riemannproblem.hh

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#ifndef DUMUX_FLUX_SHALLOW_WATER_RIEMANN_PROBLEM_HH
#define DUMUX_FLUX_SHALLOW_WATER_RIEMANN_PROBLEM_HH
 
#include <dumux/common/parameters.hh>
#include <dumux/flux/shallowwater/fluxlimiterlet.hh>
#include <dumux/flux/shallowwater/exactriemann.hh>
 
namespace Dumux {
namespace ShallowWater {
 
template<class Scalar, class GlobalPosition>
std::array<Scalar,3> riemannProblem(const Scalar waterDepthLeft,
                                    const Scalar waterDepthRight,
                                    Scalar velocityXLeft,
                                    Scalar velocityXRight,
                                    Scalar velocityYLeft,
                                    Scalar velocityYRight,
                                    const Scalar bedSurfaceLeft,
                                    const Scalar bedSurfaceRight,
                                    const Scalar gravity,
                                    const GlobalPosition& nxy)
{
    using std::max;
 
    // hydrostatic reconstrucion after Audusse
    const Scalar dzl = max(0.0, bedSurfaceRight - bedSurfaceLeft);
    const Scalar waterDepthLeftReconstructed = max(0.0, waterDepthLeft - dzl);
    const Scalar dzr = max(0.0, bedSurfaceLeft - bedSurfaceRight);
    const Scalar waterDepthRightReconstructed = max(0.0, waterDepthRight - dzr);
 
    // make rotation of the flux we compute an 1d flux
    Scalar tempFlux = velocityXLeft;
    velocityXLeft =  nxy[0] * tempFlux + nxy[1] * velocityYLeft;
    velocityYLeft = -nxy[1] * tempFlux + nxy[0] * velocityYLeft;
 
    tempFlux = velocityXRight;
    velocityXRight =  nxy[0] * tempFlux + nxy[1] * velocityYRight;
    velocityYRight = -nxy[1] * tempFlux + nxy[0] * velocityYRight;
 
    auto riemannResult = ShallowWater::exactRiemann(waterDepthLeftReconstructed,
                                                    waterDepthRightReconstructed,
                                                    velocityXLeft,
                                                    velocityXRight,
                                                    velocityYLeft,
                                                    velocityYRight,
                                                    gravity);
 
    //redo rotation
    tempFlux = riemannResult.flux[1];
    riemannResult.flux[1] = nxy[0] * tempFlux - nxy[1] * riemannResult.flux[2];
    riemannResult.flux[2] = nxy[1] * tempFlux + nxy[0] * riemannResult.flux[2];
 
    // Add reconstruction flux from Audusse reconstruction
    const Scalar hgzl = 0.5 * (waterDepthLeftReconstructed + waterDepthLeft) * (waterDepthLeftReconstructed - waterDepthLeft);
    const Scalar hdxzl = gravity * nxy[0] * hgzl;
    const Scalar hdyzl = gravity * nxy[1] * hgzl;
 
    /*Right side is computed from the other side otherwise the
      following "non-symetric" fluxes are needed:
 
      Scalar hgzr = 0.5 * (waterDepthRightReconstructed + waterDepthRight) * (waterDepthRightReconstructed - waterDepthRight);
      Scalar hdxzr = gravity * nxy[0] * hgzr;
      Scalar hdyzrhdyzr = gravity * nxy[1] * hgzr;
    */
 
    // compute the mobility of the flux with the fluxlimiter
    static const Scalar upperWaterDepthFluxLimiting = getParam<Scalar>("FluxLimiterLET.UpperWaterDepth", 1e-3);
    static const Scalar lowerWaterDepthFluxLimiting = getParam<Scalar>("FluxLimiterLET.LowerWaterDepth", 1e-5);
    static const bool upwindWaterDepthFluxLimiting = getParam<bool>("FluxLimiterLET.UpwindFluxLimiting", false);
 
    Scalar limitingDepth = (waterDepthLeftReconstructed + waterDepthRightReconstructed) * 0.5;
 
    //Using the upwind water depth from the flux direction can improve stability.
    if (upwindWaterDepthFluxLimiting)
    {
        if (riemannResult.flux[0] < 0)
        {
            limitingDepth = waterDepthRightReconstructed;
        }else
        {
            limitingDepth = waterDepthLeftReconstructed;
        }
    }
 
    const Scalar mobility = ShallowWater::fluxLimiterLET(limitingDepth,
                                                         limitingDepth,
                                                         upperWaterDepthFluxLimiting,
                                                         lowerWaterDepthFluxLimiting);
    std::array<Scalar, 3> localFlux;
    localFlux[0] = riemannResult.flux[0] * mobility;
    localFlux[1] = (riemannResult.flux[1] - hdxzl);
    localFlux[2] = (riemannResult.flux[2] - hdyzl);
 
    return localFlux;
}
 
} // end namespace ShallowWater
} // end namespace Dumux
 
#endif