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 OptionTags {
19 : /*!
20 : * \ingroup OptionGroupsGroup
21 : * Groups option tags related to the CCZ4 evolution system.
22 : */
23 1 : struct Ccz4Group {
24 0 : static std::string name() { return "Ccz4"; }
25 0 : static constexpr Options::String help{
26 : "Options for the CCZ4 evolution system"};
27 0 : using group = evolution::OptionTags::SystemGroup;
28 : };
29 :
30 : /// \copydoc Tags::Kappa1
31 1 : struct Kappa1 {
32 0 : using type = double;
33 :
34 0 : static constexpr Options::String help = {
35 : "The constraint damping parameter kappa_1."};
36 0 : using group = Ccz4Group;
37 : };
38 :
39 : /// \copydoc Tags::Kappa2
40 1 : struct Kappa2 {
41 0 : using type = double;
42 :
43 0 : static constexpr Options::String help = {
44 : "The constraint damping parameter kappa_2."};
45 0 : using group = Ccz4Group;
46 : };
47 :
48 : /// \copydoc Tags::Kappa3
49 1 : struct Kappa3 {
50 0 : using type = double;
51 :
52 0 : static constexpr Options::String help = {
53 : "The constraint damping parameter kappa_3."};
54 0 : using group = Ccz4Group;
55 : };
56 : } // namespace OptionTags
57 :
58 : /*!
59 : * \brief Tags for the CCZ4 formulation of Einstein equations.
60 : * \details The naming convention follows \cite Dumbser2017okk
61 : * eq. 12a-12m.
62 : */
63 1 : namespace Tags {
64 : /*!
65 : * \brief The conformal factor that rescales the spatial metric
66 : *
67 : * \details If \f$\gamma_{ij}\f$ is the spatial metric, then we define
68 : * \f$\phi = (det(\gamma_{ij}))^{-1/6}\f$.
69 : */
70 : template <typename DataType>
71 1 : struct ConformalFactor : db::SimpleTag {
72 0 : using type = Scalar<DataType>;
73 : };
74 :
75 : /*!
76 : * \brief The square of the conformal factor that rescales the spatial metric
77 : *
78 : * \details If \f$\gamma_{ij}\f$ is the spatial metric, then we define
79 : * \f$\phi^2 = (det(\gamma_{ij}))^{-1/3}\f$.
80 : */
81 : template <typename DataType>
82 1 : struct ConformalFactorSquared : db::SimpleTag {
83 0 : using type = Scalar<DataType>;
84 : };
85 :
86 : /*!
87 : * \brief The conformally scaled spatial metric
88 : *
89 : * \details If \f$\phi\f$ is the conformal factor and \f$\gamma_{ij}\f$ is the
90 : * spatial metric, then we define
91 : * \f$\bar{\gamma}_{ij} = \phi^2 \gamma_{ij}\f$.
92 : */
93 : template <typename DataType, size_t Dim, typename Fr = Frame::Inertial>
94 1 : using ConformalMetric =
95 : gr::Tags::Conformal<gr::Tags::SpatialMetric<DataType, Dim, Fr>, 2>;
96 :
97 : /*!
98 : * \brief The conformally scaled inverse spatial metric
99 : *
100 : * \details If \f$\phi\f$ is the conformal factor and \f$\gamma^{ij}\f$ is the
101 : * inverse spatial metric, then we define
102 : * \f$\bar{\gamma}^{ij} = \phi^{-2} \gamma^{ij}\f$.
103 : */
104 : template <typename DataType, size_t Dim, typename Frame = Frame::Inertial>
105 1 : using InverseConformalMetric =
106 : gr::Tags::Conformal<gr::Tags::InverseSpatialMetric<DataType, Dim, Frame>,
107 : -2>;
108 :
109 : /*!
110 : * \brief The trace-free part of the extrinsic curvature
111 : *
112 : * \details See `Ccz4::a_tilde()` for details.
