ccmpfa/fickslaw.hh

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#ifndef DUMUX_DISCRETIZATION_CC_MPFA_FICKS_LAW_HH
#define DUMUX_DISCRETIZATION_CC_MPFA_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 {
 
template<class TypeTag, DiscretizationMethod discMethod, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation;
 
template <class TypeTag, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation<TypeTag, DiscretizationMethod::ccmpfa, referenceSystem>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Element = typename GridView::template Codim<0>::Entity;
 
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
 
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using FluxVariablesCache = GetPropType<TypeTag, Properties::FluxVariablesCache>;
    using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>;
 
    static constexpr int numComponents = GetPropType<TypeTag, Properties::ModelTraits>::numFluidComponents();
    using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>;
 
    class MpfaFicksLawCacheFiller
    {
    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)
        {
            // get interaction volume related data from the filler class & upate the cache
            if (fvGeometry.gridGeometry().vertexUsesSecondaryInteractionVolume(scvf.vertexIndex()))
                scvfFluxVarsCache.updateDiffusion(fluxVarsCacheFiller.secondaryInteractionVolume(),
                                                  fluxVarsCacheFiller.secondaryIvLocalFaceData(),
                                                  fluxVarsCacheFiller.secondaryIvDataHandle(),
                                                  phaseIdx, compIdx);
            else
                scvfFluxVarsCache.updateDiffusion(fluxVarsCacheFiller.primaryInteractionVolume(),
                                                  fluxVarsCacheFiller.primaryIvLocalFaceData(),
                                                  fluxVarsCacheFiller.primaryIvDataHandle(),
                                                  phaseIdx, compIdx);
        }
    };
 
    class MpfaFicksLawCache
    {
        using DualGridNodalIndexSet = GetPropType<TypeTag, Properties::DualGridNodalIndexSet>;
        using Stencil = typename DualGridNodalIndexSet::NodalGridStencilType;
 
        static constexpr int numPhases = GetPropType<TypeTag, Properties::ModelTraits>::numFluidPhases();
        static constexpr bool considerSecondaryIVs = GridGeometry::MpfaHelper::considerSecondaryIVs();
        using PrimaryDataHandle = typename ElementFluxVariablesCache::PrimaryIvDataHandle::DiffusionHandle;
        using SecondaryDataHandle = typename ElementFluxVariablesCache::SecondaryIvDataHandle::DiffusionHandle;
 
        template< bool doSecondary = considerSecondaryIVs, std::enable_if_t<doSecondary, int> = 0 >
        void setHandlePointer_(const SecondaryDataHandle& dataHandle)
        { secondaryHandlePtr_ = &dataHandle; }
 
        void setHandlePointer_(const PrimaryDataHandle& dataHandle)
        { primaryHandlePtr_ = &dataHandle; }
 
    public:
        // export filler type
        using Filler = MpfaFicksLawCacheFiller;
 
        template<class IV, class LocalFaceData, class DataHandle>
        void updateDiffusion(const IV& iv,
                             const LocalFaceData& localFaceData,
                             const DataHandle& dataHandle,
                             unsigned int phaseIdx, unsigned int compIdx)
        {
            stencil_[phaseIdx][compIdx] = &iv.stencil();
            switchFluxSign_[phaseIdx][compIdx] = localFaceData.isOutsideFace();
            setHandlePointer_(dataHandle.diffusionHandle());
        }
 
        const Stencil& diffusionStencil(unsigned int phaseIdx, unsigned int compIdx) const
        { return *stencil_[phaseIdx][compIdx]; }
 
        const PrimaryDataHandle& diffusionPrimaryDataHandle() const { return *primaryHandlePtr_; }
        const SecondaryDataHandle& diffusionSecondaryDataHandle() const { return *secondaryHandlePtr_; }
 
        bool diffusionSwitchFluxSign(unsigned int phaseIdx, unsigned int compIdx) const
        { return switchFluxSign_[phaseIdx][compIdx]; }
 
 
    private:
        std::array< std::array<bool, numComponents>, numPhases > switchFluxSign_;
        std::array< std::array<const Stencil*, numComponents>, numPhases > stencil_;
 
        const PrimaryDataHandle* primaryHandlePtr_;
        const SecondaryDataHandle* secondaryHandlePtr_;
    };
 
public:
    // state the discretization method this implementation belongs to
    static const DiscretizationMethod discMethod = DiscretizationMethod::ccmpfa;
    //return the reference system
    static constexpr ReferenceSystemFormulation referenceSystemFormulation()
    { return referenceSystem; }
    // state the type for the corresponding cache and its filler
    using Cache = MpfaFicksLawCache;
 
    static ComponentFluxVector flux(const Problem& problem,
                                    const Element& element,
                                    const FVElementGeometry& fvGeometry,
                                    const ElementVolumeVariables&  elemVolVars,
                                    const SubControlVolumeFace& scvf,
                                    const int phaseIdx,
                                    const ElementFluxVariablesCache& elemFluxVarsCache)
    {
        // obtain this scvf's cache
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
 
