Line data Source code
1 1 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : /// \file
5 : /// Defines WaveEquationSolutions::PlaneWave
6 :
7 : #pragma once
8 :
9 : #include <array>
10 : #include <cstddef>
11 : #include <memory>
12 :
13 : #include "DataStructures/Tensor/TypeAliases.hpp"
14 : #include "Options/String.hpp"
15 : #include "PointwiseFunctions/AnalyticSolutions/AnalyticSolution.hpp"
16 : #include "PointwiseFunctions/InitialDataUtilities/InitialData.hpp"
17 : #include "PointwiseFunctions/MathFunctions/MathFunction.hpp"
18 : #include "Utilities/MakeArray.hpp"
19 : #include "Utilities/Serialization/CharmPupable.hpp"
20 : #include "Utilities/TMPL.hpp"
21 : #include "Utilities/TaggedTuple.hpp"
22 :
23 : /// \cond
24 : class DataVector;
25 : namespace ScalarWave::Tags {
26 : struct Psi;
27 : struct Pi;
28 : template <size_t Dim>
29 : struct Phi;
30 : } // namespace ScalarWave::Tags
31 : namespace Tags {
32 : template <typename Tag>
33 : struct dt;
34 : } // namespace Tags
35 : template <size_t VolumeDim, typename Fr>
36 : class MathFunction;
37 :
38 : namespace PUP {
39 : class er;
40 : } // namespace PUP
41 : /// \endcond
42 :
43 : namespace ScalarWave::Solutions {
44 : /*!
45 : * \brief A plane wave solution to the Euclidean wave equation
46 : *
47 : * The solution is given by \f$\Psi(\vec{x},t) = F(u(\vec{x},t))\f$
48 : * where the profile \f$F\f$ of the plane wave is an arbitrary one-dimensional
49 : * function of \f$u = \vec{k} \cdot (\vec{x} - \vec{x_o}) - \omega t\f$
50 : * with the wave vector \f$\vec{k}\f$, the frequency \f$\omega = ||\vec{k}||\f$
51 : * and initial center of the profile \f$\vec{x_o}\f$.
52 : *
53 : * \tparam Dim the spatial dimension of the solution
54 : */
55 : template <size_t Dim>
56 1 : class PlaneWave : public evolution::initial_data::InitialData,
57 : public MarkAsAnalyticSolution {
58 : public:
59 0 : static constexpr size_t volume_dim = Dim;
60 0 : struct WaveVector {
61 0 : using type = std::array<double, Dim>;
62 0 : static constexpr Options::String help = {
63 : "The direction of propagation of the wave."};
64 : };
65 :
66 0 : struct Center {
67 0 : using type = std::array<double, Dim>;
68 0 : static constexpr Options::String help = {
69 : "The initial center of the profile of the wave."};
70 : };
71 :
72 0 : struct Profile {
73 0 : using type = std::unique_ptr<MathFunction<1, Frame::Inertial>>;
74 0 : static constexpr Options::String help = {"The profile of the wave."};
75 : };
76 :
77 0 : using options = tmpl::list<WaveVector, Center, Profile>;
78 :
79 0 : static constexpr Options::String help = {
80 : "A plane wave solution of the Euclidean wave equation"};
81 0 : using tags =
82 : tmpl::list<Tags::Psi, Tags::Pi, Tags::Phi<3>, ::Tags::dt<Tags::Psi>,
83 : ::Tags::dt<Tags::Pi>, ::Tags::dt<Tags::Phi<Dim>>>;
84 :
85 0 : PlaneWave() = default;
86 0 : PlaneWave(std::array<double, Dim> wave_vector, std::array<double, Dim> center,
87 : std::unique_ptr<MathFunction<1, Frame::Inertial>> profile);
88 0 : PlaneWave(const PlaneWave&);
89 0 : PlaneWave& operator=(const PlaneWave&);
