staggered/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>
 
namespace Dumux {
 
template<class Scalar, class GridGeometry, class BoundaryTypes, class Indices>
class StaggeredVelocityGradients
{
    using FVElementGeometry = typename GridGeometry::LocalView;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
public:
 
    template<class FaceVariables>
    static Scalar velocityGradII(const SubControlVolumeFace& scvf,
                                 const FaceVariables& faceVars)
    {
        // The velocities of the dof at interest and the one of the opposite scvf.
        const Scalar velocitySelf = faceVars.velocitySelf();
        const Scalar velocityOpposite = faceVars.velocityOpposite();
 
        return ((velocityOpposite - velocitySelf) / scvf.selfToOppositeDistance()) * scvf.directionSign();
    }
 
    template<class Problem, class FaceVariables>
    static Scalar velocityGradIJ(const Problem& problem,
                                 const Element& element,
                                 const FVElementGeometry& fvGeometry,
                                 const SubControlVolumeFace& scvf,
                                 const FaceVariables& faceVars,
                                 const std::optional<BoundaryTypes>& currentScvfBoundaryTypes,
                                 const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes,
                                 const std::size_t localSubFaceIdx)
    {
        const auto eIdx = scvf.insideScvIdx();
        const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);
 
        // For the velocityGrad_ij derivative, get the velocities at the current (own) scvf
        // and at the parallel one at the neighboring scvf.
        const Scalar innerParallelVelocity = faceVars.velocitySelf();
 
        const auto outerParallelVelocity = [&]()
        {
            if (!lateralScvf.boundary())
                return faceVars.velocityParallel(localSubFaceIdx, 0);
            else if (lateralFaceBoundaryTypes->isDirichlet(Indices::velocity(scvf.directionIndex())))
            {
                // Sample the value of the Dirichlet BC at the center of the staggered lateral face.
                const auto& lateralBoundaryFacePos = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx);
                const auto lateralBoundaryFace = makeStaggeredBoundaryFace(lateralScvf, lateralBoundaryFacePos);
                return problem.dirichlet(element, lateralBoundaryFace)[Indices::velocity(scvf.directionIndex())];
            }
            else if (lateralFaceBoundaryTypes->isBeaversJoseph(Indices::velocity(scvf.directionIndex())))
            {
                return beaversJosephVelocityAtLateralScvf(problem, element, fvGeometry, scvf,  faceVars,
                                                          currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);
            }
            else
                DUNE_THROW(Dune::InvalidStateException, "Invalid lateral boundary type at " << lateralScvf.center());
        }();
 
        // The velocity gradient already accounts for the orientation
        // of the staggered face's outer normal vector. This also correctly accounts for the reduced
        // distance used in the gradient if the lateral scvf lies on a boundary.
        return (outerParallelVelocity - innerParallelVelocity)
               / scvf.parallelDofsDistance(localSubFaceIdx, 0) * lateralScvf.directionSign();
    }
 
    template<class Problem, class FaceVariables>
    static Scalar velocityGradJI(const Problem& problem,
                                 const Element& element,
                                 const FVElementGeometry& fvGeometry,
                                 const SubControlVolumeFace& scvf,
                                 const FaceVariables& faceVars,
                                 const std::optional<BoundaryTypes>& currentScvfBoundaryTypes,
                                 const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes,
                                 const std::size_t localSubFaceIdx)
    {
        const auto eIdx = scvf.insideScvIdx();
        const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);
 
        // Assume a zero velocity gradient for pressure boundary conditions.
        if (currentScvfBoundaryTypes && currentScvfBoundaryTypes->isDirichlet(Indices::pressureIdx))
            return 0.0;
 
        // For the velocityGrad_ji gradient, get the velocities perpendicular to the velocity at the current scvf.
        // The inner one is located at staggered face within the own element,
        // the outer one at the respective staggered face of the element on the other side of the
        // current scvf.
        const Scalar innerLateralVelocity = faceVars.velocityLateralInside(localSubFaceIdx);
        const Scalar outerLateralVelocity = [&]()
        {
            if (!scvf.boundary())
                return faceVars.velocityLateralOutside(localSubFaceIdx);
            else if (currentScvfBoundaryTypes->isDirichlet(Indices::velocity(lateralScvf.directionIndex())))
            {
                // Sample the value of the Dirichlet BC at the center of the lateral face intersecting with the boundary.
                const auto& lateralBoundaryFacePos = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx);
                const auto lateralBoundaryFace = makeStaggeredBoundaryFace(scvf, lateralBoundaryFacePos);
                return problem.dirichlet(element, lateralBoundaryFace)[Indices::velocity(lateralScvf.directionIndex())];
            }
            else if (currentScvfBoundaryTypes->isBeaversJoseph(Indices::velocity(lateralScvf.directionIndex())))
            {
                return beaversJosephVelocityAtCurrentScvf(problem, element, fvGeometry, scvf,  faceVars,
                                                          currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);
            }
            else
                DUNE_THROW(Dune::InvalidStateException, "Invalid lateral boundary types at " << lateralScvf.center());
        }();
 
