[staggeredGrid][nonisothermal] Implement Fourier's law for staggered grid

dumux/discretization/fourierslaw.hh

@@ -45,5 +45,6 @@ using FouriersLaw = FouriersLawImplementation<TypeTag, GET_PROP_VALUE(TypeTag, D
 #include <dumux/discretization/cellcentered/tpfa/fourierslaw.hh>
 #include <dumux/discretization/cellcentered/mpfa/fourierslaw.hh>
 #include <dumux/discretization/box/fourierslaw.hh>
+#include <dumux/discretization/staggered/freeflow/fourierslaw.hh>
 
 #endif

dumux/discretization/staggered/freeflow/fourierslaw.hh

+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 2 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ * \brief This file contains the data which is required to calculate
+ *        diffusive mass fluxes due to molecular diffusion with Fourier's law.
+ */
+#ifndef DUMUX_DISCRETIZATION_STAGGERED_FOURIERS_LAW_HH
+#define DUMUX_DISCRETIZATION_STAGGERED_FOURIERS_LAW_HH
+
+#include <dune/common/float_cmp.hh>
+
+#include <dumux/common/math.hh>
+#include <dumux/common/parameters.hh>
+
+#include <dumux/implicit/properties.hh>
+#include <dumux/discretization/methods.hh>
+#include <dumux/discretization/fluxvariablescaching.hh>
+
+namespace Dumux
+{
+
+namespace Properties
+{
+// forward declaration of properties
+NEW_PROP_TAG(CellCenterPrimaryVariables);
+}
+
+/*!
+ * \ingroup StaggeredFouriersLaw
+ * \brief Specialization of Fourier's Law for the staggered free flow method.
+ */
+template <class TypeTag>
+class FouriersLawImplementation<TypeTag, DiscretizationMethods::Staggered >
+{
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+    using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
+    using SubControlVolumeFace = typename GET_PROP_TYPE(TypeTag, SubControlVolumeFace);
+    using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
+    using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
+    using ElementVolumeVariables = typename GET_PROP_TYPE(TypeTag, ElementVolumeVariables);
+    using Element = typename GridView::template Codim<0>::Entity;
+    using CellCenterPrimaryVariables = typename GET_PROP_TYPE(TypeTag, CellCenterPrimaryVariables);
+    using ThermalConductivityModel = typename GET_PROP_TYPE(TypeTag, ThermalConductivityModel);
+    using Indices = typename GET_PROP_TYPE(TypeTag, Indices);
+
+    static const int dim = GridView::dimension;
+    static const int dimWorld = GridView::dimensionworld;
+
+    enum {
+        energyBalanceIdx = Indices::energyBalanceIdx
+    };
+
+public:
+    // state the discretization method this implementation belongs to
+    static const DiscretizationMethods myDiscretizationMethod = DiscretizationMethods::Staggered;
+
+    //! state the type for the corresponding cache and its filler
+    //! We don't cache anything for this law
+    using Cache = FluxVariablesCaching::EmptyDiffusionCache;
+    using CacheFiller = FluxVariablesCaching::EmptyCacheFiller<TypeTag>;
+
+    static CellCenterPrimaryVariables diffusiveFluxForCellCenter(const Problem& problem,
+                                                           const FVElementGeometry& fvGeometry,
+                                                           const ElementVolumeVariables& elemVolVars,
+                                                           const SubControlVolumeFace &scvf)
+    {
+        CellCenterPrimaryVariables flux(0.0);
+
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& outsideVolVars = scvf.boundary() ?  insideVolVars : elemVolVars[scvf.outsideScvIdx()];
+
+        // effective conductivity tensors
+        auto insideLambda = ThermalConductivityModel::effectiveThermalConductivity(insideVolVars, problem.spatialParams(), element, fvGeometry, insideScv);
+        auto outsideLambda = ThermalConductivityModel::effectiveThermalConductivity(outsideVolVars, problem.spatialParams(), element, fvGeometry, outsideScv);
+
+        // scale by extrusion factor
+        insideLambda *= insideVolVars.extrusionFactor();
+        outsideLambda *= outsideVolVars.extrusionFactor();
+
+        // the resulting averaged conductivity tensor
+        const auto lambda = problem.spatialParams().harmonicMean(insideLambda, outsideLambda, scvf.unitOuterNormal());
+
+        const Scalar insideTemp = insideVolVars.temperature();
+        Scalar distance(0.0), outsideTemp(insideTemp);
+
+        if(scvf.boundary())
+        {
+            const auto bcTypes = problem.boundaryTypesAtPos(scvf.center());
+            if(bcTypes.isOutflow(energyBalanceIdx))
+                return flux; // TODO flux = 0??
+            else if(bcTypes.isNeumann(energyBalanceIdx))
+                return flux; // TODO: implement neumann
+                else
+                {
+                    distance = (insideScv.dofPosition() - scvf.ipGlobal()).two_norm();
+                    outsideTemp = problem.dirichletAtPos(scvf.center())[energyBalanceIdx]);
+                }
+        }
+        else
+        {
+            distance = (insideScv.dofPosition() - outsideScv.dofPosition());
+            outsideTemp = outsideVolVars.temperature();
+        }
+
+        flux[energyBalanceIdx] = (insideTemp - outsideTemp);
+        flux[energyBalanceIdx] *= lambda / distance;
+        return -1.0*flux;
+    }
+};
+} // end namespace
+
+#endif