90 0 : PlaneWave(PlaneWave&&) = default;
91 0 : PlaneWave& operator=(PlaneWave&&) = default;
92 0 : ~PlaneWave() override = default;
93 :
94 0 : auto get_clone() const
95 : -> std::unique_ptr<evolution::initial_data::InitialData> override;
96 :
97 : /// \cond
98 : explicit PlaneWave(CkMigrateMessage* msg);
99 : using PUP::able::register_constructor;
100 : WRAPPED_PUPable_decl_template(PlaneWave);
101 : /// \endcond
102 :
103 : /// The value of the scalar field
104 : template <typename T>
105 1 : Scalar<T> psi(const tnsr::I<T, Dim>& x, double t) const;
106 :
107 : /// The time derivative of the scalar field
108 : template <typename T>
109 1 : Scalar<T> dpsi_dt(const tnsr::I<T, Dim>& x, double t) const;
110 :
111 : /// The spatial derivatives of the scalar field
112 : template <typename T>
113 1 : tnsr::i<T, Dim> dpsi_dx(const tnsr::I<T, Dim>& x, double t) const;
114 :
115 : /// The second time derivative of the scalar field
116 : template <typename T>
117 1 : Scalar<T> d2psi_dt2(const tnsr::I<T, Dim>& x, double t) const;
118 :
119 : /// The second mixed derivatives of the scalar field
120 : template <typename T>
121 1 : tnsr::i<T, Dim> d2psi_dtdx(const tnsr::I<T, Dim>& x, double t) const;
122 :
123 : /// The second spatial derivatives of the scalar field
124 : template <typename T>
125 1 : tnsr::ii<T, Dim> d2psi_dxdx(const tnsr::I<T, Dim>& x, double t) const;
126 :
127 : /// Retrieve the evolution variables at time `t` and spatial coordinates `x`
128 1 : tuples::TaggedTuple<Tags::Psi, Tags::Pi, Tags::Phi<Dim>> variables(
129 : const tnsr::I<DataVector, Dim>& x, double t,
130 : tmpl::list<Tags::Psi, Tags::Pi, Tags::Phi<Dim>> /*meta*/) const;
131 :
132 : /// Retrieve the time derivative of the evolution variables at time `t` and
133 : /// spatial coordinates `x`
134 : ///
135 : /// \note This function's expected use case is setting the past time
136 : /// derivative values for Adams-Bashforth-like steppers.
137 : tuples::TaggedTuple<::Tags::dt<Tags::Psi>, ::Tags::dt<Tags::Pi>,
138 : ::Tags::dt<Tags::Phi<Dim>>>
139 1 : variables(const tnsr::I<DataVector, Dim>& x, double t,
140 : tmpl::list<::Tags::dt<Tags::Psi>, ::Tags::dt<Tags::Pi>,
141 : ::Tags::dt<Tags::Phi<Dim>>> /*meta*/) const;
142 :
143 : // NOLINTNEXTLINE(google-runtime-references)
144 0 : void pup(PUP::er& p) override;
145 :
146 : private:
147 : template <size_t LocalDim>
148 : // NOLINTNEXTLINE(readability-redundant-declaration)
149 0 : friend bool operator==(const PlaneWave<LocalDim>& lhs,
150 : const PlaneWave<LocalDim>& rhs);
151 : template <size_t LocalDim>
152 : // NOLINTNEXTLINE(readability-redundant-declaration)
153 0 : friend bool operator!=(const PlaneWave<LocalDim>& lhs,
154 : const PlaneWave<LocalDim>& rhs);
155 :
156 : template <typename T>
157 0 : T u(const tnsr::I<T, Dim>& x, double t) const;
158 :
159 0 : std::array<double, Dim> wave_vector_{};
160 0 : std::array<double, Dim> center_{};
161 0 : std::unique_ptr<MathFunction<1, Frame::Inertial>> profile_;
162 0 : double omega_{};
163 : };
164 : } // namespace ScalarWave::Solutions
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