Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <cstddef>
7 : #include <string>
8 :
9 : #include "DataStructures/DataBox/Tag.hpp"
10 : #include "DataStructures/Tensor/TypeAliases.hpp"
11 : #include "Evolution/Systems/Ccz4/TagsDeclarations.hpp"
12 : #include "Evolution/Tags.hpp"
13 : #include "Options/String.hpp"
14 : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
15 : #include "PointwiseFunctions/GeneralRelativity/Tags/Conformal.hpp"
16 :
17 : namespace Ccz4 {
18 1 : namespace Tags {
19 : /*!
20 : * \brief The conformal factor that rescales the spatial metric
21 : *
22 : * \details If \f$\gamma_{ij}\f$ is the spatial metric, then we define
23 : * \f$\phi = (det(\gamma_{ij}))^{-1/6}\f$.
24 : */
25 : template <typename DataType>
26 1 : struct ConformalFactor : db::SimpleTag {
27 0 : using type = Scalar<DataType>;
28 : };
29 :
30 : /*!
31 : * \brief The square of the conformal factor that rescales the spatial metric
32 : *
33 : * \details If \f$\gamma_{ij}\f$ is the spatial metric, then we define
34 : * \f$\phi^2 = (det(\gamma_{ij}))^{-1/3}\f$.
35 : */
36 : template <typename DataType>
37 1 : struct ConformalFactorSquared : db::SimpleTag {
38 0 : using type = Scalar<DataType>;
39 : };
40 :
41 : /*!
42 : * \brief The conformally scaled spatial metric
43 : *
44 : * \details If \f$\phi\f$ is the conformal factor and \f$\gamma_{ij}\f$ is the
45 : * spatial metric, then we define
46 : * \f$\bar{\gamma}_{ij} = \phi^2 \gamma_{ij}\f$.
47 : */
48 : template <typename DataType, size_t Dim, typename Frame>
49 1 : using ConformalMetric =
50 : gr::Tags::Conformal<gr::Tags::SpatialMetric<DataType, Dim, Frame>, 2>;
51 :
52 : /*!
53 : * \brief The conformally scaled inverse spatial metric
54 : *
55 : * \details If \f$\phi\f$ is the conformal factor and \f$\gamma^{ij}\f$ is the
56 : * inverse spatial metric, then we define
57 : * \f$\bar{\gamma}^{ij} = \phi^{-2} \gamma^{ij}\f$.
58 : */
59 : template <typename DataType, size_t Dim, typename Frame>
60 1 : using InverseConformalMetric =
61 : gr::Tags::Conformal<gr::Tags::InverseSpatialMetric<DataType, Dim, Frame>,
62 : -2>;
63 :
64 : /*!
65 : * \brief The trace-free part of the extrinsic curvature
66 : *
67 : * \details See `Ccz4::a_tilde()` for details.
68 : */
69 : template <typename DataType, size_t Dim, typename Frame>
70 1 : struct ATilde : db::SimpleTag {
71 0 : using type = tnsr::ii<DataType, Dim, Frame>;
72 : };
73 :
74 : /*!
75 : * \brief The trace of the trace-free part of the extrinsic curvature
76 : *
77 : * \details We define:
78 : *
79 : * \f{align}
80 : * tr\tilde{A} &= \tilde{\gamma}^{ij} \tilde{A}_{ij}
81 : * \f}
82 : *
83 : * where \f$\tilde{\gamma}^{ij}\f$ is the inverse conformal spatial metric
84 : * defined by `Ccz4::Tags::InverseConformalMetric` and \f$\tilde{A}_{ij}\f$ is
85 : * the trace-free part of the extrinsic curvature defined by
86 : * `Ccz4::Tags::ATilde`.
87 : */
88 : template <typename DataType>
89 1 : struct TraceATilde : db::SimpleTag {
90 0 : using type = Scalar<DataType>;
91 : };
92 :
93 : /*!
94 : * \brief The natural log of the lapse
95 : */
96 : template <typename DataType>
97 1 : struct LogLapse : db::SimpleTag {
98 0 : using type = Scalar<DataType>;
99 : };
100 :
101 : /*!
102 : * \brief Auxiliary variable which is analytically the spatial derivative of the
103 : * natural log of the lapse
104 : *
105 : * \details If \f$ \alpha \f$ is the lapse, then we define
106 : * \f$A_i = \partial_i ln(\alpha) = \frac{\partial_i \alpha}{\alpha}\f$.
