cctpfa/fickslaw.hh

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#ifndef DUMUX_DISCRETIZATION_CC_TPFA_FICKS_LAW_HH
#define DUMUX_DISCRETIZATION_CC_TPFA_FICKS_LAW_HH
 
#include <dumux/common/parameters.hh>
#include <dumux/common/properties.hh>
 
#include <dumux/discretization/method.hh>
#include <dumux/discretization/cellcentered/tpfa/computetransmissibility.hh>
 
#include <dumux/flux/referencesystemformulation.hh>
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, DiscretizationMethod discMethod, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation;
 
template <class TypeTag, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation<TypeTag, DiscretizationMethod::cctpfa, referenceSystem>
{
    using Implementation = FicksLawImplementation<TypeTag, DiscretizationMethod::cctpfa, referenceSystem>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using FluxVariablesCache = GetPropType<TypeTag, Properties::FluxVariablesCache>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>;
 
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using Indices = typename ModelTraits::Indices;
 
    static const int dim = GridView::dimension;
    static const int dimWorld = GridView::dimensionworld;
    static const int numPhases = ModelTraits::numFluidPhases();
    static const int numComponents = ModelTraits::numFluidComponents();
 
    using DimWorldMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
    using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>;
 
    class TpfaFicksLawCacheFiller
    {
    public:
        template<class FluxVariablesCacheFiller>
        static void fill(FluxVariablesCache& scvfFluxVarsCache,
                         unsigned int phaseIdx, unsigned int compIdx,
                         const Problem& problem,
                         const Element& element,
                         const FVElementGeometry& fvGeometry,
                         const ElementVolumeVariables& elemVolVars,
                         const SubControlVolumeFace& scvf,
                         const FluxVariablesCacheFiller& fluxVarsCacheFiller)
        {
            scvfFluxVarsCache.updateDiffusion(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, compIdx);
        }
    };
 
    class TpfaFicksLawCache
    {
    public:
        using Filler = TpfaFicksLawCacheFiller;
 
        void updateDiffusion(const Problem& problem,
                             const Element& element,
                             const FVElementGeometry& fvGeometry,
                             const ElementVolumeVariables& elemVolVars,
                             const SubControlVolumeFace &scvf,
                             const unsigned int phaseIdx,
                             const unsigned int compIdx)
        {
            tij_[phaseIdx][compIdx] = Implementation::calculateTransmissibility(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, compIdx);
        }
 
        const Scalar& diffusionTij(unsigned int phaseIdx, unsigned int compIdx) const
        { return tij_[phaseIdx][compIdx]; }
 
    private:
        std::array< std::array<Scalar, numComponents>, numPhases> tij_;
    };
 
public:
    static const DiscretizationMethod discMethod = DiscretizationMethod::cctpfa;
    static constexpr ReferenceSystemFormulation referenceSystemFormulation()
    { return referenceSystem; }
 
    using Cache = TpfaFicksLawCache;
 
    static ComponentFluxVector flux(const Problem& problem,
                                    const Element& element,
                                    const FVElementGeometry& fvGeometry,
                                    const ElementVolumeVariables& elemVolVars,
                                    const SubControlVolumeFace& scvf,
                                    const int phaseIdx,
                                    const ElementFluxVariablesCache& elemFluxVarsCache)
    {
        ComponentFluxVector componentFlux(0.0);
        for (int compIdx = 0; compIdx < numComponents; compIdx++)
        {
            if(compIdx == FluidSystem::getMainComponent(phaseIdx))
                continue;
 
            // diffusion tensors are always solution dependent
            Scalar tij = elemFluxVarsCache[scvf].diffusionTij(phaseIdx, compIdx);
 
