
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    using type = PoreNetwork::FluidSpatialParams<GridGeometry, Scalar>;
+};
+
+} // end namespace Dumux::Properties
+
+#include <dumux/multidomain/traits.hh>
+#include <dumux/multidomain/dualnetwork/couplingmanager.hh>
+
+namespace Dumux::Properties {
+
+template<class TypeTag>
+struct CouplingManager<TypeTag, TTag::PNMSolidModel>
+{
+    using Traits = MultiDomainTraits<TypeTag, Properties::TTag::PNMVoidModel>;
+    using type = PoreNetwork::PNMHeatTransferCouplingManager<Traits>;
+};
+
+template<class TypeTag>
+struct CouplingManager<TypeTag, TTag::PNMVoidModel>
+{
+    using Traits = MultiDomainTraits<Properties::TTag::PNMSolidModel, TypeTag>;
+    using type = PoreNetwork::PNMHeatTransferCouplingManager<Traits>;
+};
+
+} // end namespace Dumux::Properties
+
+#endif
diff --git a/test/multidomain/dualnetwork/spatialparams.hh b/test/multidomain/dualnetwork/spatialparams.hh
new file mode 100644
index 0000000000000000000000000000000000000000..06d515003445461e0e73f992550d0398b86f1e5f
--- /dev/null
+++ b/test/multidomain/dualnetwork/spatialparams.hh
@@ -0,0 +1,130 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \brief The spatial parameters class for the Hhat problem with multiple solid spheres
+ */
+
+#ifndef DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_SPATIALPARAMS_HH
+#define DUMUX_TEST_MULTIDOMAIN_DUALNETWORK_SPATIALPARAMS_HH
+
+#include <dumux/porenetwork/solidenergy/spatialparams.hh>
+#include <dumux/porenetwork/1p/spatialparams.hh>
+
+namespace Dumux::PoreNetwork {
+
+/*!
+ * \brief The spatial parameters class.
+ */
+template<class GridGeometry, class Scalar>
+class FluidSpatialParams
+: public PoreNetwork::OnePDefaultSpatialParams<GridGeometry, Scalar>
+{
+    using ParentType = PoreNetwork::OnePDefaultSpatialParams<GridGeometry, Scalar>;
+    using GlobalPosition = typename GridGeometry::GlobalCoordinate;
+public:
+    // export permeability type
+    using PermeabilityType = Scalar;
+
+    template<class GridData>
+    FluidSpatialParams(std::shared_ptr<const GridGeometry> fvGridGeometry, const GridData& gridData)
+    : ParentType(fvGridGeometry)
+    {
+        throatCenter_.resize(fvGridGeometry->gridView().size(0));
+        poreExtendedRadius_.resize(fvGridGeometry->gridView().size(1));
+
+        for (const auto& element : elements(fvGridGeometry->gridView()))
+        {
+            const auto eIdx = fvGridGeometry->elementMapper().index(element);
+            const auto& params = gridData.parameters(element);
+            const auto posX = params[gridData.parameterIndex("ThroatCenterX")];
+            const auto posY = params[gridData.parameterIndex("ThroatCenterY")];
+            const auto posZ = params[gridData.parameterIndex("ThroatCenterZ")];
+            throatCenter_[eIdx] = GlobalPosition{posX, posY, posZ};
+        }
+
+        for (const auto& vertex : vertices(fvGridGeometry->gridView()))
+        {
+            const auto vIdx = fvGridGeometry->vertexMapper().index(vertex);
+            poreExtendedRadius_[vIdx] = gridData.getParameter(vertex, "PoreExtendedRadius");
+        }
+    }
+
+    const GlobalPosition& throatCenter(const std::size_t eIdx) const
+    { return throatCenter_[eIdx]; }
+
+    template<class Element, class SubControlVolume, class ElementSolutionVector>
+    Scalar poreExtendedRadius(const Element& element,
+                              const SubControlVolume& scv,
+                              const ElementSolutionVector& elemSol) const
+    { return poreExtendedRadius_[scv.dofIndex()]; }
+
+    Scalar poreExtendedRadius(std::size_t dofIdx) const
+    { return poreExtendedRadius_[dofIdx]; }
+
+private:
+    std::vector<GlobalPosition> throatCenter_;
+    std::vector<Scalar> poreExtendedRadius_;
+};
+
+/*!