107 : */
108 : template <typename DataType, size_t Dim, typename Frame>
109 1 : struct FieldA : db::SimpleTag {
110 0 : using type = tnsr::i<DataType, Dim, Frame>;
111 : };
112 :
113 : /*!
114 : * \brief Auxiliary variable which is analytically the spatial derivative of the
115 : * shift
116 : */
117 : template <typename DataType, size_t Dim, typename Frame>
118 1 : struct FieldB : db::SimpleTag {
119 0 : using type = tnsr::iJ<DataType, Dim, Frame>;
120 : };
121 :
122 : /*!
123 : * \brief Auxiliary variable which is analytically half the spatial derivative
124 : * of the conformal spatial metric
125 : *
126 : * \details If \f$\bar{\gamma}_{ij}\f$ is the conformal spatial metric, then we
127 : * define
128 : * \f$D_{kij} = \frac{1}{2} \partial_k \bar{\gamma}_{ij}\f$.
129 : */
130 : template <typename DataType, size_t Dim, typename Frame>
131 1 : struct FieldD : db::SimpleTag {
132 0 : using type = tnsr::ijj<DataType, Dim, Frame>;
133 : };
134 :
135 : /*!
136 : * \brief The natural log of the conformal factor
137 : */
138 : template <typename DataType>
139 1 : struct LogConformalFactor : db::SimpleTag {
140 0 : using type = Scalar<DataType>;
141 : };
142 :
143 : /*!
144 : * \brief Auxiliary variable which is analytically the spatial derivative of the
145 : * natural log of the conformal factor
146 : *
147 : * \details If \f$\phi\f$ is the conformal factor, then we define
148 : * \f$P_i = \partial_i ln(\phi) = \frac{\partial_i \phi}{\phi}\f$.
149 : */
150 : template <typename DataType, size_t Dim, typename Frame>
151 1 : struct FieldP : db::SimpleTag {
152 0 : using type = tnsr::i<DataType, Dim, Frame>;
153 : };
154 :
155 : /*!
156 : * \brief Identity which is analytically negative one half the spatial
157 : * derivative of the inverse conformal spatial metric
158 : *
159 : * \details We define:
160 : * \f{align}
161 : * D_k{}^{ij} &=
162 : * \tilde{\gamma}^{in} \tilde{\gamma}^{mj} D_{knm} =
163 : * -\frac{1}{2} \partial_k \tilde{\gamma}^{ij}
164 : * \f}
165 : * where \f$\tilde{\gamma}^{ij}\f$ and \f$D_{ijk}\f$ are the inverse conformal
166 : * spatial metric and the CCZ4 auxiliary variable defined by
167 : * `Ccz4::Tags::FieldD`, respectively.
168 : */
169 : template <typename DataType, size_t Dim, typename Frame>
170 1 : struct FieldDUp : db::SimpleTag {
171 0 : using type = tnsr::iJJ<DataType, Dim, Frame>;
172 : };
173 :
174 : /*!
175 : * \brief The conformal spatial christoffel symbols of the second kind
176 : *
177 : * \details We define:
178 : * \f{align}
179 : * \tilde{\Gamma}^k_{ij} &=
180 : * \tilde{\gamma}^{kl} (D_{ijl} + D_{jil} - D_{lij})
181 : * \f}
182 : * where \f$\tilde{\gamma}^{ij}\f$ and \f$D_{ijk}\f$ are the inverse conformal
183 : * spatial metric and the CCZ4 auxiliary variable defined by
184 : * `Ccz4::Tags::InverseConformalMetric` and `Ccz4::Tags::FieldD`, respectively.
185 : */
186 : template <typename DataType, size_t Dim, typename Frame>
187 1 : struct ConformalChristoffelSecondKind : db::SimpleTag {
188 0 : using type = tnsr::Ijj<DataType, Dim, Frame>;
189 : };
190 :
191 : /*!
192 : * \brief The spatial derivative of the conformal spatial christoffel symbols
193 : * of the second kind
194 : *
195 : * \details We define:
196 : * \f{align}
197 : * \partial_k \tilde{\Gamma}^m{}_{ij} &=
198 : * -2 D_k{}^{ml} (D_{ijl} + D_{jil} - D_{lij}) +
199 : * \tilde{\gamma}^{ml}(\partial_{(k} D_{i)jl} + \partial_{(k} D_{j)il} -
200 : * \partial_{(k} D_{l)ij})
201 : * \f}
202 : * where \f$\tilde{\gamma}^{ij}\f$, \f$D_{ijk}\f$, \f$\partial_l D_{ijk}\f$, and
203 : * \f$D_k{}^{ij}\f$ are the inverse conformal spatial metric defined by
204 : * `Ccz4::Tags::InverseConformalMetric`, the CCZ4 auxiliary variable defined by
205 : * `Ccz4::Tags::FieldD`, its spatial derivative, and the CCZ4 identity defined
206 : * by `Ccz4::Tags::FieldDUp`.
