Advection.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
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// furnished to do so, subject to the following conditions:
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// SOFTWARE.
 
#ifndef FUB_EQUATIONS_ADVECTION_HPP
#define FUB_EQUATIONS_ADVECTION_HPP
 
// #include "fub/Equation.hpp"
#include "fub/Direction.hpp"
#include "fub/ExactRiemannSolver.hpp"
#include "fub/State.hpp"
#include "fub/StateArray.hpp"
#include "fub/ext/Eigen.hpp"
 
#include "fub/flux_method/FluxMethod.hpp"
#include "fub/flux_method/GodunovMethod.hpp"
#include "fub/flux_method/MusclHancockMethod.hpp"
 
#include <array>
 
namespace fub {
template <typename Mass> struct AdvectionVariables { Mass mass; };
 
template <typename... Xs> struct StateTraits<AdvectionVariables<Xs...>> {
  static constexpr auto names = std::make_tuple("Mass");
  static constexpr auto pointers_to_member =
      std::make_tuple(&AdvectionVariables<Xs...>::mass);
  
  template <int Rank> using Depths = AdvectionVariables<ScalarDepth>;
};
 
/// \ingroup Equations
/// This class descibes the 2-dimensional advection equation with constant
/// transport velocity.
struct Advection2d {
  using ConservativeDepths = AdvectionVariables<ScalarDepth>;
  using CompleteDepths = ConservativeDepths;
 
  using Complete = ::fub::Complete<Advection2d>;
  using Conservative = ::fub::Conservative<Advection2d>;
 
  using CompleteArray = ::fub::CompleteArray<Advection2d>;
  using ConservativeArray = ::fub::ConservativeArray<Advection2d>;
 
  /// Constructs an equation object with velocity `v`.
  Advection2d(const std::array<double, 2>& v) noexcept : velocity{v} {}
 
  /// Returns 2, which is the space dimension for this equation.
  static constexpr int Rank() { return 2; }
 
  /// Computes the linear transport flux in the specified direction.
  ///
  /// \param[out] flux The conservative state which will store the results.
  /// \param[in] state The input state.
  /// \param[in] dir   The split direction of this flux.
  void Flux(Conservative& flux, const Complete& state, Direction dir) const
      noexcept;
 
  /// Computes the linear transport flux in the specified direction (Array
  /// version).
  ///
  /// \param[out] flux The conservative state which will store the results.
  /// \param[in] state The input state.
  /// \param[in] dir   The split direction of this flux.
  void Flux(ConservativeArray& flux, const CompleteArray& state,
            Direction dir) const noexcept;
 
  /// This member variable stores the constant transport velocity.
  std::array<double, 2> velocity;
};
 
template <> class ExactRiemannSolver<Advection2d> {
public:
  using Complete = typename Advection2d::Complete;
  using CompleteArray = typename Advection2d::CompleteArray;
 
  ExactRiemannSolver(const Advection2d& 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, 1> ComputeSignals(const Complete&, const Complete&,
                                       Direction dir);
 
  /// Returns the upwind velocity in the specified direction.
  std::array<Array1d, 1> ComputeSignals(const CompleteArray&,
                                        const CompleteArray&, Direction dir);
 
private:
  Advection2d equation_;
};
 
extern template class FluxMethod<Godunov<Advection2d>>;
extern template class FluxMethod<MusclHancock<Advection2d>>;
 
} // namespace fub
 
#endif