+ * \brief The spatial parameters class.
+ */
+template<class GridGeometry, class Scalar>
+class SolidSpatialParams
+: public PoreNetwork::SolidEnergySpatialParams<GridGeometry, Scalar>
+{
+    using ParentType = PoreNetwork::SolidEnergySpatialParams<GridGeometry, Scalar>;
+    using GlobalPosition = typename GridGeometry::GlobalCoordinate;
+public:
+    // export permeability type
+    using PermeabilityType = Scalar;
+
+    template<class GridData>
+    SolidSpatialParams(std::shared_ptr<const GridGeometry> fvGridGeometry, const GridData& gridData)
+    : ParentType(fvGridGeometry)
+    {
+        throatCenter_.resize(fvGridGeometry->gridView().size(0));
+        poreExtendedRadius_.resize(fvGridGeometry->gridView().size(1));
+
+        for (const auto& element : elements(fvGridGeometry->gridView()))
+        {
+            const auto eIdx = fvGridGeometry->elementMapper().index(element);
+            const auto& params = gridData.parameters(element);
+            const auto posX = params[gridData.parameterIndex("ThroatCenterX")];
+            const auto posY = params[gridData.parameterIndex("ThroatCenterY")];
+            const auto posZ = params[gridData.parameterIndex("ThroatCenterZ")];
+            throatCenter_[eIdx] = GlobalPosition{posX, posY, posZ};
+        }
+
+        for (const auto& vertex : vertices(fvGridGeometry->gridView()))
+        {
+            const auto vIdx = fvGridGeometry->vertexMapper().index(vertex);
+            poreExtendedRadius_[vIdx] = gridData.getParameter(vertex, "PoreExtendedRadius");
+        }
+    }
+
+    const GlobalPosition& throatCenter(const std::size_t eIdx) const
+    { return throatCenter_[eIdx]; }
+
+    template<class Element, class SubControlVolume, class ElementSolutionVector>
+    Scalar poreExtendedRadius(const Element& element,
+                              const SubControlVolume& scv,
+                              const ElementSolutionVector& elemSol) const
+    { return poreExtendedRadius_[scv.dofIndex()]; }
+
+    Scalar poreExtendedRadius(std::size_t dofIdx) const
+    { return poreExtendedRadius_[dofIdx]; }
+
+private:
+    std::vector<GlobalPosition> throatCenter_;
+    std::vector<Scalar> poreExtendedRadius_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/porenetwork/CMakeLists.txt b/test/porenetwork/CMakeLists.txt
index c3eb5c37ae8bf98ae7390d244c0e6eac72e11329..4cb5469ebdb3bb3d4f3ba1ca00c9383c560f2ca5 100644
--- a/test/porenetwork/CMakeLists.txt
+++ b/test/porenetwork/CMakeLists.txt
@@ -4,3 +4,4 @@
 add_subdirectory(1p)
 add_subdirectory(1pnc)
 add_subdirectory(2p)
+add_subdirectory(solidenergy)
diff --git a/test/porenetwork/solidenergy/CMakeLists.txt b/test/porenetwork/solidenergy/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f051aa4d597158622764eb2766e4c0cbf4eb128b
--- /dev/null
+++ b/test/porenetwork/solidenergy/CMakeLists.txt
@@ -0,0 +1,28 @@
+# SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+dune_symlink_to_source_files(FILES grids "params.input")
+
+add_executable(test_porenetwork_solid_energy EXCLUDE_FROM_ALL main.cc)
+
+dumux_add_test(NAME test_porenetwork_solid_energy_stationary
+              LABELS porenetwork solid energy
+              TARGET test_porenetwork_solid_energy
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND HAVE_UMFPACK )"
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_pnm_solid_energy-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_pnm_solid_energy_stationary-00001.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_porenetwork_solid_energy params.input
+                                    -Problem.Name test_pnm_solid_energy_stationary -Problem.IsStationary true")
+
+dumux_add_test(NAME test_porenetwork_solid_energy_transient
+              LABELS porenetwork solid energy
+              TARGET test_porenetwork_solid_energy
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND HAVE_UMFPACK )"
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_pnm_solid_energy-reference.vtp
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_pnm_solid_energy_transient-00033.vtp
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_porenetwork_solid_energy params.input
+                                    -Problem.Name test_pnm_solid_energy_transient -Problem.IsStationary false")