113 : */
114 : template <typename DataType, size_t Dim, typename Frame>
115 1 : struct ATilde : db::SimpleTag {
116 0 : using type = tnsr::ii<DataType, Dim, Frame>;
117 : };
118 :
119 : /*!
120 : * \brief The trace of the trace-free part of the extrinsic curvature
121 : *
122 : * \details We define:
123 : *
124 : * \f{align}
125 : * tr\tilde{A} &= \tilde{\gamma}^{ij} \tilde{A}_{ij}
126 : * \f}
127 : *
128 : * where \f$\tilde{\gamma}^{ij}\f$ is the inverse conformal spatial metric
129 : * defined by `Ccz4::Tags::InverseConformalMetric` and \f$\tilde{A}_{ij}\f$ is
130 : * the trace-free part of the extrinsic curvature defined by
131 : * `Ccz4::Tags::ATilde`.
132 : */
133 : template <typename DataType>
134 1 : struct TraceATilde : db::SimpleTag {
135 0 : using type = Scalar<DataType>;
136 : };
137 :
138 : /*!
139 : * \brief The natural log of the lapse
140 : */
141 : template <typename DataType>
142 1 : struct LogLapse : db::SimpleTag {
143 0 : using type = Scalar<DataType>;
144 : };
145 :
146 : /*!
147 : * \brief Auxiliary variable which is analytically the spatial derivative of the
148 : * natural log of the lapse
149 : *
150 : * \details If \f$ \alpha \f$ is the lapse, then we define
151 : * \f$A_i = \partial_i ln(\alpha) = \frac{\partial_i \alpha}{\alpha}\f$.
152 : */
153 : template <typename DataType, size_t Dim, typename Frame>
154 1 : struct FieldA : db::SimpleTag {
155 0 : using type = tnsr::i<DataType, Dim, Frame>;
156 : };
157 :
158 : /*!
159 : * \brief Auxiliary variable which is analytically the spatial derivative of the
160 : * shift
161 : */
162 : template <typename DataType, size_t Dim, typename Frame>
163 1 : struct FieldB : db::SimpleTag {
164 0 : using type = tnsr::iJ<DataType, Dim, Frame>;
165 : };
166 :
167 : /*!
168 : * \brief Auxiliary variable which is analytically half the spatial derivative
169 : * of the conformal spatial metric
170 : *
171 : * \details If \f$\bar{\gamma}_{ij}\f$ is the conformal spatial metric, then we
172 : * define
173 : * \f$D_{kij} = \frac{1}{2} \partial_k \bar{\gamma}_{ij}\f$.
174 : */
175 : template <typename DataType, size_t Dim, typename Frame>
176 1 : struct FieldD : db::SimpleTag {
177 0 : using type = tnsr::ijj<DataType, Dim, Frame>;
178 : };
179 :
180 : /*!
181 : * \brief The natural log of the conformal factor
182 : */
183 : template <typename DataType>
184 1 : struct LogConformalFactor : db::SimpleTag {
185 0 : using type = Scalar<DataType>;
186 : };
187 :
188 : /*!
189 : * \brief Auxiliary variable which is analytically the spatial derivative of the
190 : * natural log of the conformal factor
191 : *
192 : * \details If \f$\phi\f$ is the conformal factor, then we define
193 : * \f$P_i = \partial_i ln(\phi) = \frac{\partial_i \phi}{\phi}\f$.
194 : */
195 : template <typename DataType, size_t Dim, typename Frame>
196 1 : struct FieldP : db::SimpleTag {
197 0 : using type = tnsr::i<DataType, Dim, Frame>;
198 : };
199 :
200 : /*!
