Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <array>
7 : #include <cstddef>
8 : #include <memory>
9 : #include <optional>
10 : #include <pup.h>
11 : #include <string>
12 : #include <type_traits>
13 :
14 : #include "DataStructures/DataBox/Prefixes.hpp"
15 : #include "DataStructures/DataVector.hpp"
16 : #include "DataStructures/Tensor/Tensor.hpp"
17 : #include "DataStructures/Variables.hpp"
18 : #include "Evolution/BoundaryConditions/Type.hpp"
19 : #include "Evolution/Systems/GeneralizedHarmonic/BoundaryConditions/BoundaryCondition.hpp"
20 : #include "Evolution/Systems/GeneralizedHarmonic/Tags.hpp"
21 : #include "Options/Options.hpp"
22 : #include "Options/String.hpp"
23 : #include "PointwiseFunctions/AnalyticData/Tags.hpp"
24 : #include "PointwiseFunctions/AnalyticSolutions/AnalyticSolution.hpp"
25 : #include "PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic/ConstraintDampingTags.hpp"
26 : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
27 : #include "Utilities/Gsl.hpp"
28 : #include "Utilities/Serialization/CharmPupable.hpp"
29 : #include "Utilities/TMPL.hpp"
30 :
31 : /// \cond
32 : namespace domain::Tags {
33 : template <size_t Dim, typename Frame>
34 : struct Coordinates;
35 : } // namespace domain::Tags
36 : /// \endcond
37 :
38 1 : namespace gh::BoundaryConditions::detail {
39 : enum class ConstraintPreservingBjorhusType {
40 : ConstraintPreserving,
41 : ConstraintPreservingPhysical
42 : };
43 :
44 : ConstraintPreservingBjorhusType
45 : convert_constraint_preserving_bjorhus_type_from_yaml(
46 : const Options::Option& options);
47 : } // namespace gh::BoundaryConditions::detail
48 :
49 : namespace gh::BoundaryConditions {
50 : /*!
51 : * \brief Sets constraint preserving boundary conditions using the Bjorhus
52 : * method.
53 : *
54 : * \details Boundary conditions for the generalized harmonic evolution system
55 : * can be divided in to three parts, constraint-preserving, physical and gauge
56 : * boundary conditions.
57 : *
58 : * The generalized harmonic (GH) evolution system is a first-order reduction of
59 : * Einstein equations brought about by the imposition of GH gauge. This
60 : * introduces constraints on the free (evolved) variables in addition to the
61 : * standard Hamiltonian and momentum constraints. The constraint-preserving
62 : * portion of the boundary conditions is designed to prevent the influx of
63 : * constraint violations from external faces of the evolution domain, by damping
64 : * them away on a controlled and short time-scale. These conditions are imposed
65 : * as corrections to the characteristic projections of the right-hand-sides of
66 : * the GH evolution equations (i.e. using Bjorhus' method \cite Bjorhus1995),
67 : * as written down in Eq. (63) - (65) of \cite Lindblom2005qh . In addition to
68 : * these equations, the fourth projection is simply frozen in the unlikely case
69 : * its coordinate speed becomes negative, i.e. \f$d_t u^{\hat{1}+}{}_{ab}=0\f$
70 : * (in the notation of \cite Lindblom2005qh). The gauge degrees
71 : * of freedom are controlled by imposing a Sommerfeld-type condition (\f$L=0\f$
72 : * member of the hierarchy derived in \cite BaylissTurkel) that allow gauge
73 : * perturbations to pass through the boundary without strong reflections. These
74 : * assume a spherical outer boundary, and can be written down as in Eq. (25) of
75 : * \cite Rinne2007ui . Finally, the physical boundary conditions control the
76 : * influx of inward propagating gravitational-wave solutions from the external
77 : * boundaries. These are derived by considering the evolution system of the Weyl
78 : * curvature tensor, and controlling the inward propagating characteristics of
79 : * the system that are proportional to the Newman-Penrose curvature spinor
80 : * components \f$\Psi_4\f$ and \f$\Psi_0\f$. Here we use Eq. (68) of
81 : * \cite Lindblom2005qh to disallow any incoming waves. It is to be noted that
82 : * all the above conditions are also imposed on characteristic modes with speeds
83 : * exactly zero.