diff --git a/test/porenetwork/solidenergy/main.cc b/test/porenetwork/solidenergy/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..31e1885fd1a1c7baad98c6587fe998d261f0b1bb
--- /dev/null
+++ b/test/porenetwork/solidenergy/main.cc
@@ -0,0 +1,173 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \file
+ * \brief heat conduction test for the pore network model (with solid properties)
+ */
+#include <config.h>
+
+#include <iostream>
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/timer.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/initialize.hh>
+
+#include <dumux/linear/istlsolvers.hh>
+#include <dumux/linear/linearsolvertraits.hh>
+#include <dumux/linear/linearalgebratraits.hh>
+#include <dumux/assembly/fvassembler.hh>
+#include <dumux/nonlinear/newtonsolver.hh>
+
+#include <dumux/io/grid/porenetwork/gridmanager.hh>
+#include <dumux/io/grid/porenetwork/griddata.hh>
+
+#include <dumux/porenetwork/common/pnmvtkoutputmodule.hh>
+#include <dumux/porenetwork/common/boundaryflux.hh>
+
+#include "properties.hh"
+
+int main(int argc, char** argv)
+{
+    using namespace Dumux;
+
+    using SolidTypeTag = Properties::TTag::PNMSolidModel;
+
+    // initialize MPI, finalize is done automatically on exit
+    Dumux::initialize(argc, argv);
+    const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+    // print dumux start message
+    if (mpiHelper.rank() == 0)
+        DumuxMessage::print(/*firstCall=*/true);
+
+    ////////////////////////////////////////////////////////////
+    // parse the command line arguments and input file
+    ////////////////////////////////////////////////////////////
+
+    // parse command line arguments
+    Parameters::init(argc, argv);
+
+    //////////////////////////////////////////////////////////////////////
+    // try to create a grid (from the given grid file or the input file)
+    /////////////////////////////////////////////////////////////////////
+
+    using GridManager = PoreNetwork::GridManager<3>;
+    GridManager gridManager;
+    gridManager.init();
+
+    // we compute on the leaf grid view
+    const auto solidLeafGridView = gridManager.grid().leafGridView();
+    const auto solidGridData = gridManager.getGridData();
+
+    // create the finite volume grid geometry
+    using SolidGridGeometry = GetPropType<SolidTypeTag, Properties::GridGeometry>;
+    auto solidGridGeometry = std::make_shared<SolidGridGeometry>(solidLeafGridView,*solidGridData);
+
+    // the spatial parameters
+    using SolidSpatialParams = GetPropType<SolidTypeTag, Properties::SpatialParams>;
+    auto solidSpatialParams = std::make_shared<SolidSpatialParams>(solidGridGeometry); // from common/spatialparams constructor
+
+    // the problem (boundary conditions)
+    using SolidProblem = GetPropType<SolidTypeTag, Properties::Problem>;
+    auto solidProblem = std::make_shared<SolidProblem>(solidGridGeometry, solidSpatialParams);
+
+    // the solution vector
+    using GridView = typename SolidGridGeometry::GridView;
+    using SolutionVector = GetPropType<SolidTypeTag, Properties::SolutionVector>;
+    SolutionVector sol(solidLeafGridView.size(GridView::dimension));;
+    solidProblem->applyInitialSolution(sol);
+    auto solOld = sol;
+
+    // the grid variables
+    using SolidGridVariables = GetPropType<SolidTypeTag, Properties::GridVariables>;
+    auto solidGridVariables = std::make_shared<SolidGridVariables>(solidProblem, solidGridGeometry);
+    solidGridVariables->init(sol);
+
+    // get some time loop parameters
+    using Scalar = GetPropType<SolidTypeTag, Properties::Scalar>;
+    const auto tEnd = getParam<Scalar>("TimeLoop.TEnd", 1.0);
+    const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize", 1.0);
+    auto dt = getParam<Scalar>("TimeLoop.DtInitial", 1.0);
+
+    // initialize the vtk output modules
+    using SolidVtkWriter = PoreNetwork::VtkOutputModule<SolidGridVariables, GetPropType<SolidTypeTag, Properties::FluxVariables>, SolutionVector>;
+    SolidVtkWriter solidVtkWriter(*solidGridVariables, sol, solidProblem->name());
+    using IOFields = GetPropType<SolidTypeTag, Properties::IOFields>;
+    IOFields::initOutputModule(solidVtkWriter);
+
+    solidVtkWriter.write(0.0);
+
+    // instantiate time loop
