flux/box/fourierslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_FOURIERS_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_FOURIERS_LAW_HH
 
#include <dumux/common/math.hh>
#include <dumux/common/properties.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, DiscretizationMethod discMethod>
class FouriersLawImplementation;

template <class TypeTag>
class FouriersLawImplementation<TypeTag, DiscretizationMethod::box>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
 
public:
    static Scalar flux(const Problem& problem,
                       const Element& element,
                       const FVElementGeometry& fvGeometry,
                       const ElementVolumeVariables& elemVolVars,
                       const SubControlVolumeFace& scvf,
                       const ElementFluxVariablesCache& elemFluxVarsCache)
    {
        // get inside and outside diffusion tensors and calculate the harmonic mean
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& outsideVolVars = elemVolVars[outsideScv];
 
        // effective diffusion tensors
        auto insideLambda = insideVolVars.effectiveThermalConductivity();
        auto outsideLambda = outsideVolVars.effectiveThermalConductivity();
 
        // scale by extrusion factor
        insideLambda *= insideVolVars.extrusionFactor();
        outsideLambda *= outsideVolVars.extrusionFactor();
 
        // the resulting averaged diffusion tensor
        const auto lambda = problem.spatialParams().harmonicMean(insideLambda, outsideLambda, scvf.unitOuterNormal());
 
        // evaluate gradTemp at integration point
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
 
        // compute the temperature gradient with the shape functions
        Dune::FieldVector<Scalar, GridView::dimensionworld> gradTemp(0.0);
        for (auto&& scv : scvs(fvGeometry))
            gradTemp.axpy(elemVolVars[scv].temperature(), fluxVarsCache.gradN(scv.indexInElement()));
 
        // comute the heat conduction flux
        return -1.0*vtmv(scvf.unitOuterNormal(), lambda, gradTemp)*Extrusion::area(scvf);
    }
};
 
} // end namespace Dumux
 
#endif