201 : * \brief Identity which is analytically negative one half the spatial
202 : * derivative of the inverse conformal spatial metric
203 : *
204 : * \details We define:
205 : * \f{align}
206 : * D_k{}^{ij} &=
207 : * \tilde{\gamma}^{in} \tilde{\gamma}^{mj} D_{knm} =
208 : * -\frac{1}{2} \partial_k \tilde{\gamma}^{ij}
209 : * \f}
210 : * where \f$\tilde{\gamma}^{ij}\f$ and \f$D_{ijk}\f$ are the inverse conformal
211 : * spatial metric and the CCZ4 auxiliary variable defined by
212 : * `Ccz4::Tags::FieldD`, respectively.
213 : */
214 : template <typename DataType, size_t Dim, typename Frame>
215 1 : struct FieldDUp : db::SimpleTag {
216 0 : using type = tnsr::iJJ<DataType, Dim, Frame>;
217 : };
218 :
219 : /*!
220 : * \brief The conformal spatial christoffel symbols of the second kind
221 : *
222 : * \details We define:
223 : * \f{align}
224 : * \tilde{\Gamma}^k_{ij} &=
225 : * \tilde{\gamma}^{kl} (D_{ijl} + D_{jil} - D_{lij})
226 : * \f}
227 : * where \f$\tilde{\gamma}^{ij}\f$ and \f$D_{ijk}\f$ are the inverse conformal
228 : * spatial metric and the CCZ4 auxiliary variable defined by
229 : * `Ccz4::Tags::InverseConformalMetric` and `Ccz4::Tags::FieldD`, respectively.
230 : */
231 : template <typename DataType, size_t Dim, typename Frame>
232 1 : struct ConformalChristoffelSecondKind : db::SimpleTag {
233 0 : using type = tnsr::Ijj<DataType, Dim, Frame>;
234 : };
235 :
236 : /*!
237 : * \brief The spatial derivative of the conformal spatial christoffel symbols
238 : * of the second kind
239 : *
240 : * \details We define:
241 : * \f{align}
242 : * \partial_k \tilde{\Gamma}^m{}_{ij} &=
243 : * -2 D_k{}^{ml} (D_{ijl} + D_{jil} - D_{lij}) +
244 : * \tilde{\gamma}^{ml}(\partial_{(k} D_{i)jl} + \partial_{(k} D_{j)il} -
245 : * \partial_{(k} D_{l)ij})
246 : * \f}
247 : * where \f$\tilde{\gamma}^{ij}\f$, \f$D_{ijk}\f$, \f$\partial_l D_{ijk}\f$, and
248 : * \f$D_k{}^{ij}\f$ are the inverse conformal spatial metric defined by
249 : * `Ccz4::Tags::InverseConformalMetric`, the CCZ4 auxiliary variable defined by
250 : * `Ccz4::Tags::FieldD`, its spatial derivative, and the CCZ4 identity defined
251 : * by `Ccz4::Tags::FieldDUp`.
252 : */
253 : template <typename DataType, size_t Dim, typename Frame>
254 1 : struct DerivConformalChristoffelSecondKind : db::SimpleTag {
255 0 : using type = tnsr::iJkk<DataType, Dim, Frame>;
256 : };
257 :
258 : /*!
259 : * \brief The spatial christoffel symbols of the second kind
260 : *
261 : * \details We define:
262 : * \f{align}
263 : * \Gamma^k_{ij} &= \tilde{\Gamma}^k_{ij} -
264 : * \tilde{\gamma}^{kl} (\tilde{\gamma}_{jl} P_i +
265 : * \tilde{\gamma}_{il} P_j -
266 : * \tilde{\gamma}_{ij} P_l)
267 : * \f}
268 : * where \f$\tilde{\gamma}^{ij}\f$, \f$\tilde{\gamma}_{ij}\f$,
269 : * \f$\tilde{\Gamma}^k_{ij}\f$, and \f$P_i\f$ are the conformal spatial metric,
270 : * the inverse conformal spatial metric, the conformal spatial christoffel
271 : * symbols of the second kind, and the CCZ4 auxiliary variable defined by
272 : * `Ccz4::Tags::ConformalMetric`, `Ccz4::Tags::InverseConformalMetric`,
273 : * `Ccz4::Tags::ConformalChristoffelSecondKind`, and `Ccz4::Tags::FieldP`,
274 : * respectively.
