momentum/velocitygradients.hh

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#ifndef DUMUX_NAVIERSTOKES_STAGGERED_VELOCITYGRADIENTS_HH
#define DUMUX_NAVIERSTOKES_STAGGERED_VELOCITYGRADIENTS_HH
 
#include <optional>
#include <dumux/common/exceptions.hh>
#include <dumux/common/parameters.hh>
#include <dune/common/fmatrix.hh>
#include <dumux/common/typetraits/problem.hh>
#include <dumux/discretization/facecentered/staggered/elementboundarytypes.hh>
 
// forward declare
namespace Dune {
 
template<class ct, int dim, template< int > class Ref, class Comm>
class SPGrid;
}
 
namespace Dumux {
 
namespace Detail
{
 
template<class Grid>
struct SupportsPeriodicity : public std::false_type {};
 
template<class ct, int dim, template< int > class Ref, class Comm>
struct SupportsPeriodicity<Dune::SPGrid<ct, dim, Ref, Comm>> : public std::true_type {};
}
 
class StaggeredVelocityGradients
{
public:
 
    template<class FVElementGeometry, class ElemVolVars>
    static auto velocityGradient(const FVElementGeometry& fvGeometry,
                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                 const ElemVolVars& elemVolVars,
                                 bool fullGradient = false)
    {
        const auto& problem = elemVolVars.gridVolVars().problem();
        using BoundaryTypes = typename ProblemTraits<std::decay_t<decltype(problem)>>::BoundaryTypes;
        using ElementBoundaryTypes = FaceCenteredStaggeredElementBoundaryTypes<BoundaryTypes>;
        ElementBoundaryTypes elemBcTypes;
        elemBcTypes.update(problem, fvGeometry.element(), fvGeometry);
        return velocityGradient(fvGeometry, scvf, elemVolVars, elemBcTypes, fullGradient);
    }
 
    template<class FVElementGeometry, class ElemVolVars, class BoundaryTypes>
    static auto velocityGradient(const FVElementGeometry& fvGeometry,
                                 const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                 const ElemVolVars& elemVolVars,
                                 const FaceCenteredStaggeredElementBoundaryTypes<BoundaryTypes>& elemBcTypes,
                                 bool fullGradient = false)
    {
        using Scalar = typename FVElementGeometry::GridGeometry::GlobalCoordinate::value_type;
        static constexpr auto dim = FVElementGeometry::GridGeometry::GlobalCoordinate::dimension;
        Dune::FieldMatrix<Scalar, dim, dim> gradient(0.0);
        const auto& scv = fvGeometry.scv(scvf.insideScvIdx());
 
        if (scvf.isFrontal() && !scvf.boundary())
        {
            gradient[scv.dofAxis()][scv.dofAxis()] = velocityGradII(fvGeometry, scvf, elemVolVars);
 
            if (fullGradient)
            {
                Dune::FieldMatrix<std::size_t, dim, dim> counter(0.0);
 
                for (const auto& otherScvf : scvfs(fvGeometry))
                {
                    if (otherScvf.index() == scvf.index())
                        continue;
 
                    const auto& otherScv = fvGeometry.scv(otherScvf.insideScvIdx());
 
                    if (otherScvf.isFrontal() && !otherScvf.boundary())
                        gradient[otherScv.dofAxis()][otherScv.dofAxis()] = velocityGradII(fvGeometry, otherScvf, elemVolVars);
                    else if (otherScvf.isLateral())
                    {
                        assert(otherScv.dofAxis() != otherScvf.normalAxis());
                        const auto i = otherScv.dofAxis();
                        const auto j = otherScvf.normalAxis();
 
                        if (!fvGeometry.hasBoundaryScvf() || !elemBcTypes[otherScvf.localIndex()].isNeumann(i))
                        {
                            gradient[i][j] += velocityGradIJ(fvGeometry, otherScvf, elemVolVars);
                            ++counter[i][j];
                        }
                        if (!fvGeometry.hasBoundaryScvf() || !otherScv.boundary() ||
                            !elemBcTypes[fvGeometry.frontalScvfOnBoundary(otherScv).localIndex()].isNeumann(j))
                        {
                            gradient[j][i] += velocityGradJI(fvGeometry, otherScvf, elemVolVars);
                             ++counter[j][i];
                        }
                    }
                }
 
