SemidiscretizedDg.hpp

// Distributed under the MIT License.
// See LICENSE.txt for details.
 
#pragma once
 
#include <array>
 
#include "DataStructures/Tensor/Tensor.hpp"
#include "Evolution/Systems/ScalarWave/Tags.hpp"  // IWYU pragma: keep
#include "Options/Options.hpp"
#include "PointwiseFunctions/AnalyticSolutions/AnalyticSolution.hpp"
#include "Utilities/TMPL.hpp"
#include "Utilities/TaggedTuple.hpp"
 
/// \cond
class DataVector;
// IWYU pragma: no_forward_declare Tensor
namespace PUP {
class er;
}  // namespace PUP
/// \endcond
 
namespace ScalarWave {
namespace Solutions {
/*!
 * \brief An exact solution to the semidiscretized DG ScalarWave
 * system with an upwind flux
 *
 * This solution takes into account the spatial discretization error,
 * and so should show convergence in time integration accuracy to
 * roundoff at any resolution.
 *
 * \warning This is not really a pointwise function, as the solution
 * depends on the spatial discretization.  It will only work on a
 * periodic domain of length \f$2 \pi\f$ (or an integer multiple) with
 * equally sized linear elements.
 */
class SemidiscretizedDg : public MarkAsAnalyticSolution {
 public:
  using tags = tmpl::list<ScalarWave::Pi, ScalarWave::Phi<1>, ScalarWave::Psi>;
 
  struct Harmonic {
    using type = int;
    static constexpr OptionString help =
        "Number of wave periods across the domain";
  };
 
  struct Amplitudes {
    using type = std::array<double, 4>;
    static constexpr OptionString help =
        "Amplitudes of the independent modes of the harmonic";
  };
 
  using options = tmpl::list<Harmonic, Amplitudes>;
 
  static constexpr OptionString help =
      "A solution of the semidiscretized DG system on linear elements\n"
      "with spatial period 2 pi.";
 
  SemidiscretizedDg(int harmonic,
                    const std::array<double, 4>& amplitudes) noexcept;
 
  SemidiscretizedDg() = default;
 
  /// Retrieve the evolution variables at time `t` and spatial coordinates `x`
  template <typename... Tags>
  tuples::TaggedTuple<Tags...> variables(const tnsr::I<DataVector, 1>& x,
                                         double t,
                                         tmpl::list<Tags...> /*meta*/) const
      noexcept {
    static_assert(
        tmpl2::flat_all_v<tmpl::list_contains_v<tags, Tags>...>,
        "At least one of the requested tags is not supported. The requested "
        "tags are listed as template parameters of the `variables` function.");
    return {get<Tags>(variables(x, t, tmpl::list<Tags>{}))...};
  }
 
  /// \cond
  tuples::TaggedTuple<ScalarWave::Pi> variables(
      const tnsr::I<DataVector, 1>& x, double t,
      tmpl::list<ScalarWave::Pi> /*meta*/) const noexcept;
 
  tuples::TaggedTuple<ScalarWave::Phi<1>> variables(
      const tnsr::I<DataVector, 1>& x, double t,
      tmpl::list<ScalarWave::Phi<1>> /*meta*/) const noexcept;
 
  tuples::TaggedTuple<ScalarWave::Psi> variables(
      const tnsr::I<DataVector, 1>& x, double t,
      tmpl::list<ScalarWave::Psi> /*meta*/) const noexcept;
  /// \endcond
 
  void pup(PUP::er& p) noexcept;  // NOLINT(google-runtime-references)
 
 private:
  int harmonic_;
  std::array<double, 4> amplitudes_;
};
}  // namespace Solutions
}  // namespace ScalarWave