        // Calculate the velocity gradient in positive coordinate direction.
        const Scalar lateralDeltaV = scvf.normalInPosCoordDir()
                                    ? (outerLateralVelocity - innerLateralVelocity)
                                    : (innerLateralVelocity - outerLateralVelocity);
 
        return lateralDeltaV / scvf.pairData(localSubFaceIdx).lateralDistance;
    }
 
    template<class Problem, class FaceVariables>
    static Scalar beaversJosephVelocityAtCurrentScvf(const Problem& problem,
                                                     const Element& element,
                                                     const FVElementGeometry& fvGeometry,
                                                     const SubControlVolumeFace& scvf,
                                                     const FaceVariables& faceVars,
                                                     const std::optional<BoundaryTypes>& currentScvfBoundaryTypes,
                                                     const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes,
                                                     const std::size_t localSubFaceIdx)
    {
        const auto eIdx = scvf.insideScvIdx();
        const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);
        const Scalar innerLateralVelocity = faceVars.velocityLateralInside(localSubFaceIdx);
 
        const auto tangentialVelocityGradient = [&]()
        {
            // If the current scvf is on a boundary and if a Dirichlet BC for the pressure or a BJ condition for
            // the slip velocity is set there, assume a tangential velocity gradient of zero along the lateral face
            // (towards the current scvf).
            static const bool unsymmetrizedGradientForBJ = getParamFromGroup<bool>(problem.paramGroup(),
                                                           "FreeFlow.EnableUnsymmetrizedVelocityGradientForBeaversJoseph", false);
 
            if (unsymmetrizedGradientForBJ)
                return 0.0;
 
            if (lateralScvf.boundary())
            {
                if (lateralFaceBoundaryTypes->isDirichlet(Indices::pressureIdx) ||
                    lateralFaceBoundaryTypes->isBeaversJoseph(Indices::velocity(scvf.directionIndex())))
                    return 0.0;
            }
 
            return velocityGradIJ(problem, element, fvGeometry, scvf, faceVars, currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);
        }();
 
        return problem.beaversJosephVelocity(element,
                                             fvGeometry.scv(scvf.insideScvIdx()),
                                             lateralScvf,
                                             scvf, /*on boundary*/
                                             innerLateralVelocity,
                                             tangentialVelocityGradient);
    }
 
    template<class Problem, class FaceVariables>
    static Scalar beaversJosephVelocityAtLateralScvf(const Problem& problem,
                                                     const Element& element,
                                                     const FVElementGeometry& fvGeometry,
                                                     const SubControlVolumeFace& scvf,
                                                     const FaceVariables& faceVars,
                                                     const std::optional<BoundaryTypes>& currentScvfBoundaryTypes,
                                                     const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes,
                                                     const std::size_t localSubFaceIdx)
    {
        const auto eIdx = scvf.insideScvIdx();
        const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);
        const Scalar innerParallelVelocity = faceVars.velocitySelf();
 
        const auto tangentialVelocityGradient = [&]()
        {
            // If the current scvf is on a boundary and if a Dirichlet BC for the pressure or a BJ condition for
            // the slip velocity is set there, assume a tangential velocity gradient of zero along the lateral face
            // (towards the current scvf).
            static const bool unsymmetrizedGradientForBJ = getParamFromGroup<bool>(problem.paramGroup(),
                                                           "FreeFlow.EnableUnsymmetrizedVelocityGradientForBeaversJoseph", false);
 
            if (unsymmetrizedGradientForBJ)
                return 0.0;
 
            if (scvf.boundary())
            {
                if (currentScvfBoundaryTypes->isDirichlet(Indices::pressureIdx) ||
                    currentScvfBoundaryTypes->isBeaversJoseph(Indices::velocity(lateralScvf.directionIndex())))
                    return 0.0;
            }
 
            return velocityGradJI(problem, element, fvGeometry, scvf, faceVars, currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);
        }();
 
        return problem.beaversJosephVelocity(element,
                                             fvGeometry.scv(scvf.insideScvIdx()),
                                             scvf,
                                             lateralScvf, /*on boundary*/
                                             innerParallelVelocity,
                                             tangentialVelocityGradient);
    }
 
private:
 
    static const GlobalPosition& lateralStaggeredFaceCenter_(const SubControlVolumeFace& scvf, const int localSubFaceIdx)
    {
        return scvf.pairData(localSubFaceIdx).lateralStaggeredFaceCenter;
    };
};
 
} // end namespace Dumux
 
#endif