                for (int i = 0; i < dim; ++i)
                    for (int j = 0; j < dim; ++j)
                        if (i != j)
                            gradient[i][j] /= counter[i][j];
            }
        }
        else
        {
            if (fullGradient)
                DUNE_THROW(Dune::NotImplemented, "Full gradient for lateral staggered faces not implemented");
 
            gradient[scv.dofAxis()][scvf.normalAxis()] = velocityGradIJ(fvGeometry, scvf, elemVolVars);
            gradient[scvf.normalAxis()][scv.dofAxis()] = velocityGradJI(fvGeometry, scvf, elemVolVars);
        }
 
        return gradient;
    }
 
    template<class FVElementGeometry, class ElemVolVars>
    static auto velocityGradII(const FVElementGeometry& fvGeometry,
                               const typename FVElementGeometry::SubControlVolumeFace& scvf,
                               const ElemVolVars& elemVolVars)
    {
        assert(scvf.isFrontal());
        // The velocities of the dof at interest and the one of the opposite scvf.
        const auto velocitySelf = elemVolVars[scvf.insideScvIdx()].velocity();
        const auto velocityOpposite = elemVolVars[scvf.outsideScvIdx()].velocity();
        const auto distance = (fvGeometry.scv(scvf.outsideScvIdx()).dofPosition() - fvGeometry.scv(scvf.insideScvIdx()).dofPosition()).two_norm();
 
        return (velocityOpposite - velocitySelf) / distance * scvf.directionSign();
    }
 
    template<class FVElementGeometry, class ElemVolVars>
    static auto velocityGradIJ(const FVElementGeometry& fvGeometry,
                               const typename FVElementGeometry::SubControlVolumeFace& scvf,
                               const ElemVolVars& elemVolVars)
    {
        assert(scvf.isLateral());
        const auto innerVelocity = elemVolVars[scvf.insideScvIdx()].velocity();
        const auto outerVelocity = elemVolVars[scvf.outsideScvIdx()].velocity();
        const auto distance = getDistanceIJ_(fvGeometry, scvf);
        return (outerVelocity - innerVelocity) / distance * scvf.directionSign();
    }
 
    template<class FVElementGeometry, class ElemVolVars>
    static auto velocityGradJI(const FVElementGeometry& fvGeometry,
                               const typename FVElementGeometry::SubControlVolumeFace& scvf,
                               const ElemVolVars& elemVolVars)
    {
        assert(scvf.isLateral());
        const auto& orthogonalScvf = fvGeometry.lateralOrthogonalScvf(scvf);
        const auto innerVelocity = elemVolVars[orthogonalScvf.insideScvIdx()].velocity();
        const auto outerVelocity = elemVolVars[orthogonalScvf.outsideScvIdx()].velocity();
        const auto distance = getDistanceJI_(fvGeometry, scvf, orthogonalScvf);
        return (outerVelocity - innerVelocity) / distance * orthogonalScvf.directionSign();
    }
 
private:
 
    template<class FVElementGeometry>
    static auto getDistanceIJ_(const FVElementGeometry& fvGeometry,
                               const typename FVElementGeometry::SubControlVolumeFace& scvf)
    {
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        // The scvf is on a boundary, hence there is no outer DOF.
        // We take the distance to the boundary instead.
        if (scvf.boundary())
            return getDistanceToBoundary_(insideScv, scvf);
 
        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
 
        // The standard case: Our grid does not support periodic boundaries.
        if constexpr (!Detail::SupportsPeriodicity<typename FVElementGeometry::GridGeometry::Grid>())
            return getStandardDistance_(insideScv, outsideScv);
        else
        {
            const auto& gridGeometry = fvGeometry.gridGeometry();
            const auto& orthogonalScvf = fvGeometry.lateralOrthogonalScvf(scvf);
            const auto& orthogonalInsideScv = fvGeometry.scv(orthogonalScvf.insideScvIdx());
 
            // The standard case: Our grid is not periodic or the lateral scvf does not lie on a periodic boundary.
            if (!gridGeometry.isPeriodic() || !gridGeometry.dofOnPeriodicBoundary(orthogonalInsideScv.dofIndex()))
                return getStandardDistance_(insideScv, outsideScv);
 
