PDE.cpph

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// This file is part of the ExaHyPE2 project. For conditions of distribution and
// use, please see the copyright notice at www.peano-framework.org
 
template <class T, class Shortcuts, int NumberOfUnknowns>
static inline GPU_CALLABLE_METHOD void applications::exahype2::ShallowWater::flux(
  const T* const NOALIAS                       Q,
  const tarch::la::Vector<DIMENSIONS, double>& x,
  const tarch::la::Vector<DIMENSIONS, double>& h,
  const double                                 t,
  const double                                 dt,
  const int                                    normal,
  T* const NOALIAS                             F
) {
  for (int n = 0; n < NumberOfUnknowns; n++) {
    F[n] = 0.0;
  }
 
  if (Q[Shortcuts::h] <= hThreshold) {
    return;
  }
 
  const auto Vn{Q[Shortcuts::hu + normal] / Q[Shortcuts::h]};
  F[Shortcuts::h]  = Q[Shortcuts::hu + normal];                             // Mass flux
  F[Shortcuts::hu] = Vn * Q[Shortcuts::hu];                                 // Momentum-x flux
  F[Shortcuts::hv] = Vn * Q[Shortcuts::hv];                                 // Momentum-y flux
  //F[Shortcuts::hu + normal] += 0.5 * g * Q[Shortcuts::h] * Q[Shortcuts::h]; // Hydrostatic pressure
}
 
template <class T, class Shortcuts>
static inline GPU_CALLABLE_METHOD double applications::exahype2::ShallowWater::maxEigenvalue(
  const T* const NOALIAS                       Q,
  const tarch::la::Vector<DIMENSIONS, double>& x,
  const tarch::la::Vector<DIMENSIONS, double>& h,
  const double                                 t,
  const double                                 dt,
  const int                                    normal
) {
  if (Q[Shortcuts::h] <= hThreshold) {
    return 0.0;
  }
 
  // Wave speed estimation based on the flux Jacobian
  const auto Vn{Q[Shortcuts::hu + normal] / Q[Shortcuts::h]};
  const auto c{std::sqrt(g * Q[Shortcuts::h])};
  return {std::fmax(std::fabs(Vn + c), std::fabs(Vn - c))};
}
 
template <class T, class Shortcuts, int NumberOfUnknowns>
static inline GPU_CALLABLE_METHOD void applications::exahype2::ShallowWater::nonconservativeProduct(
  const T* const NOALIAS                       Q,
  const T* const NOALIAS                       deltaQ,
  const tarch::la::Vector<DIMENSIONS, double>& x,
  const tarch::la::Vector<DIMENSIONS, double>& h,
  const double                                 t,
  const double                                 dt,
  const int                                    normal,
  T* const NOALIAS                             BTimesDeltaQ
) {
  for (int n = 0; n < NumberOfUnknowns; n++) {
    BTimesDeltaQ[n] = 0.0;
  }
 
  if (Q[Shortcuts::h] <= hThreshold) {
    return;
  }
 
  // Bathymetry/topography-related effects
  BTimesDeltaQ[Shortcuts::hu + normal] = g * Q[Shortcuts::h] * (deltaQ[Shortcuts::h] + deltaQ[Shortcuts::z]);
}