275 : */
276 : template <typename DataType, size_t Dim, typename Frame>
277 1 : struct ChristoffelSecondKind : db::SimpleTag {
278 0 : using type = tnsr::Ijj<DataType, Dim, Frame>;
279 : };
280 :
281 : /*!
282 : * \brief The spatial Ricci tensor
283 : *
284 : * \details See `Ccz4::spatial_ricci_tensor()` for details.
285 : */
286 : template <typename DataType, size_t Dim, typename Frame>
287 1 : struct Ricci : db::SimpleTag {
288 0 : using type = tnsr::ii<DataType, Dim, Frame>;
289 : };
290 :
291 : /*!
292 : * \brief The gradient of the gradient of the lapse
293 : *
294 : * \details We define:
295 : * \f{align}
296 : * \nabla_i \nabla_j \alpha &= \alpha A_i A_j -
297 : * \alpha \Gamma^k{}_{ij} A_k + \alpha \partial_{(i} A_{j)}
298 : * \f}
299 : * where \f$\alpha\f$, \f$\Gamma^k{}_{ij}\f$, \f$A_i\f$, and
300 : * \f$\partial_j A_i\f$ are the lapse, spatial christoffel symbols of the second
301 : * kind, the CCZ4 auxiliary variable defined by `Ccz4::Tags::FieldA`, and its
302 : * spatial derivative, respectively.
303 : */
304 : template <typename DataType, size_t Dim, typename Frame>
305 1 : struct GradGradLapse : db::SimpleTag {
306 0 : using type = tnsr::ij<DataType, Dim, Frame>;
307 : };
308 :
309 : /*!
310 : * \brief The divergence of the lapse
311 : *
312 : * \details We define:
313 : * \f{align}
314 : * \nabla^i \nabla_i \alpha &= \phi^2 \tilde{\gamma}^{ij}
315 : * (\nabla_i \nabla_j \alpha)
316 : * \f}
317 : * where \f$\phi\f$, \f$\tilde{\gamma}^{ij}\f$, and
318 : * \f$\nabla_i \nabla_j \alpha\f$ are the conformal factor, inverse conformal
319 : * spatial metric, and the gradient of the gradient of the lapse defined by
320 : * `Ccz4::Tags::ConformalFactor`, `Ccz4::Tags::InverseConformalMetric`, and
321 : * `Ccz4::Tags::GradGradLapse`, respectively.
322 : */
323 : template <typename DataType>
324 1 : struct DivergenceLapse : db::SimpleTag {
325 0 : using type = Scalar<DataType>;
326 : };
327 :
328 : /*!
329 : * \brief The contraction of the conformal spatial Christoffel symbols of the
330 : * second kind
331 : *
332 : * \details See `Ccz4::contracted_conformal_christoffel_second_kind()` for
333 : * details.
334 : */
335 : template <typename DataType, size_t Dim, typename Frame>
336 1 : struct ContractedConformalChristoffelSecondKind : db::SimpleTag {
337 0 : using type = tnsr::I<DataType, Dim, Frame>;
338 : };
339 :
340 : /*!
341 : * \brief The spatial derivative of the contraction of the conformal spatial
342 : * Christoffel symbols of the second kind
343 : *
344 : * \details See `Ccz4::deriv_contracted_conformal_christoffel_second_kind()` for
345 : * details.
346 : */
347 : template <typename DataType, size_t Dim, typename Frame>
348 1 : struct DerivContractedConformalChristoffelSecondKind : db::SimpleTag {
349 0 : using type = tnsr::iJ<DataType, Dim, Frame>;
350 : };
351 :
352 : /*!