            // get inside/outside volume variables
            const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
            const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
            // the inside and outside mass/mole fractions fractions
            const Scalar xInside = massOrMoleFraction(insideVolVars, referenceSystem, phaseIdx, compIdx);
            const Scalar massOrMoleFractionOutside = massOrMoleFraction(outsideVolVars, referenceSystem, phaseIdx, compIdx);
            const Scalar xOutside = scvf.numOutsideScvs() == 1 ? massOrMoleFractionOutside
                                  : branchingFacetX(problem, element, fvGeometry, elemVolVars,
                                                    elemFluxVarsCache, scvf, xInside, tij, phaseIdx, compIdx);
 
            const Scalar rhoInside = massOrMolarDensity(insideVolVars, referenceSystem, phaseIdx);
            const Scalar rhoOutside = massOrMolarDensity(outsideVolVars, referenceSystem, phaseIdx);
 
            const Scalar rho = scvf.numOutsideScvs() == 1 ? 0.5*(rhoInside + rhoOutside)
                                                        : branchingFacetDensity(elemVolVars, scvf, phaseIdx, rhoInside);
 
            componentFlux[compIdx] = rho*tij*(xInside - xOutside);
            if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx) && !FluidSystem::isTracerFluidSystem())
                componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx];
        }
 
        return componentFlux;
    }
 
    static Scalar calculateTransmissibility(const Problem& problem,
                                            const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const SubControlVolumeFace& scvf,
                                            const int phaseIdx, const int compIdx)
    {
        Scalar tij;
 
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& insideVolVars = elemVolVars[insideScvIdx];
 
        using EffDiffModel = GetPropType<TypeTag, Properties::EffectiveDiffusivityModel>;
        const auto insideD = EffDiffModel::effectiveDiffusivity(insideVolVars.porosity(),
                                                                insideVolVars.saturation(phaseIdx),
                                                                insideVolVars.diffusionCoefficient(phaseIdx, compIdx));
        const Scalar ti = computeTpfaTransmissibility(scvf, insideScv, insideD, insideVolVars.extrusionFactor());
 
        // for the boundary (dirichlet) or at branching points we only need ti
        if (scvf.boundary() || scvf.numOutsideScvs() > 1)
        {
            tij = scvf.area()*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 outsideD = EffDiffModel::effectiveDiffusivity(outsideVolVars.porosity(),
                                                                     outsideVolVars.saturation(phaseIdx),
                                                                     outsideVolVars.diffusionCoefficient(phaseIdx, compIdx));
 
            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, outsideD, outsideVolVars.extrusionFactor());
            else
                tj = computeTpfaTransmissibility(fvGeometry.flipScvf(scvf.index()),
                                                 outsideScv,
                                                 outsideD,
                                                 outsideVolVars.extrusionFactor());
 
            // check if we are dividing by zero!
            if (ti*tj <= 0.0)
                tij = 0;
            else
                tij = scvf.area()*(ti * tj)/(ti + tj);
        }
 
        return tij;
    }
 
private:
    static Scalar branchingFacetX(const Problem& problem,
                                  const Element& element,
                                  const FVElementGeometry& fvGeometry,
                                  const ElementVolumeVariables& elemVolVars,
                                  const ElementFluxVariablesCache& elemFluxVarsCache,
                                  const SubControlVolumeFace& scvf,
                                  const Scalar insideX, const Scalar insideTi,
                                  const int phaseIdx, const int compIdx)
    {
        Scalar sumTi(insideTi);
        Scalar sumXTi(insideTi*insideX);
 
        for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
        {
            const auto outsideScvIdx = scvf.outsideScvIdx(i);
            const auto& outsideVolVars = elemVolVars[outsideScvIdx];
            const Scalar massOrMoleFractionOutside = massOrMoleFraction(outsideVolVars, referenceSystem, phaseIdx, compIdx);
            const auto& flippedScvf = fvGeometry.flipScvf(scvf.index(), i);
 
            const Scalar outsideTi = elemFluxVarsCache[flippedScvf].diffusionTij(phaseIdx, compIdx);
            sumTi += outsideTi;
            sumXTi += outsideTi*massOrMoleFractionOutside;
        }
 
        return sumTi > 0 ? sumXTi/sumTi : 0;
    }
 
    static Scalar branchingFacetDensity(const ElementVolumeVariables& elemVolVars,
                                        const SubControlVolumeFace& scvf,
                                        const int phaseIdx,
                                        const Scalar insideRho)
    {
        Scalar rho(insideRho);
        for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
        {
            const auto outsideScvIdx = scvf.outsideScvIdx(i);
            const auto& outsideVolVars = elemVolVars[outsideScvIdx];
            const Scalar rhoOutside = massOrMolarDensity(outsideVolVars, referenceSystem, phaseIdx);
            rho += rhoOutside;
        }
        return rho/(scvf.numOutsideScvs()+1);
    }
};
 
} // end namespace Dumux
 
#endif