        ComponentFluxVector componentFlux(0.0);
        for (int compIdx = 0; compIdx < numComponents; compIdx++)
        {
            if(compIdx == FluidSystem::getMainComponent(phaseIdx))
                continue;
 
            // get the scaling factor for the effective diffusive fluxes
            const auto effFactor = computeEffectivityFactor(elemVolVars, scvf, phaseIdx);
 
            // if factor is zero, the flux will end up zero anyway
            if (effFactor == 0.0)
                continue;
 
            // calculate the density at the interface
            const auto rho = interpolateDensity(elemVolVars, scvf, phaseIdx);
 
            // compute the flux
            if (fluxVarsCache.usesSecondaryIv())
                componentFlux[compIdx] = rho*effFactor*computeVolumeFlux(problem,
                                                                         fluxVarsCache,
                                                                         fluxVarsCache.diffusionSecondaryDataHandle(),
                                                                         phaseIdx, compIdx);
            else
                componentFlux[compIdx] = rho*effFactor*computeVolumeFlux(problem,
                                                                         fluxVarsCache,
                                                                         fluxVarsCache.diffusionPrimaryDataHandle(),
                                                                         phaseIdx, compIdx);
        }
 
        // accumulate the phase component flux
        for(int compIdx = 0; compIdx < numComponents; compIdx++)
            if(compIdx != FluidSystem::getMainComponent(phaseIdx) && BalanceEqOpts::mainComponentIsBalanced(phaseIdx) && !FluidSystem::isTracerFluidSystem())
                componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx];
 
        return componentFlux;
    }
 
private:
    template< class Problem, class FluxVarsCache, class DataHandle >
    static Scalar computeVolumeFlux(const Problem& problem,
                                    const FluxVarsCache& cache,
                                    const DataHandle& dataHandle,
                                    int phaseIdx, int compIdx)
    {
        dataHandle.setPhaseIndex(phaseIdx);
        dataHandle.setComponentIndex(compIdx);
 
        const bool switchSign = cache.diffusionSwitchFluxSign(phaseIdx, compIdx);
 
        const auto localFaceIdx = cache.ivLocalFaceIndex();
        const auto idxInOutside = cache.indexInOutsideFaces();
        const auto& xj = dataHandle.uj();
        const auto& tij = dim == dimWorld ? dataHandle.T()[localFaceIdx]
                                          : (!switchSign ? dataHandle.T()[localFaceIdx]
                                                         : dataHandle.tijOutside()[localFaceIdx][idxInOutside]);
        Scalar scvfFlux = tij*xj;
 
        // switch the sign if necessary
        if (switchSign)
            scvfFlux *= -1.0;
 
        return scvfFlux;
    }
 
    static Scalar interpolateDensity(const ElementVolumeVariables& elemVolVars,
                                     const SubControlVolumeFace& scvf,
                                     const unsigned int phaseIdx)
    {
        // use arithmetic mean of the densities around the scvf
        if (!scvf.boundary())
        {
            const Scalar rhoInside = massOrMolarDensity(elemVolVars[scvf.insideScvIdx()], referenceSystem, phaseIdx);
 
            Scalar rho = rhoInside;
            for (const auto outsideIdx : scvf.outsideScvIndices())
            {
                const Scalar rhoOutside = massOrMolarDensity(elemVolVars[outsideIdx], referenceSystem, phaseIdx);
                rho += rhoOutside;
            }
            return rho/(scvf.outsideScvIndices().size()+1);
        }
        else
            return massOrMolarDensity(elemVolVars[scvf.outsideScvIdx()], referenceSystem, phaseIdx);
    }
 
    static Scalar computeEffectivityFactor(const ElementVolumeVariables& elemVolVars,
                                           const SubControlVolumeFace& scvf,
                                           const unsigned int phaseIdx)
    {
        using EffDiffModel = GetPropType<TypeTag, Properties::EffectiveDiffusivityModel>;
 
        // use the harmonic mean between inside and outside
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
        const auto factor = EffDiffModel::effectiveDiffusivity(insideVolVars.porosity(),
                                                               insideVolVars.saturation(phaseIdx),
                                                               /*Diffusion coefficient*/ 1.0);
 
        if (!scvf.boundary())
        {
            // interpret outside factor as arithmetic mean
            Scalar outsideFactor = 0.0;
            for (const auto outsideIdx : scvf.outsideScvIndices())
            {
                const auto& outsideVolVars = elemVolVars[outsideIdx];
                outsideFactor += EffDiffModel::effectiveDiffusivity(outsideVolVars.porosity(),
                                                                    outsideVolVars.saturation(phaseIdx),
                                                                    /*Diffusion coefficient*/ 1.0);
            }
            outsideFactor /= scvf.outsideScvIndices().size();
 
            // use the harmonic mean of the two
            return harmonicMean(factor, outsideFactor);
        }
 
        return factor;
    }
};
 
} // end namespace
 
#endif