207 : */
208 : template <typename DataType, size_t Dim, typename Frame>
209 1 : struct DerivConformalChristoffelSecondKind : db::SimpleTag {
210 0 : using type = tnsr::iJkk<DataType, Dim, Frame>;
211 : };
212 :
213 : /*!
214 : * \brief The spatial christoffel symbols of the second kind
215 : *
216 : * \details We define:
217 : * \f{align}
218 : * \Gamma^k_{ij} &= \tilde{\Gamma}^k_{ij} -
219 : * \tilde{\gamma}^{kl} (\tilde{\gamma}_{jl} P_i +
220 : * \tilde{\gamma}_{il} P_j -
221 : * \tilde{\gamma}_{ij} P_l)
222 : * \f}
223 : * where \f$\tilde{\gamma}^{ij}\f$, \f$\tilde{\gamma}_{ij}\f$,
224 : * \f$\tilde{\Gamma}^k_{ij}\f$, and \f$P_i\f$ are the conformal spatial metric,
225 : * the inverse conformal spatial metric, the conformal spatial christoffel
226 : * symbols of the second kind, and the CCZ4 auxiliary variable defined by
227 : * `Ccz4::Tags::ConformalMetric`, `Ccz4::Tags::InverseConformalMetric`,
228 : * `Ccz4::Tags::ConformalChristoffelSecondKind`, and `Ccz4::Tags::FieldP`,
229 : * respectively.
230 : */
231 : template <typename DataType, size_t Dim, typename Frame>
232 1 : struct ChristoffelSecondKind : db::SimpleTag {
233 0 : using type = tnsr::Ijj<DataType, Dim, Frame>;
234 : };
235 :
236 : /*!
237 : * \brief The spatial Ricci tensor
238 : *
239 : * \details See `Ccz4::spatial_ricci_tensor()` for details.
240 : */
241 : template <typename DataType, size_t Dim, typename Frame>
242 1 : struct Ricci : db::SimpleTag {
243 0 : using type = tnsr::ii<DataType, Dim, Frame>;
244 : };
245 :
246 : /*!
247 : * \brief The gradient of the gradient of the lapse
248 : *
249 : * \details We define:
250 : * \f{align}
251 : * \nabla_i \nabla_j \alpha &= \alpha A_i A_j -
252 : * \alpha \Gamma^k{}_{ij} A_k + \alpha \partial_{(i} A_{j)}
253 : * \f}
254 : * where \f$\alpha\f$, \f$\Gamma^k{}_{ij}\f$, \f$A_i\f$, and
255 : * \f$\partial_j A_i\f$ are the lapse, spatial christoffel symbols of the second
256 : * kind, the CCZ4 auxiliary variable defined by `Ccz4::Tags::FieldA`, and its
257 : * spatial derivative, respectively.
258 : */
259 : template <typename DataType, size_t Dim, typename Frame>
260 1 : struct GradGradLapse : db::SimpleTag {
261 0 : using type = tnsr::ij<DataType, Dim, Frame>;
262 : };
263 :
264 : /*!
265 : * \brief The divergence of the lapse
266 : *
267 : * \details We define:
268 : * \f{align}
269 : * \nabla^i \nabla_i \alpha &= \phi^2 \tilde{\gamma}^{ij}
270 : * (\nabla_i \nabla_j \alpha)
271 : * \f}
272 : * where \f$\phi\f$, \f$\tilde{\gamma}^{ij}\f$, and
273 : * \f$\nabla_i \nabla_j \alpha\f$ are the conformal factor, inverse conformal
274 : * spatial metric, and the gradient of the gradient of the lapse defined by
275 : * `Ccz4::Tags::ConformalFactor`, `Ccz4::Tags::InverseConformalMetric`, and
276 : * `Ccz4::Tags::GradGradLapse`, respectively.
277 : */
278 : template <typename DataType>
279 1 : struct DivergenceLapse : db::SimpleTag {
280 0 : using type = Scalar<DataType>;
281 : };
282 :
283 : /*!
