ShallowWater.hpp

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// Copyright (c) 2019 Maikel Nadolski
//
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// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// furnished to do so, subject to the following conditions:
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// SOFTWARE.
 
#ifndef FUB_EQUATIONS_SHALLOW_WATER_HPP
#define FUB_EQUATIONS_SHALLOW_WATER_HPP
 
#include "fub/Equation.hpp"
#include "fub/ExactRiemannSolver.hpp"
#include "fub/State.hpp"
#include "fub/ext/Eigen.hpp"
 
#include "fub/flux_method/FluxMethod.hpp"
#include "fub/flux_method/GodunovMethod.hpp"
#include "fub/flux_method/HllMethod.hpp"
#include "fub/flux_method/MusclHancockMethod.hpp"
 
#include <array>
 
namespace fub {
template <typename Heigth, typename Momentum> struct ShallowWaterVariables {
  Heigth height;
  Momentum momentum;
};
 
template <typename... Xs> struct StateTraits<ShallowWaterVariables<Xs...>> {
  static constexpr auto names = std::make_tuple("Height", "Momentum");
 
  static constexpr auto pointers_to_member =
      std::make_tuple(&ShallowWaterVariables<Xs...>::height,
                      &ShallowWaterVariables<Xs...>::momentum);
 
  template <int Rank> using Depths = ShallowWaterVariables<ScalarDepth, VectorDepth<Rank>>;
};
 
struct ShallowWater {
  using ConservativeDepths = ShallowWaterVariables<ScalarDepth, VectorDepth<2>>;
  using CompleteDepths = ConservativeDepths;
 
  using Conservative = ::fub::Conservative<ShallowWater>;
  using Complete = ::fub::Complete<ShallowWater>;
 
  using ConservativeArray = ::fub::ConservativeArray<ShallowWater>;
  using CompleteArray = ::fub::CompleteArray<ShallowWater>;
 
  static constexpr int Rank() noexcept { return 2; }
 
  void Flux(Conservative& flux, const Complete& state, Direction dir) const
      noexcept;
 
  void Flux(ConservativeArray& flux, const CompleteArray& state,
            Direction dir) const noexcept;
 
  double gravity_{10.0};
};
 
template <> class ExactRiemannSolver<ShallowWater> {
public:
  using Complete = typename ShallowWater::Complete;
  using CompleteArray = typename ShallowWater::CompleteArray;
 
  ExactRiemannSolver(const ShallowWater& equation) : equation_{equation} {}
 
  /// Returns either left or right, depending on the upwind velocity.
  void SolveRiemannProblem(Complete& state, const Complete& left,
                           const Complete& right, Direction dir);
 
  /// Returns either left or right, depending on the upwind velocity.
  void SolveRiemannProblem(CompleteArray& state, const CompleteArray& left,
                           const CompleteArray& right, Direction dir);
 
  /// Returns the upwind velocity in the specified direction.
  std::array<double, 2> ComputeSignals(const Complete&, const Complete&,
                                       Direction dir);
 
  /// Returns the upwind velocity in the specified direction.
  std::array<Array1d, 2> ComputeSignals(const CompleteArray&,
                                        const CompleteArray&, Direction dir);
 
  Complete ComputeMiddleState(const Complete& left, const Complete& right,
                              Direction dir);
 
private:
  ShallowWater equation_;
};
 
struct ShallowWaterSignalVelocities {
  using Complete = fub::Complete<ShallowWater>;
  using CompleteArray = fub::CompleteArray<ShallowWater>;
 
  std::array<double, 2> operator()(const ShallowWater& equation,
                                   const Complete& left, const Complete& right,
                                   Direction dir);
 
  std::array<Array1d, 2> operator()(const ShallowWater& equation,
                                    const CompleteArray& left,
                                    const CompleteArray& right, Direction dir);
};
 
extern template class FluxMethod<
    Hll<ShallowWater, ShallowWaterSignalVelocities>>;
 
extern template class FluxMethod<Godunov<ShallowWater>>;
 
extern template class FluxMethod<MusclHancock<ShallowWater>>;
 
extern template class FluxMethod<MusclHancock<
    ShallowWater, HllMethod<ShallowWater, ShallowWaterSignalVelocities>>>;
 
} // namespace fub
 
#endif