multidomain/facet/box/fickslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_FACET_COUPLING_FICKS_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_FACET_COUPLING_FICKS_LAW_HH
 
#include <vector>
#include <cmath>
 
#include <dune/common/exceptions.hh>
#include <dune/common/fvector.hh>
#include <dune/common/float_cmp.hh>
 
#include <dumux/common/parameters.hh>
#include <dumux/common/properties.hh>
 
#include <dumux/flux/referencesystemformulation.hh>
#include <dumux/flux/box/fickslaw.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
 
namespace Dumux {

template<class TypeTag, ReferenceSystemFormulation referenceSystem = ReferenceSystemFormulation::massAveraged>
class BoxFacetCouplingFicksLaw
: public FicksLawImplementation<TypeTag, DiscretizationMethod::box, referenceSystem>
{
    using ParentType = FicksLawImplementation<TypeTag, DiscretizationMethod::box, referenceSystem>;
 
    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 Element = typename GridView::template Codim<0>::Entity;
 
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
 
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>;
    static constexpr int numComponents = ModelTraits::numFluidComponents();
 
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>;
 
public:
 
    template<class Problem, class ElementVolumeVariables, class ElementFluxVarsCache>
    static ComponentFluxVector flux(const Problem& problem,
                                    const Element& element,
                                    const FVElementGeometry& fvGeometry,
                                    const ElementVolumeVariables& elemVolVars,
                                    const SubControlVolumeFace& scvf,
                                    const int phaseIdx,
                                    const ElementFluxVarsCache& elemFluxVarCache)
    {
        // if this scvf is not on an interior boundary, use the standard law
        if (!scvf.interiorBoundary())
            return ParentType::flux(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, elemFluxVarCache);
 
        static const Scalar xi = getParamFromGroup<Scalar>(problem.paramGroup(), "FacetCoupling.Xi", 1.0);
        if ( !Dune::FloatCmp::eq(xi, 1.0, 1e-6) )
            DUNE_THROW(Dune::NotImplemented, "Xi != 1.0 cannot be used with the Box-Facet-Coupling scheme");
 
        // get some references for convenience
        const auto& fluxVarCache = elemFluxVarCache[scvf];
        const auto& shapeValues = fluxVarCache.shapeValues();
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
 
        // interpolate density to scvf integration point
        Scalar rho = 0.0;
        for (const auto& scv : scvs(fvGeometry))
            rho += massOrMolarDensity(elemVolVars[scv], referenceSystem, phaseIdx)*shapeValues[scv.indexInElement()][0];
 
        // on interior Neumann boundaries, evaluate the flux using the facet effective diffusion coefficient
        ComponentFluxVector componentFlux(0.0);
        const auto bcTypes = problem.interiorBoundaryTypes(element, scvf);
        if (bcTypes.hasOnlyNeumann())
        {
            // compute tpfa flux from integration point to facet centerline
            const auto& facetVolVars = problem.couplingManager().getLowDimVolVars(element, scvf);
 
            using std::sqrt;
            // If this is a surface grid, use the square root of the facet extrusion factor
            // as an approximate average distance from scvf ip to facet center
            using std::sqrt;
            const auto a = facetVolVars.extrusionFactor();
            auto preGradX = scvf.unitOuterNormal();
            preGradX *= dim == dimWorld ? 0.5*a : 0.5*sqrt(a);
            preGradX /= preGradX.two_norm2();
 
            for (int compIdx = 0; compIdx < numComponents; compIdx++)
            {
                if (compIdx == FluidSystem::getMainComponent(phaseIdx))
                    continue;
 
                // interpolate mole fraction to scvf integration point
                Scalar x = 0.0;
                for (const auto& scv : scvs(fvGeometry))
                    x += massOrMoleFraction(elemVolVars[scv], referenceSystem, phaseIdx, compIdx)*shapeValues[scv.indexInElement()][0];
 
                // compute the diffusive flux by means of a finite difference
                auto gradX = preGradX;
                gradX *= (massOrMoleFraction(facetVolVars, referenceSystem, phaseIdx, compIdx) - x);
 
                componentFlux[compIdx] = -1.0*rho*Extrusion::area(scvf)
                                             *insideVolVars.extrusionFactor()
                                             *vtmv(scvf.unitOuterNormal(),
                                                   facetVolVars.effectiveDiffusionCoefficient(phaseIdx, phaseIdx, compIdx),
                                                   gradX);
 
                if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx) && !FluidSystem::isTracerFluidSystem())
                    componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx];
            }
 
            return componentFlux;
        }
 
        // on interior Dirichlet boundaries use the facet mass/mole fraction and evaluate flux
        else if (bcTypes.hasOnlyDirichlet())
        {
            for (int compIdx = 0; compIdx < numComponents; compIdx++)
            {
                if (compIdx == FluidSystem::getMainComponent(phaseIdx))
                    continue;
 
                // create vector with nodal mole/mass fractions
                std::vector<Scalar> xFractions(element.subEntities(dim));
                for (const auto& scv : scvs(fvGeometry))
                    xFractions[scv.localDofIndex()] = massOrMoleFraction(elemVolVars[scv], referenceSystem, phaseIdx, compIdx);
 
                // substitute with facet mole/mass fractions for those scvs touching this facet
                for (const auto& scvfJ : scvfs(fvGeometry))
                    if (scvfJ.interiorBoundary() && scvfJ.facetIndexInElement() == scvf.facetIndexInElement())
                        xFractions[ fvGeometry.scv(scvfJ.insideScvIdx()).localDofIndex() ]
                                 = massOrMoleFraction(problem.couplingManager().getLowDimVolVars(element, scvfJ), referenceSystem, phaseIdx, compIdx);
 
                // evaluate gradX at integration point
                Dune::FieldVector<Scalar, dimWorld> gradX(0.0);
                for (const auto& scv : scvs(fvGeometry))
                    gradX.axpy(xFractions[scv.localDofIndex()], fluxVarCache.gradN(scv.indexInElement()));
 
                // apply matrix diffusion coefficient and return the flux
                componentFlux[compIdx] = -1.0*rho*Extrusion::area(scvf)
                                             *insideVolVars.extrusionFactor()
                                             *vtmv(scvf.unitOuterNormal(),
                                                   insideVolVars.effectiveDiffusionCoefficient(phaseIdx, phaseIdx, compIdx),
                                                   gradX);
 
                if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx) && !FluidSystem::isTracerFluidSystem())
                    componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx];
            }
 
            return componentFlux;
        }
 
        // mixed boundary types are not supported
        else
            DUNE_THROW(Dune::NotImplemented, "Mixed boundary types are not supported");
    }
 
    // compute transmissibilities ti for analytical jacobians
    template<class Problem, class ElementVolumeVariables, class FluxVarCache>
    static std::vector<Scalar> calculateTransmissibilities(const Problem& problem,
                                                           const Element& element,
                                                           const FVElementGeometry& fvGeometry,
                                                           const ElementVolumeVariables& elemVolVars,
                                                           const SubControlVolumeFace& scvf,
                                                           const FluxVarCache& fluxVarCache,
                                                           unsigned int phaseIdx)
    {
        DUNE_THROW(Dune::NotImplemented, "transmissibilty computation for BoxFacetCouplingFicksLaw");
    }
};
 
} // end namespace Dumux
 
#endif