284 : * \brief The contraction of the conformal spatial Christoffel symbols of the
285 : * second kind
286 : *
287 : * \details See `Ccz4::contracted_conformal_christoffel_second_kind()` for
288 : * details.
289 : */
290 : template <typename DataType, size_t Dim, typename Frame>
291 1 : struct ContractedConformalChristoffelSecondKind : db::SimpleTag {
292 0 : using type = tnsr::I<DataType, Dim, Frame>;
293 : };
294 :
295 : /*!
296 : * \brief The spatial derivative of the contraction of the conformal spatial
297 : * Christoffel symbols of the second kind
298 : *
299 : * \details See `Ccz4::deriv_contracted_conformal_christoffel_second_kind()` for
300 : * details.
301 : */
302 : template <typename DataType, size_t Dim, typename Frame>
303 1 : struct DerivContractedConformalChristoffelSecondKind : db::SimpleTag {
304 0 : using type = tnsr::iJ<DataType, Dim, Frame>;
305 : };
306 :
307 : /*!
308 : * \brief The CCZ4 evolved variable \f$\hat{\Gamma}^i\f$
309 : *
310 : * \details This must satisfy the identity:
311 : *
312 : * \f{align}
313 : * \hat{\Gamma}^i &= \tilde{\Gamma}^i + 2 \tilde{\gamma}^{ij} Z_j
314 : * \f}
315 : *
316 : * where \f$\tilde{\gamma}^{ij}\f$ is the inverse conformal spatial metric
317 : * defined by `Ccz4::Tags::InverseConformalMetric`, \f$Z_i\f$ is the spatial
318 : * part of the Z4 constraint defined by `Ccz4::Tags::SpatialZ4Constraint`, and
319 : * \f$\tilde{\Gamma}^i\f$ is the contraction of the conformal spatial
320 : * christoffel symbols of the second kind defined by
321 : * `Ccz4::Tags::ContractedConformalChristoffelSecondKind`.
322 : */
323 : template <typename DataType, size_t Dim, typename Frame>
324 1 : struct GammaHat : db::SimpleTag {
325 0 : using type = tnsr::I<DataType, Dim, Frame>;
326 : };
327 :
328 : /*!
329 : * \brief The spatial part of the Z4 constraint
330 : *
331 : * \details See `Ccz4::spatial_z4_constraint` for details.
332 : */
333 : template <typename DataType, size_t Dim, typename Frame>
334 1 : struct SpatialZ4Constraint : db::SimpleTag {
335 0 : using type = tnsr::i<DataType, Dim, Frame>;
336 : };
337 :
338 : /*!
339 : * \brief The spatial part of the upper Z4 constraint
340 : *
341 : * \details See `Ccz4::upper_spatial_z4_constraint` for details.
342 : */
343 : template <typename DataType, size_t Dim, typename Frame>
344 1 : struct SpatialZ4ConstraintUp : db::SimpleTag {
345 0 : using type = tnsr::I<DataType, Dim, Frame>;
346 : };
347 :
348 : /*!
349 : * \brief The gradient of the spatial part of the Z4 constraint
350 : *
351 : * \details See `Ccz4::grad_spatial_z4_constraint` for details.
352 : */
353 : template <typename DataType, size_t Dim, typename Frame>
354 1 : struct GradSpatialZ4Constraint : db::SimpleTag {
355 0 : using type = tnsr::ij<DataType, Dim, Frame>;
356 : };
357 :
358 : /*!
359 : * \brief The sum of the Ricci scalar and twice the divergence of the upper
360 : * spatial Z4 constraint
361 : *
362 : * \details See `Ccz4::ricci_scalar_plus_divergence_z4_constraint` for details.
363 : */
364 : template <typename DataType>
365 1 : struct RicciScalarPlusDivergenceZ4Constraint : db::SimpleTag {
366 0 : using type = Scalar<DataType>;
367 : };
368 : } // namespace Tags
369 :
370 1 : namespace OptionTags {
371 : /*!
372 : * \ingroup OptionGroupsGroup
373 : * Groups option tags related to the CCZ4 evolution system.
374 : */
375 1 : struct Group {
376 0 : static std::string name() { return "Ccz4"; }
377 0 : static constexpr Options::String help{
378 : "Options for the CCZ4 evolution system"};
379 0 : using group = evolution::OptionTags::SystemGroup;
380 : };
381 : } // namespace OptionTags
382 : } // namespace Ccz4
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