box/fickslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_FICKS_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_FICKS_LAW_HH
 
#include <dumux/common/math.hh>
#include <dumux/common/properties.hh>
#include <dumux/discretization/method.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::box, referenceSystem>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using FluxVarCache = GetPropType<TypeTag, Properties::FluxVariablesCache>;
    using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Element = typename GridView::template Codim<0>::Entity;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using Indices = typename ModelTraits::Indices;
 
    enum { dim = GridView::dimension} ;
    enum { dimWorld = GridView::dimensionworld} ;
    enum
    {
        numPhases = ModelTraits::numFluidPhases(),
        numComponents = ModelTraits::numFluidComponents()
    };
    using DimWorldMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
    using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>;
 
public:
    //return the reference system
    static constexpr ReferenceSystemFormulation referenceSystemFormulation()
    { return referenceSystem; }
 
    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);
 
        // get inside and outside diffusion tensors and calculate the harmonic mean
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
        // evaluate gradX at integration point and interpolate density
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
        const auto& shapeValues = fluxVarsCache.shapeValues();
 
        // density interpolation
        Scalar rho(0.0);
        for (auto&& scv : scvs(fvGeometry))
            rho += massOrMolarDensity(elemVolVars[scv], referenceSystem, phaseIdx)*shapeValues[scv.indexInElement()][0];
 
        for (int compIdx = 0; compIdx < numComponents; compIdx++)
        {
            if (compIdx == FluidSystem::getMainComponent(phaseIdx))
                continue;
 
            // effective diffusion tensors
            using EffDiffModel = GetPropType<TypeTag, Properties::EffectiveDiffusivityModel>;
            auto insideD = EffDiffModel::effectiveDiffusivity(insideVolVars.porosity(),
                                                              insideVolVars.saturation(phaseIdx),
                                                              insideVolVars.diffusionCoefficient(phaseIdx, compIdx));
            auto outsideD = EffDiffModel::effectiveDiffusivity(outsideVolVars.porosity(),
                                                               outsideVolVars.saturation(phaseIdx),
                                                               outsideVolVars.diffusionCoefficient(phaseIdx, compIdx));
 
            // scale by extrusion factor
            insideD *= insideVolVars.extrusionFactor();
            outsideD *= outsideVolVars.extrusionFactor();
 
            // the resulting averaged diffusion tensor
            const auto D = problem.spatialParams().harmonicMean(insideD, outsideD, scvf.unitOuterNormal());
 
            // the mole/mass fraction gradient
            Dune::FieldVector<Scalar, dimWorld> gradX(0.0);
            for (auto&& scv : scvs(fvGeometry))
                gradX.axpy(massOrMoleFraction(elemVolVars[scv], referenceSystem, phaseIdx, compIdx), fluxVarsCache.gradN(scv.indexInElement()));
 
            // compute the diffusive flux
            componentFlux[compIdx] = -1.0*rho*vtmv(scvf.unitOuterNormal(), D, gradX)*scvf.area();
            if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx) && !FluidSystem::isTracerFluidSystem())
                componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx];
        }
        return componentFlux;
    }
 
    // compute transmissibilities ti for analytical jacobians
    static std::array<std::vector<Scalar>, numComponents>
    calculateTransmissibilities(const Problem& problem,
                                const Element& element,
                                const FVElementGeometry& fvGeometry,
                                const ElementVolumeVariables& elemVolVars,
                                const SubControlVolumeFace& scvf,
                                const FluxVarCache& fluxVarCache,
                                const int phaseIdx)
    {
        Scalar rho(0.0);
        const auto& shapeValues = fluxVarCache.shapeValues();
        for (auto&& scv : scvs(fvGeometry))
            rho += massOrMolarDensity(elemVolVars[scv], referenceSystem, phaseIdx)*shapeValues[scv.indexInElement()][0];
 
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
        std::array<std::vector<Scalar>, numComponents> ti;
        for (int compIdx = 0; compIdx < numComponents; compIdx++)
        {
            if(compIdx == FluidSystem::getMainComponent(phaseIdx))
                continue;
 
            // effective diffusion tensors
            using EffDiffModel = GetPropType<TypeTag, Properties::EffectiveDiffusivityModel>;
            auto insideD = EffDiffModel::effectiveDiffusivity(insideVolVars.porosity(),
                                                              insideVolVars.saturation(phaseIdx),
                                                              insideVolVars.diffusionCoefficient(phaseIdx, compIdx));
            auto outsideD = EffDiffModel::effectiveDiffusivity(outsideVolVars.porosity(),
                                                               outsideVolVars.saturation(phaseIdx),
                                                               outsideVolVars.diffusionCoefficient(phaseIdx, compIdx));
 
            // scale by extrusion factor
            insideD *= insideVolVars.extrusionFactor();
            outsideD *= outsideVolVars.extrusionFactor();
 
            // the resulting averaged diffusion tensor
            const auto D = problem.spatialParams().harmonicMean(insideD, outsideD, scvf.unitOuterNormal());
 
            ti[compIdx].resize(fvGeometry.numScv());
            for (auto&& scv : scvs(fvGeometry))
                ti[compIdx][scv.indexInElement()] = -rho*vtmv(scvf.unitOuterNormal(), D, fluxVarCache.gradN(scv.indexInElement()))*scvf.area();
        }
 
        return ti;
    }
};
 
} // end namespace Dumux
 
#endif