flux/cctpfa/fourierslaw.hh

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#ifndef DUMUX_DISCRETIZATION_CC_TPFA_FOURIERS_LAW_HH
#define DUMUX_DISCRETIZATION_CC_TPFA_FOURIERS_LAW_HH
 
#include <dumux/common/parameters.hh>
#include <dumux/common/properties.hh>
 
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/discretization/cellcentered/tpfa/computetransmissibility.hh>
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, DiscretizationMethod discMethod>
class FouriersLawImplementation;
 
template <class TypeTag>
class FouriersLawImplementation<TypeTag, DiscretizationMethod::cctpfa>
{
    using Implementation = FouriersLawImplementation<TypeTag, DiscretizationMethod::cctpfa>;
    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 GridView = typename GridGeometry::GridView;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementFluxVarsCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using FluxVariablesCache = GetPropType<TypeTag, Properties::FluxVariablesCache>;
 
    static const int dim = GridView::dimension;
    static const int dimWorld = GridView::dimensionworld;
 
    class TpfaFouriersLawCacheFiller
    {
    public:
        template<class FluxVariablesCacheFiller>
        static void fill(FluxVariablesCache& scvfFluxVarsCache,
                         const Problem& problem,
                         const Element& element,
                         const FVElementGeometry& fvGeometry,
                         const ElementVolumeVariables& elemVolVars,
                         const SubControlVolumeFace& scvf,
                         const FluxVariablesCacheFiller& fluxVarsCacheFiller)
        {
            scvfFluxVarsCache.updateHeatConduction(problem, element, fvGeometry, elemVolVars, scvf);
        }
    };
 
    class TpfaFouriersLawCache
    {
    public:
        using Filler = TpfaFouriersLawCacheFiller;
 
        void updateHeatConduction(const Problem& problem,
                                  const Element& element,
                                  const FVElementGeometry& fvGeometry,
                                  const ElementVolumeVariables& elemVolVars,
                                  const SubControlVolumeFace &scvf)
        {
            tij_ = Implementation::calculateTransmissibility(problem, element, fvGeometry, elemVolVars, scvf);
        }
 
        const Scalar& heatConductionTij() const
        { return tij_; }
 
    private:
        Scalar tij_;
    };
 
public:
    static const DiscretizationMethod discMethod = DiscretizationMethod::cctpfa;
 
    using Cache = TpfaFouriersLawCache;
 
    static Scalar flux(const Problem& problem,
                       const Element& element,
                       const FVElementGeometry& fvGeometry,
                       const ElementVolumeVariables& elemVolVars,
                       const SubControlVolumeFace& scvf,
                       const ElementFluxVarsCache& elemFluxVarsCache)
    {
        // heat conductivities are always solution dependent (?)
        Scalar tij = elemFluxVarsCache[scvf].heatConductionTij();
 
        // get the inside/outside temperatures
        const auto tInside = elemVolVars[scvf.insideScvIdx()].temperature();
        const auto tOutside = scvf.numOutsideScvs() == 1 ? elemVolVars[scvf.outsideScvIdx()].temperature()
                              : branchingFacetTemperature_(problem, element, fvGeometry, elemVolVars, elemFluxVarsCache, scvf, tInside, tij);
 
        return tij*(tInside - tOutside);
    }
 
    static Scalar calculateTransmissibility(const Problem& problem,
                                            const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const SubControlVolumeFace& scvf)
    {
        Scalar tij;
 
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& insideVolVars = elemVolVars[insideScvIdx];
 
        const auto insideLambda = insideVolVars.effectiveThermalConductivity();
        const Scalar ti = computeTpfaTransmissibility(scvf, insideScv, insideLambda, insideVolVars.extrusionFactor());
 
        // for the boundary (dirichlet) or at branching points we only need ti
        if (scvf.boundary() || scvf.numOutsideScvs() > 1)
        {
            tij = Extrusion::area(scvf)*ti;
        }
        // otherwise we compute a tpfa harmonic mean
        else
        {
            const auto outsideScvIdx = scvf.outsideScvIdx();
            const auto& outsideScv = fvGeometry.scv(outsideScvIdx);
            const auto& outsideVolVars = elemVolVars[outsideScvIdx];
 
            const auto outsideLambda = outsideVolVars.effectiveThermalConductivity();
            Scalar tj;
            if (dim == dimWorld)
                // assume the normal vector from outside is anti parallel so we save flipping a vector
                tj = -1.0*computeTpfaTransmissibility(scvf, outsideScv, outsideLambda, outsideVolVars.extrusionFactor());
            else
                tj = computeTpfaTransmissibility(fvGeometry.flipScvf(scvf.index()), outsideScv, outsideLambda, outsideVolVars.extrusionFactor());
 
            // check for division by zero!
            if (ti*tj <= 0.0)
                tij = 0;
            else
                tij = Extrusion::area(scvf)*(ti * tj)/(ti + tj);
        }
 
        return tij;
    }
 
private:
 
    static Scalar branchingFacetTemperature_(const Problem& problem,
                                             const Element& element,
                                             const FVElementGeometry& fvGeometry,
                                             const ElementVolumeVariables& elemVolVars,
                                             const ElementFluxVarsCache& elemFluxVarsCache,
                                             const SubControlVolumeFace& scvf,
                                             Scalar insideTemperature,
                                             Scalar insideTi)
    {
        Scalar sumTi(insideTi);
        Scalar sumTempTi(insideTi*insideTemperature);
 
        for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
        {
            const auto outsideScvIdx = scvf.outsideScvIdx(i);
            const auto& outsideVolVars = elemVolVars[outsideScvIdx];
            const auto& flippedScvf = fvGeometry.flipScvf(scvf.index(), i);
            const auto& outsideFluxVarsCache = elemFluxVarsCache[flippedScvf];
 
            auto outsideTi = outsideFluxVarsCache.heatConductionTij();
            sumTi += outsideTi;
            sumTempTi += outsideTi*outsideVolVars.temperature();
        }
        return sumTempTi/sumTi;
    }
};
 
} // end namespace Dumux
 
#endif