84 : *
85 : * This class provides two choices of combinations of the above corrections:
86 : * - `ConstraintPreserving` : this imposes the constraint-preserving and
87 : * gauge-controlling corrections;
88 : * - `ConstraintPreservingPhysical` : this additionally restricts the influx of
89 : * any physical gravitational waves from the outer boundary, in addition to
90 : * preventing the influx of constraint violations and gauge perturbations.
91 : *
92 : * We refer to `Bjorhus::constraint_preserving_corrections_dt_v_psi()`,
93 : * `Bjorhus::constraint_preserving_corrections_dt_v_zero()`,
94 : * `Bjorhus::constraint_preserving_gauge_corrections_dt_v_minus()`, and
95 : * `Bjorhus::constraint_preserving_gauge_physical_corrections_dt_v_minus()`
96 : * for the further details on implementation.
97 : *
98 : * \note These boundary conditions assume a spherical outer boundary. Also, we
99 : * do not yet have an option to inject incoming gravitational waves at the outer
100 : * boundary.
101 : */
102 : template <size_t Dim>
103 1 : class ConstraintPreservingBjorhus final : public BoundaryCondition<Dim> {
104 : public:
105 0 : struct TypeOptionTag {
106 0 : using type = detail::ConstraintPreservingBjorhusType;
107 0 : static std::string name() { return "Type"; }
108 0 : static constexpr Options::String help{
109 : "Whether to impose ConstraintPreserving, with or without physical "
110 : "terms for VMinus."};
111 : };
112 :
113 0 : using options = tmpl::list<TypeOptionTag>;
114 0 : static constexpr Options::String help{
115 : "ConstraintPreservingBjorhus boundary conditions setting the value of the"
116 : "time derivatives of the spacetime metric, Phi and Pi to expressions that"
117 : "prevent the influx of constraint violations and reflections."};
118 0 : static std::string name() { return "ConstraintPreservingBjorhus"; }
119 :
120 0 : explicit ConstraintPreservingBjorhus(
121 : detail::ConstraintPreservingBjorhusType type);
122 :
123 0 : ConstraintPreservingBjorhus() = default;
124 : /// \cond
125 : ConstraintPreservingBjorhus(ConstraintPreservingBjorhus&&) = default;
126 : ConstraintPreservingBjorhus& operator=(ConstraintPreservingBjorhus&&) =
127 : default;
128 : ConstraintPreservingBjorhus(const ConstraintPreservingBjorhus&) = default;
129 : ConstraintPreservingBjorhus& operator=(const ConstraintPreservingBjorhus&) =
130 : default;
131 : /// \endcond
132 0 : ~ConstraintPreservingBjorhus() override = default;
133 :
134 0 : explicit ConstraintPreservingBjorhus(CkMigrateMessage* msg);
135 :
136 0 : WRAPPED_PUPable_decl_base_template(
137 : domain::BoundaryConditions::BoundaryCondition,
138 : ConstraintPreservingBjorhus);
139 :
140 0 : auto get_clone() const -> std::unique_ptr<
141 : domain::BoundaryConditions::BoundaryCondition> override;
142 :
143 0 : static constexpr evolution::BoundaryConditions::Type bc_type =
144 : evolution::BoundaryConditions::Type::TimeDerivative;
145 :
146 0 : void pup(PUP::er& p) override;
147 :
148 0 : using dg_interior_evolved_variables_tags =
149 : tmpl::list<gr::Tags::SpacetimeMetric<DataVector, Dim>,
150 : Tags::Pi<DataVector, Dim>, Tags::Phi<DataVector, Dim>>;
151 0 : using dg_interior_temporary_tags =
152 : tmpl::list<domain::Tags::Coordinates<Dim, Frame::Inertial>,
153 : Tags::ConstraintGamma1, Tags::ConstraintGamma2,
154 : gr::Tags::Lapse<DataVector>, gr::Tags::Shift<DataVector, Dim>,
155 : gr::Tags::InverseSpacetimeMetric<DataVector, Dim>,