            // Treating periodic boundaries is more involved:
            // 1. Consider the outside scv within the element adjacent to the other periodic boundary.
            // 2. Iterate over this scv's faces until you find the face parallel to our own scvf.
            //    This face would lie directly next to our own scvf if the grid was not periodic.
            // 3. Calculate the total distance by summing up the distances between the DOFs and the respective integration points
            //    corresponding to the inside and outside scvfs.
            auto periodicFvGeometry = localView(gridGeometry);
            const auto& periodicElement = gridGeometry.element(outsideScv.elementIndex());
            periodicFvGeometry.bindElement(periodicElement);
 
            for (const auto& outsideScvf : scvfs(periodicFvGeometry, outsideScv))
            {
                if (outsideScvf.normalAxis() == scvf.normalAxis() && outsideScvf.directionSign() != scvf.directionSign())
                {
                    const auto insideDistance = (insideScv.dofPosition() - scvf.ipGlobal()).two_norm();
                    const auto outsideDistance = (outsideScv.dofPosition() - outsideScvf.ipGlobal()).two_norm();
                    return insideDistance + outsideDistance;
                }
            }
            DUNE_THROW(Dune::InvalidStateException, "Could not find scvf in periodic element");
        }
    }
 
    template<class FVElementGeometry>
    static auto getDistanceJI_(const FVElementGeometry& fvGeometry,
                               const typename FVElementGeometry::SubControlVolumeFace& scvf,
                               const typename FVElementGeometry::SubControlVolumeFace& orthogonalScvf)
    {
        const auto& orthogonalInsideScv = fvGeometry.scv(orthogonalScvf.insideScvIdx());
 
        // The orthogonal scvf is on a boundary, hence there is no outer DOF.
        // We take the distance to the boundary instead.
        if (orthogonalScvf.boundary())
            return getDistanceToBoundary_(orthogonalInsideScv, orthogonalScvf);
 
        const auto& orthogonalOutsideScv = fvGeometry.scv(orthogonalScvf.outsideScvIdx());
 
        // The standard case: Our grid does not support periodic boundaries.
        if constexpr (!Detail::SupportsPeriodicity<typename FVElementGeometry::GridGeometry::Grid>())
            return getStandardDistance_(orthogonalInsideScv, orthogonalOutsideScv);
        else
        {
            const auto& gridGeometry = fvGeometry.gridGeometry();
            const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
 
            // The standard case: Our grid is not periodic or our own DOF does not lie on a periodic boundary.
            if (!gridGeometry.isPeriodic() || !gridGeometry.dofOnPeriodicBoundary(insideScv.dofIndex()))
                return getStandardDistance_(orthogonalInsideScv, orthogonalOutsideScv);
 
            // Treating periodic boundaries is more involved:
            // 1. Consider the orthogonal outside scv within the element adjacent to the other periodic boundary.
            // 2. Iterate over this scv's faces until you find the orthogonal face parallel to our own orthogonal scvf.
            //    This face would lie directly next to our own orthogonal scvf if the grid was not periodic.
            // 3. Calculate the total distance by summing up the distances between the DOFs and the respective integration points
            //    corresponding to the orthogonal scvfs.
            auto periodicFvGeometry = localView(gridGeometry);
            const auto& periodicElement = gridGeometry.element(orthogonalOutsideScv.elementIndex());
            periodicFvGeometry.bindElement(periodicElement);
 
            for (const auto& outsideOrthogonalScvf : scvfs(periodicFvGeometry, orthogonalOutsideScv))
            {
                if (outsideOrthogonalScvf.normalAxis() == orthogonalScvf.normalAxis() && outsideOrthogonalScvf.directionSign() != orthogonalScvf.directionSign())
                {
                    const auto insideDistance = (orthogonalInsideScv.dofPosition() - orthogonalScvf.ipGlobal()).two_norm();
                    const auto outsideDistance = (orthogonalOutsideScv.dofPosition() - outsideOrthogonalScvf.ipGlobal()).two_norm();
                    return insideDistance + outsideDistance;
                }
            }
            DUNE_THROW(Dune::InvalidStateException, "Could not find scvf in periodic element");
        }
    }
 
    template<class SubControlVolume>
    static auto getStandardDistance_(const SubControlVolume& insideScv,
                                     const SubControlVolume& outsideScv)
    {
        return (insideScv.dofPosition() - outsideScv.dofPosition()).two_norm();
    }
 
    template<class SubControlVolume, class SubControlVolumeFace>
    static auto getDistanceToBoundary_(const SubControlVolume& scv,
                                       const SubControlVolumeFace& scvf)
    {
        return (scv.dofPosition() - scvf.ipGlobal()).two_norm();
    }
};
 
} // end namespace Dumux
 
#endif // DUMUX_NAVIERSTOKES_STAGGERED_VELOCITYGRADIENTS_HH