multidomain/facet/box/darcyslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_FACET_COUPLING_DARCYS_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_FACET_COUPLING_DARCYS_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/discretization/method.hh>
#include <dumux/flux/box/darcyslaw.hh>
 
namespace Dumux {

template<class Scalar, class GridGeometry>
class BoxFacetCouplingDarcysLaw
{
    using DefaultBoxDarcysLaw = BoxDarcysLaw<Scalar, GridGeometry>;
 
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using CoordScalar = typename GridView::ctype;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
 
public:
 
    template<class Problem, class ElementVolumeVariables, class ElementFluxVarsCache>
    static Scalar 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 DefaultBoxDarcysLaw::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];
 
        // evaluate user-defined interior boundary types
        const auto bcTypes = problem.interiorBoundaryTypes(element, scvf);
 
        static const bool enableGravity = getParamFromGroup<bool>(problem.paramGroup(), "Problem.EnableGravity");
 
        // on interior Neumann boundaries, evaluate the flux using the facet permeability
        if (bcTypes.hasOnlyNeumann())
        {
            // interpolate pressure/density to scvf integration point
            Scalar p = 0.0;
            Scalar rho = 0.0;
            for (const auto& scv : scvs(fvGeometry))
            {
                const auto& volVars = elemVolVars[scv];
                p += volVars.pressure(phaseIdx)*shapeValues[scv.indexInElement()][0];
                rho += volVars.density(phaseIdx)*shapeValues[scv.indexInElement()][0];
            }
 
            // 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 gradP = scvf.unitOuterNormal();
            gradP *= dim == dimWorld ? 0.5*a : 0.5*sqrt(a);
            gradP /= gradP.two_norm2();
            gradP *= (facetVolVars.pressure(phaseIdx) - p);
            if (enableGravity)
                gradP.axpy(-rho, problem.spatialParams().gravity(scvf.center()));
 
            // apply facet permeability and return the flux
            return -1.0*scvf.area()
                       *insideVolVars.extrusionFactor()
                       *vtmv(scvf.unitOuterNormal(), facetVolVars.permeability(), gradP);
        }
 
        // on interior Dirichlet boundaries use the facet pressure and evaluate flux
        else if (bcTypes.hasOnlyDirichlet())
        {
            // create vector with nodal pressures
            std::vector<Scalar> pressures(element.subEntities(dim));
            for (const auto& scv : scvs(fvGeometry))
                pressures[scv.localDofIndex()] = elemVolVars[scv].pressure(phaseIdx);
 
            // substitute with facet pressures for those scvs touching this facet
            for (const auto& scvfJ : scvfs(fvGeometry))
                if (scvfJ.interiorBoundary() && scvfJ.facetIndexInElement() == scvf.facetIndexInElement())
                    pressures[ fvGeometry.scv(scvfJ.insideScvIdx()).localDofIndex() ]
                             = problem.couplingManager().getLowDimVolVars(element, scvfJ).pressure(phaseIdx);
 
            // evaluate gradP - rho*g at integration point
            Scalar rho(0.0);
            Dune::FieldVector<Scalar, dimWorld> gradP(0.0);
            for (const auto& scv : scvs(fvGeometry))
            {
                rho += elemVolVars[scv].density(phaseIdx)*shapeValues[scv.indexInElement()][0];
                gradP.axpy(pressures[scv.localDofIndex()], fluxVarCache.gradN(scv.indexInElement()));
            }
 
            if (enableGravity)
                gradP.axpy(-rho, problem.spatialParams().gravity(scvf.center()));
 
            // apply matrix permeability and return the flux
            return -1.0*scvf.area()
                       *insideVolVars.extrusionFactor()
                       *vtmv(scvf.unitOuterNormal(), insideVolVars.permeability(), gradP);
        }
 
        // 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)
    {
        DUNE_THROW(Dune::NotImplemented, "transmissibilty computation for BoxFacetCouplingDarcysLaw");
    }
};
 
} // end namespace Dumux
 
#endif