+    auto timeLoop = std::make_shared<TimeLoop<Scalar>>(0, dt, tEnd);
+    timeLoop->setMaxTimeStepSize(maxDt);
+
+    static const bool isStationary = getParam<bool>("Problem.IsStationary", true);
+
+    // the assembler
+    using Assembler = FVAssembler<SolidTypeTag, DiffMethod::numeric>;
+    auto assembler = isStationary ? std::make_shared<Assembler>(solidProblem, solidGridGeometry, solidGridVariables) //stationary case
+                                  : std::make_shared<Assembler>(solidProblem, solidGridGeometry, solidGridVariables, timeLoop, solOld); // transient case -> timeloop needed
+
+    using LinearSolver =  UMFPackIstlSolver<SeqLinearSolverTraits, LinearAlgebraTraitsFromAssembler<Assembler>>;
+    auto linearSolver = std::make_shared<LinearSolver>();
+
+    // the non-linear solver
+    using NewtonSolver = NewtonSolver<Assembler, LinearSolver>;
+    NewtonSolver nonLinearSolver(assembler, linearSolver);
+
+    if(isStationary) //check if stationary or transient problem
+    {
+        // solve the non-linear system without time step control
+        nonLinearSolver.solve(sol);
+
+        // write vtk output
+        solidVtkWriter.write(1);
+
+    }else{ //solve transient problem
+        // time loop
+        timeLoop->start(); do
+        {
+            // solve the non-linear system with time step control
+            nonLinearSolver.solve(sol, *timeLoop);
+
+            // make the new solution the old solution
+            solOld = sol;
+            solidGridVariables->advanceTimeStep();
+
+            // advance to the time loop to the next step
+            timeLoop->advanceTimeStep();
+
+            // write vtk output
+            solidVtkWriter.write(timeLoop->time());
+
+            // report statistics of this time step
+            timeLoop->reportTimeStep();
+
+            // set new dt as suggested by newton solver
+            timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+
+        } while (!timeLoop->finished());
+
+        timeLoop->finalize(solidLeafGridView.comm());
+    }
+
+    ////////////////////////////////////////////////////////////
+    // finalize, print dumux message to say goodbye
+    ////////////////////////////////////////////////////////////
+
+    // print dumux end message
+    if (mpiHelper.rank() == 0)
+    {
+        Parameters::print();
+        DumuxMessage::print(/*firstCall=*/false);
+    }
+
+    return 0;
+}
diff --git a/test/porenetwork/solidenergy/params.input b/test/porenetwork/solidenergy/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..183e61a8d4f717ae15da8081e75ea52af541bc7b
--- /dev/null
+++ b/test/porenetwork/solidenergy/params.input
@@ -0,0 +1,31 @@
+[TimeLoop]
+TEnd      = 10 # [s]
+DtInitial = 1e-5 # [s]
+
+[Grid]
+PoreGeometry            = Sphere
+ThroatCrossSectionShape = Circle
+UpperRight = 1e-3 1e-3 1e-3
+NumPores   = 4 4 4
+PoreInscribedRadius   = 2e-5
+ThroatInscribedRadius = 2e-6
+BoundaryPoreLabels = xMin:5 xMax:6 yMin:0 yMax:0 zMin:0 zMax:0 #Labels to specify different BCs
+PriorityList       = 0 1 2 3 4 5 #order of how BCs are set (0 1 2 3 4 5 = xMin, xMax, yMin, yMax, zMin,zMax)
+
+[Problem]
+Name = test_pnm_solid_energy
+IsStationary  = false #solving stationary or transient problem
+EnableGravity = false
+InitialTemperature = 300 # [K]
+LeftTemperature    = 400 # [K]
+LeftIndex  = 5  #specifies which pores are on left/heated boundary
+RightIndex = 6  #specifies, which pores are on right boundary
+
+[Vtk]
+OutputName  = test
+AddVelocity = 0
+
+[1.Component] #solid phase (values for granite)
+SolidHeatCapacity        = 790
+SolidDensity             = 2700
+SolidThermalConductivity = 2.600038292
diff --git a/test/porenetwork/solidenergy/problem.hh b/test/porenetwork/solidenergy/problem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..867c328a6b1dce0cb9d233ee06e4bd21705e330b
--- /dev/null
+++ b/test/porenetwork/solidenergy/problem.hh
@@ -0,0 +1,115 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+#ifndef DUMUX_TEST_PORENETWORK_SOLID_ENERGY_PROBLEM_HH
+#define DUMUX_TEST_PORENETWORK_SOLID_ENERGY_PROBLEM_HH
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/boundarytypes.hh>
+#include <dumux/common/numeqvector.hh>
+#include <dumux/porousmediumflow/problem.hh>
+
+namespace Dumux {
+
+/*!
