flux/box/fickslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_FICKS_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_FICKS_LAW_HH
 
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dumux/common/math.hh>
#include <dumux/common/properties.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
 
#include <dumux/flux/fickiandiffusioncoefficients.hh>
#include <dumux/flux/referencesystemformulation.hh>
#include <dumux/flux/facetensoraverage.hh>
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation;
 
template <class TypeTag, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation<TypeTag, DiscretizationMethods::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 GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using GridFluxVariablesCache = GetPropType<TypeTag, Properties::GridFluxVariablesCache>;
    using ElementFluxVariablesCache = typename GridFluxVariablesCache::LocalView;
    using FluxVarCache = typename GridFluxVariablesCache::FluxVariablesCache;
    using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>;
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
 
    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:
    using DiffusionCoefficientsContainer = FickianDiffusionCoefficients<Scalar, numPhases, numComponents>;
 
    //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)
    {
        // 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];
 
        ComponentFluxVector componentFlux(0.0);
        for (int compIdx = 0; compIdx < numComponents; compIdx++)
        {
            if constexpr (!FluidSystem::isTracerFluidSystem())
                if (compIdx == FluidSystem::getMainComponent(phaseIdx))
                    continue;
 
            const auto diffCoeff = averageDiffusionCoefficient_(phaseIdx, compIdx, insideVolVars, outsideVolVars, problem, scvf);
 
            // compute the diffusive flux
            const auto massOrMoleFrac = [&](const SubControlVolume& scv){ return massOrMoleFraction(elemVolVars[scv], referenceSystem, phaseIdx, compIdx); };
            componentFlux[compIdx] = discreteFlux_(fvGeometry, scvf, fluxVarsCache, massOrMoleFrac, diffCoeff, rho);
 
            // if the main component is balanced subtract the same flux from there (conservation)
            if constexpr (!FluidSystem::isTracerFluidSystem())
                if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx))
                    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 constexpr (!FluidSystem::isTracerFluidSystem())
                if (compIdx == FluidSystem::getMainComponent(phaseIdx))
                    continue;
 
            const auto diffCoeff = averageDiffusionCoefficient_(phaseIdx, compIdx, insideVolVars, outsideVolVars, problem, scvf);
 
            ti[compIdx].resize(fvGeometry.numScv());
            for (auto&& scv : scvs(fvGeometry))
                ti[compIdx][scv.indexInElement()] = -rho*vtmv(scvf.unitOuterNormal(), diffCoeff, fluxVarCache.gradN(scv.indexInElement()))*Extrusion::area(fvGeometry, scvf);
        }
 
        return ti;
    }
 
private:
    static Scalar averageDiffusionCoefficient_(const int phaseIdx, const int compIdx,
                                               const VolumeVariables& insideVV, const VolumeVariables& outsideVV,
                                               const Problem& problem,
                                               const SubControlVolumeFace& scvf)
    {
        // effective diffusion tensors
        auto [insideDiffCoeff, outsideDiffCoeff] = diffusionCoefficientsAtInterface_(phaseIdx, compIdx, insideVV, outsideVV);
 
        // scale by extrusion factor
        insideDiffCoeff *= insideVV.extrusionFactor();
        outsideDiffCoeff *= outsideVV.extrusionFactor();
 
        // the resulting averaged diffusion tensor
        return faceTensorAverage(insideDiffCoeff, outsideDiffCoeff, scvf.unitOuterNormal());
    }
 
    static std::pair<Scalar, Scalar>
    diffusionCoefficientsAtInterface_([[maybe_unused]] const int phaseIdx, const int compIdx,
                                      const VolumeVariables& insideVV, const VolumeVariables& outsideVV)
    {
        if constexpr (!FluidSystem::isTracerFluidSystem())
        {
            const auto mainCompIdx = FluidSystem::getMainComponent(phaseIdx);
            const auto insideDiffCoeff = insideVV.effectiveDiffusionCoefficient(phaseIdx, mainCompIdx, compIdx);
            const auto outsideDiffCoeff = outsideVV.effectiveDiffusionCoefficient(phaseIdx, mainCompIdx, compIdx);
            return { std::move(insideDiffCoeff), std::move(outsideDiffCoeff) };
        }
        else
        {
            const auto insideDiffCoeff = insideVV.effectiveDiffusionCoefficient(0, 0, compIdx);
            const auto outsideDiffCoeff = outsideVV.effectiveDiffusionCoefficient(0, 0, compIdx);
            return { std::move(insideDiffCoeff), std::move(outsideDiffCoeff) };
        }
    }
 
    template<class EvaluateVariable, class Tensor>
    static Scalar discreteFlux_(const FVElementGeometry& fvGeometry,
                                const SubControlVolumeFace& scvf,
                                const FluxVarCache& fluxVarsCache,
                                const EvaluateVariable& massOrMoleFraction,
                                const Tensor& D, const Scalar preFactor)
    {
        Dune::FieldVector<Scalar, dimWorld> gradX(0.0);
        for (auto&& scv : scvs(fvGeometry))
            gradX.axpy(massOrMoleFraction(scv), fluxVarsCache.gradN(scv.indexInElement()));
        return -1.0*preFactor*vtmv(scvf.unitOuterNormal(), D, gradX)*Extrusion::area(fvGeometry, scvf);
    }
};
 
} // end namespace Dumux
 
#endif