156 : gr::Tags::SpacetimeNormalVector<DataVector, Dim>,
157 : Tags::ThreeIndexConstraint<DataVector, Dim>,
158 : Tags::GaugeH<DataVector, Dim>,
159 : Tags::SpacetimeDerivGaugeH<DataVector, Dim>>;
160 0 : using dg_interior_dt_vars_tags =
161 : tmpl::list<::Tags::dt<gr::Tags::SpacetimeMetric<DataVector, Dim>>,
162 : ::Tags::dt<Tags::Pi<DataVector, Dim>>,
163 : ::Tags::dt<Tags::Phi<DataVector, Dim>>>;
164 0 : using dg_interior_deriv_vars_tags =
165 : tmpl::list<::Tags::deriv<gr::Tags::SpacetimeMetric<DataVector, Dim>,
166 : tmpl::size_t<Dim>, Frame::Inertial>,
167 : ::Tags::deriv<Tags::Pi<DataVector, Dim>, tmpl::size_t<Dim>,
168 : Frame::Inertial>,
169 : ::Tags::deriv<Tags::Phi<DataVector, Dim>, tmpl::size_t<Dim>,
170 : Frame::Inertial>>;
171 0 : using dg_gridless_tags = tmpl::list<>;
172 :
173 0 : std::optional<std::string> dg_time_derivative(
174 : gsl::not_null<tnsr::aa<DataVector, Dim, Frame::Inertial>*>
175 : dt_spacetime_metric_correction,
176 : gsl::not_null<tnsr::aa<DataVector, Dim, Frame::Inertial>*>
177 : dt_pi_correction,
178 : gsl::not_null<tnsr::iaa<DataVector, Dim, Frame::Inertial>*>
179 : dt_phi_correction,
180 :
181 : const std::optional<tnsr::I<DataVector, Dim, Frame::Inertial>>&
182 : face_mesh_velocity,
183 : const tnsr::i<DataVector, Dim, Frame::Inertial>& normal_covector,
184 : const tnsr::I<DataVector, Dim, Frame::Inertial>& /*normal_vector*/,
185 : // c.f. dg_interior_evolved_variables_tags
186 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& spacetime_metric,
187 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& pi,
188 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& phi,
189 : // c.f. dg_interior_temporary_tags
190 : const tnsr::I<DataVector, Dim, Frame::Inertial>& coords,
191 : const Scalar<DataVector>& gamma1, const Scalar<DataVector>& gamma2,
192 : const Scalar<DataVector>& lapse,
193 : const tnsr::I<DataVector, Dim, Frame::Inertial>& shift,
194 : const tnsr::AA<DataVector, Dim, Frame::Inertial>&
195 : inverse_spacetime_metric,
196 : const tnsr::A<DataVector, Dim, Frame::Inertial>&
197 : spacetime_unit_normal_vector,
198 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& three_index_constraint,
199 : const tnsr::a<DataVector, Dim, Frame::Inertial>& gauge_source,
200 : const tnsr::ab<DataVector, Dim, Frame::Inertial>&
201 : spacetime_deriv_gauge_source,
202 : // c.f. dg_interior_dt_vars_tags
203 : const tnsr::aa<DataVector, Dim, Frame::Inertial>&
204 : logical_dt_spacetime_metric,
205 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& logical_dt_pi,
206 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& logical_dt_phi,
207 : // c.f. dg_interior_deriv_vars_tags
208 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& d_spacetime_metric,
209 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& d_pi,
210 : const tnsr::ijaa<DataVector, Dim, Frame::Inertial>& d_phi) const;
211 :
212 : private:
213 0 : void compute_intermediate_vars(
214 : gsl::not_null<tnsr::I<DataVector, Dim, Frame::Inertial>*>
215 : unit_interface_normal_vector,
216 : gsl::not_null<tnsr::iaa<DataVector, Dim, Frame::Inertial>*>
217 : four_index_constraint,
218 : gsl::not_null<tnsr::II<DataVector, Dim, Frame::Inertial>*>
219 : inverse_spatial_metric,
220 : gsl::not_null<tnsr::ii<DataVector, Dim, Frame::Inertial>*>
221 : extrinsic_curvature,
222 : gsl::not_null<tnsr::a<DataVector, Dim, Frame::Inertial>*>
223 : incoming_null_one_form,