+ * \brief Heat conduction problem with multiple solid spheres
+ */
+template <class TypeTag>
+class SolidProblem : public PorousMediumFlowProblem<TypeTag>
+{
+    using ParentType = PorousMediumFlowProblem<TypeTag>;
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using GridView = typename GridGeometry::GridView;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+    using NumEqVector = Dumux::NumEqVector<PrimaryVariables>;
+    using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+    using FVElementGeometry = typename GridGeometry::LocalView;
+    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
+
+    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+
+public:
+    template<class SpatialParams>
+    SolidProblem(std::shared_ptr<const GridGeometry> gridGeometry,
+                    std::shared_ptr<SpatialParams> spatialParams)
+    : ParentType(gridGeometry, spatialParams)
+    {
+        problemName_  =  getParam<std::string>("Problem.Name");
+        initialTemperature_ = getParam<Scalar>("Problem.InitialTemperature");
+        temperatureLeft_ = getParam<Scalar>("Problem.LeftTemperature");
+
+        leftIndex_ = getParam<int>("Problem.LeftIndex");
+        rightIndex_ = getParam<int>("Problem.RightIndex");
+    }
+
+    const std::string& name() const
+    { return problemName_; }
+
+    BoundaryTypes boundaryTypes(const Element &element, const SubControlVolume& scv) const
+    {
+        BoundaryTypes values;
+        values.setAllNeumann();
+
+        if (onLeftBoundary_(scv) || onRightBoundary_(scv))
+            values.setAllDirichlet();
+
+        return values;
+    }
+
+    template<class ElementVolumeVariables>
+    NumEqVector source(const Element& element,
+                       const FVElementGeometry& fvGeometry,
+                       const ElementVolumeVariables& elemVolVars,
+                       const SubControlVolume& scv) const
+    {
+        NumEqVector value = 0.0; //isolating boundary condition
+        return value;
+    }
+
+    PrimaryVariables dirichlet(const Element& element, const SubControlVolume& scv) const
+    {
+        auto values = initialAtPos(scv.dofPosition()); //onRightBoundary_(scv)
+
+        if (onLeftBoundary_(scv))
+        {
+            values = temperatureLeft_;
+        }
+
+        return values;
+    }
+
+    PrimaryVariables initialAtPos(const GlobalPosition& pos) const
+    {
+        PrimaryVariables values(initialTemperature_); //uniform initial temperature
+        return values;
+    }
+
+private:
+
+    bool onLeftBoundary_(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == leftIndex_; }
+
+    bool onRightBoundary_(const SubControlVolume& scv) const
+    { return this->gridGeometry().poreLabel(scv.dofIndex()) == rightIndex_; }
+
+    std::string problemName_;
+
+    Scalar initialTemperature_;
+    Scalar temperatureLeft_;
+
+    int leftIndex_;
+    int rightIndex_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/porenetwork/solidenergy/properties.hh b/test/porenetwork/solidenergy/properties.hh
new file mode 100644
index 0000000000000000000000000000000000000000..5c0f7ba9487211514393716303c03f8a784810af
--- /dev/null
+++ b/test/porenetwork/solidenergy/properties.hh
@@ -0,0 +1,75 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+/*!
