flux/upwindscheme.hh

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#ifndef DUMUX_DISCRETIZATION_UPWINDSCHEME_HH
#define DUMUX_DISCRETIZATION_UPWINDSCHEME_HH
 
#include <dumux/common/parameters.hh>
#include <dumux/discretization/method.hh>
 
namespace Dumux {

template<class GridGeometry, DiscretizationMethod discMethod>
class UpwindSchemeImpl;

template<class GridGeometry>
using UpwindScheme = UpwindSchemeImpl<GridGeometry, GridGeometry::discMethod>;

template<class GridGeometry>
class UpwindSchemeImpl<GridGeometry, DiscretizationMethod::box>
{
public:
    // applies a simple upwind scheme to the precalculated advective flux
    template<class FluxVariables, class UpwindTermFunction, class Scalar>
    static Scalar apply(const FluxVariables& fluxVars,
                        const UpwindTermFunction& upwindTerm,
                        Scalar flux, int phaseIdx)
    {
        // TODO: pass this from outside?
        static const Scalar upwindWeight = getParam<Scalar>("Flux.UpwindWeight");
 
        const auto& elemVolVars = fluxVars.elemVolVars();
        const auto& scvf = fluxVars.scvFace();
        const auto& insideScv = fluxVars.fvGeometry().scv(scvf.insideScvIdx());
        const auto& outsideScv = fluxVars.fvGeometry().scv(scvf.outsideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& outsideVolVars = elemVolVars[outsideScv];
 
        if (std::signbit(flux)) // if sign of flux is negative
            return flux*(upwindWeight*upwindTerm(outsideVolVars)
                         + (1.0 - upwindWeight)*upwindTerm(insideVolVars));
        else
            return flux*(upwindWeight*upwindTerm(insideVolVars)
                         + (1.0 - upwindWeight)*upwindTerm(outsideVolVars));
    }
};

template<class GridGeometry>
class UpwindSchemeImpl<GridGeometry, DiscretizationMethod::cctpfa>
{
    using GridView = typename GridGeometry::GridView;
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
 
public:
    // For surface and network grids (dim < dimWorld) we have to do a special upwind scheme
    template<class FluxVariables, class UpwindTermFunction, class Scalar, int d = dim, int dw = dimWorld>
    static typename std::enable_if<(d < dw), Scalar>::type
    apply(const FluxVariables& fluxVars,
          const UpwindTermFunction& upwindTerm,
          Scalar flux, int phaseIdx)
    {
        static const Scalar upwindWeight = getParam<Scalar>("Flux.UpwindWeight");
 
        // the volume variables of the inside sub-control volume
        const auto& scvf = fluxVars.scvFace();
        const auto& elemVolVars = fluxVars.elemVolVars();
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
 
        // check if this is a branching point
        if (scvf.numOutsideScvs() > 1)
        {
            // more complicated upwind scheme
            // we compute a flux-weighted average of all inflowing branches
            Scalar branchingPointUpwindTerm = 0.0;
            Scalar sumUpwindFluxes = 0.0;
 
            // if the inside flux is positive (outflow) do fully upwind and return flux
            if (!std::signbit(flux))
                return upwindTerm(insideVolVars)*flux;
            else
                sumUpwindFluxes += flux;
 
            for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
            {
                // compute the outside flux
                const auto& fvGeometry = fluxVars.fvGeometry();
                const auto outsideScvIdx = scvf.outsideScvIdx(i);
                const auto outsideElement = fvGeometry.gridGeometry().element(outsideScvIdx);
                const auto& flippedScvf = fvGeometry.flipScvf(scvf.index(), i);
 
                using AdvectionType = typename FluxVariables::AdvectionType;
                const auto outsideFlux = AdvectionType::flux(fluxVars.problem(),
                                                             outsideElement,
                                                             fvGeometry,
                                                             elemVolVars,
                                                             flippedScvf,
                                                             phaseIdx,
                                                             fluxVars.elemFluxVarsCache());
 
                if (!std::signbit(outsideFlux))
                    branchingPointUpwindTerm += upwindTerm(elemVolVars[outsideScvIdx])*outsideFlux;
                else
                    sumUpwindFluxes += outsideFlux;
            }
 
            // the flux might be zero
            if (sumUpwindFluxes != 0.0)
                branchingPointUpwindTerm /= -sumUpwindFluxes;
            else
                branchingPointUpwindTerm = 0.0;
 
            // upwind scheme (always do fully upwind at branching points)
            // a weighting here would lead to an error since the derivation is based on a fully upwind scheme
            // TODO How to implement a weight of e.g. 0.5
            if (std::signbit(flux))
                return flux*branchingPointUpwindTerm;
            else
                return flux*upwindTerm(insideVolVars);
        }
        // non-branching points and boundaries
        else
        {
            // upwind scheme
            const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
            if (std::signbit(flux))
                return flux*(upwindWeight*upwindTerm(outsideVolVars)
                             + (1.0 - upwindWeight)*upwindTerm(insideVolVars));
            else
                return flux*(upwindWeight*upwindTerm(insideVolVars)
                             + (1.0 - upwindWeight)*upwindTerm(outsideVolVars));
        }
    }
 
    // For grids with dim == dimWorld we use a simple upwinding scheme
    template<class FluxVariables, class UpwindTermFunction, class Scalar, int d = dim, int dw = dimWorld>
    static typename std::enable_if<(d == dw), Scalar>::type
    apply(const FluxVariables& fluxVars,
          const UpwindTermFunction& upwindTerm,
          Scalar flux, int phaseIdx)
    {
        static const Scalar upwindWeight = getParam<Scalar>("Flux.UpwindWeight");
 
        const auto& scvf = fluxVars.scvFace();
        const auto& elemVolVars = fluxVars.elemVolVars();
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
        if (std::signbit(flux)) // if sign of flux is negative
            return flux*(upwindWeight*upwindTerm(outsideVolVars)
                         + (1.0 - upwindWeight)*upwindTerm(insideVolVars));
        else
            return flux*(upwindWeight*upwindTerm(insideVolVars)
                         + (1.0 - upwindWeight)*upwindTerm(outsideVolVars));
    }
};

template<class GridGeometry>
class UpwindSchemeImpl<GridGeometry, DiscretizationMethod::ccmpfa>
: public UpwindSchemeImpl<GridGeometry, DiscretizationMethod::cctpfa> {};
 
} // end namespace Dumux
 
#endif