224 : gsl::not_null<tnsr::a<DataVector, Dim, Frame::Inertial>*>
225 : outgoing_null_one_form,
226 : gsl::not_null<tnsr::A<DataVector, Dim, Frame::Inertial>*>
227 : incoming_null_vector,
228 : gsl::not_null<tnsr::A<DataVector, Dim, Frame::Inertial>*>
229 : outgoing_null_vector,
230 : gsl::not_null<tnsr::aa<DataVector, Dim, Frame::Inertial>*> projection_ab,
231 : gsl::not_null<tnsr::Ab<DataVector, Dim, Frame::Inertial>*> projection_Ab,
232 : gsl::not_null<tnsr::AA<DataVector, Dim, Frame::Inertial>*> projection_AB,
233 : gsl::not_null<tnsr::aa<DataVector, Dim, Frame::Inertial>*>
234 : char_projected_rhs_dt_v_psi,
235 : gsl::not_null<tnsr::iaa<DataVector, Dim, Frame::Inertial>*>
236 : char_projected_rhs_dt_v_zero,
237 : gsl::not_null<tnsr::aa<DataVector, Dim, Frame::Inertial>*>
238 : char_projected_rhs_dt_v_plus,
239 : gsl::not_null<tnsr::aa<DataVector, Dim, Frame::Inertial>*>
240 : char_projected_rhs_dt_v_minus,
241 : gsl::not_null<tnsr::a<DataVector, Dim, Frame::Inertial>*>
242 : constraint_char_zero_plus,
243 : gsl::not_null<tnsr::a<DataVector, Dim, Frame::Inertial>*>
244 : constraint_char_zero_minus,
245 : gsl::not_null<std::array<DataVector, 4>*> char_speeds,
246 :
247 : const std::optional<tnsr::I<DataVector, Dim, Frame::Inertial>>&
248 : face_mesh_velocity,
249 : const tnsr::i<DataVector, Dim, Frame::Inertial>& normal_covector,
250 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& pi,
251 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& phi,
252 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& spacetime_metric,
253 : const tnsr::I<DataVector, Dim, Frame::Inertial>& coords,
254 : const Scalar<DataVector>& gamma1, const Scalar<DataVector>& gamma2,
255 : const Scalar<DataVector>& lapse,
256 : const tnsr::I<DataVector, Dim, Frame::Inertial>& shift,
257 : const tnsr::AA<DataVector, Dim, Frame::Inertial>&
258 : inverse_spacetime_metric,
259 : const tnsr::A<DataVector, Dim, Frame::Inertial>&
260 : spacetime_unit_normal_vector,
261 : const tnsr::a<DataVector, Dim, Frame::Inertial>&
262 : spacetime_unit_normal_one_form,
263 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& three_index_constraint,
264 : const tnsr::a<DataVector, Dim, Frame::Inertial>& gauge_source,
265 : const tnsr::ab<DataVector, Dim, Frame::Inertial>&
266 : spacetime_deriv_gauge_source,
267 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& dt_pi,
268 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& dt_phi,
269 : const tnsr::aa<DataVector, Dim, Frame::Inertial>& dt_spacetime_metric,
270 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& d_pi,
271 : const tnsr::ijaa<DataVector, Dim, Frame::Inertial>& d_phi,
272 : const tnsr::iaa<DataVector, Dim, Frame::Inertial>& d_spacetime_metric)
273 : const;
274 :
275 0 : detail::ConstraintPreservingBjorhusType type_{
276 : detail::ConstraintPreservingBjorhusType::ConstraintPreservingPhysical};
277 : };
278 : } // namespace gh::BoundaryConditions
279 :
280 : template <>
281 : struct Options::create_from_yaml<
282 : gh::BoundaryConditions::detail::ConstraintPreservingBjorhusType> {
283 : template <typename Metavariables>
284 : static
285 : typename gh::BoundaryConditions::detail::ConstraintPreservingBjorhusType
286 : create(const Options::Option& options) {
287 : return gh::BoundaryConditions::detail::
288 : convert_constraint_preserving_bjorhus_type_from_yaml(options);
289 : }
290 : };
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