+ * \filegrid
+ * \brief Heat conduction problem with multiple solid spheres
+ */
+#ifndef DUMUX_TEST_PORENETWORK_SOLID_ENERGY_PROPERTIES_HH
+#define DUMUX_TEST_PORENETWORK_SOLID_ENERGY_PROPERTIES_HH
+
+#include <dumux/common/properties.hh>
+#include <dune/foamgrid/foamgrid.hh>
+
+#include <dumux/porenetwork/solidenergy/model.hh>
+#include <dumux/porenetwork/solidenergy/spatialparams.hh>
+
+#include <dumux/material/components/constant.hh>
+
+#include "problem.hh"
+
+namespace Dumux::Properties {
+
+// Create new type tags
+namespace TTag {
+struct PNMSolidModel { using InheritsFrom = std::tuple<PNMSolidEnergy>; };
+} // end namespace TTag
+
+// Set the problem property
+template<class TypeTag>
+struct Problem<TypeTag, TTag::PNMSolidModel>
+{ using type = Dumux::SolidProblem<TypeTag>; };
+
+// Set the grid type
+template<class TypeTag>
+struct Grid<TypeTag, TTag::PNMSolidModel>
+{ using type = Dune::FoamGrid<1, 3>; };
+
+//! The spatial parameters to be employed.
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::PNMSolidModel>
+{
+private:
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    using type = PoreNetwork::SolidEnergySpatialParams<GridGeometry, Scalar>;
+};
+
+// per default the solid system is inert with one constant component
+template<class TypeTag>
+struct SolidSystem<TypeTag, TTag::PNMSolidModel>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using InertComponent = Components::Constant<1, Scalar>;
+public:
+    using type = SolidSystems::InertSolidPhase<Scalar, InertComponent>;
+};
+
+template<class TypeTag>
+struct HeatConductionType<TypeTag, TTag::PNMSolidModel>
+{
+private:
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+    // from grainfourierslaw.hh (specified in solidenergy/model.hh)
+    using type = PoreNetwork::TruncatedPyramidGrainFouriersLaw<Scalar>;
+};
+
+} // end namespace Dumux::Properties
+
+#endif
diff --git a/test/references/test_md_dualnetwork_heat_solid-reference.vtp b/test/references/test_md_dualnetwork_heat_solid-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..6ad1d3dc7c4c2e6282561fadbfe11ff437e3b0b8
--- /dev/null
+++ b/test/references/test_md_dualnetwork_heat_solid-reference.vtp
@@ -0,0 +1,1835 @@
+<?xml version="1.0"?>
+<VTKFile type="PolyData" version="0.1" byte_order="LittleEndian">
+  <PolyData>
+    <Piece NumberOfLines="2184" NumberOfPoints="560">
+      <PointData Scalars="poreInscribedRadius">
+        <DataArray type="Float32" Name="poreInscribedRadius" NumberOfComponents="1" format="ascii">
+          6.08337e-05 8.43296e-05 6.42366e-05 9.15811e-05 5.97334e-05 5.44085e-05 2.69925e-05 3.39144e-05 2.78835e-05 6.19158e-05 7.6959e-05 6.48561e-05
+          6.8071e-05 4.49386e-05 6.46502e-05 6.8071e-05 3.60774e-05 4.88211e-05 1.9865e-05 4.49386e-05 3.04206e-05 4.49386e-05 5.83877e-05 3.81311e-05
+          3.39144e-05 7.30117e-05 5.60786e-05 8.91755e-05 3.74577e-05 2.04414e-05 3.81311e-05 5.9955e-05 1.30985e-05 1.0489e-05 2.41548e-05 5.29385e-05
+          5.97334e-05 5.24401e-05 7.55461e-05 4.07249e-05 9.67853e-05 3.94471e-05 5.0141e-05 5.34327e-05 5.81606e-05 3.60774e-05 1.9865e-05 7.16094e-07
+          4.88211e-05 2.20961e-05 3.27861e-05 9.40729e-05 4.07249e-05 2.74411e-05 1.92747e-05 5.67805e-05 6.23438e-05 1.14061e-05 6.25567e-05 3.3166e-05
+          5.29385e-05 5.41661e-05 1.14061e-05 5.06602e-05 5.65474e-05 4.13505e-05 2.65375e-05 1.22735e-05 4.46496e-05 5.44085e-05 2.78835e-05 1.67511e-05
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diff --git a/test/references/test_md_dualnetwork_heat_void-reference.vtp b/test/references/test_md_dualnetwork_heat_void-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..382be1c4e0bb47477cd382c442df5614bd003347
--- /dev/null
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diff --git a/test/references/test_pnm_solid_energy-reference.vtp b/test/references/test_pnm_solid_energy-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..8dc55745e29741aab3d78c23aee1cf679b3c489a
--- /dev/null
+++ b/test/references/test_pnm_solid_energy-reference.vtp
@@ -0,0 +1,350 @@
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