353 : * \brief The CCZ4 evolved variable \f$\hat{\Gamma}^i\f$
354 : *
355 : * \details This must satisfy the identity:
356 : *
357 : * \f{align}
358 : * \hat{\Gamma}^i &= \tilde{\Gamma}^i + 2 \tilde{\gamma}^{ij} Z_j
359 : * \f}
360 : *
361 : * where \f$\tilde{\gamma}^{ij}\f$ is the inverse conformal spatial metric
362 : * defined by `Ccz4::Tags::InverseConformalMetric`, \f$Z_i\f$ is the spatial
363 : * part of the Z4 constraint defined by `Ccz4::Tags::SpatialZ4Constraint`, and
364 : * \f$\tilde{\Gamma}^i\f$ is the contraction of the conformal spatial
365 : * christoffel symbols of the second kind defined by
366 : * `Ccz4::Tags::ContractedConformalChristoffelSecondKind`.
367 : */
368 : template <typename DataType, size_t Dim, typename Frame>
369 1 : struct GammaHat : db::SimpleTag {
370 0 : using type = tnsr::I<DataType, Dim, Frame>;
371 : };
372 :
373 : /*!
374 : * \brief The spatial part of the Z4 constraint
375 : *
376 : * \details See `Ccz4::spatial_z4_constraint` for details.
377 : */
378 : template <typename DataType, size_t Dim, typename Frame>
379 1 : struct SpatialZ4Constraint : db::SimpleTag {
380 0 : using type = tnsr::i<DataType, Dim, Frame>;
381 : };
382 :
383 : /*!
384 : * \brief The spatial part of the upper Z4 constraint
385 : *
386 : * \details See `Ccz4::upper_spatial_z4_constraint` for details.
387 : */
388 : template <typename DataType, size_t Dim, typename Frame>
389 1 : struct SpatialZ4ConstraintUp : db::SimpleTag {
390 0 : using type = tnsr::I<DataType, Dim, Frame>;
391 : };
392 :
393 : /*!
394 : * \brief The gradient of the spatial part of the Z4 constraint
395 : *
396 : * \details See `Ccz4::grad_spatial_z4_constraint` for details.
397 : */
398 : template <typename DataType, size_t Dim, typename Frame>
399 1 : struct GradSpatialZ4Constraint : db::SimpleTag {
400 0 : using type = tnsr::ij<DataType, Dim, Frame>;
401 : };
402 :
403 : /*!
404 : * \brief The sum of the Ricci scalar and twice the divergence of the upper
405 : * spatial Z4 constraint
406 : *
407 : * \details See `Ccz4::ricci_scalar_plus_divergence_z4_constraint` for details.
408 : */
409 : template <typename DataType>
410 1 : struct RicciScalarPlusDivergenceZ4Constraint : db::SimpleTag {
411 0 : using type = Scalar<DataType>;
412 : };
413 :
414 : /*!
415 : * \brief The projection of the Z4 constraint vector along the normal direction.
416 : *
417 : *
418 : */
419 : template <typename DataType>
420 1 : struct Theta : db::SimpleTag {
421 0 : using type = Scalar<DataType>;
422 : };
423 :
424 : /*!
425 : * \brief Auxiliary variable b in the gamma-driver condition
426 : * eq. 12c of \cite Dumbser2017okk.
427 : */
428 : template <typename DataType, size_t Dim, typename Frame>
429 1 : struct AuxiliaryShiftB : db::SimpleTag {
430 0 : using type = tnsr::I<DataType, Dim, Frame>;
431 : };
432 :
433 : /*!
434 : * \brief The parameter f in the gamma-driver condition
435 : * eq. 12c of \cite Dumbser2017okk.
436 : *
437 : */
438 1 : struct GammaDriverParam
439 : : db::SimpleTag {
440 0 : using type = double;
441 : };
442 :
443 : /*!
444 : * \brief Free parameter \f$ kappa_1 \f$ related to
445 : * constraint damping
446 : * in eq. 12f of \cite Dumbser2017okk.
447 : */
448 1 : struct Kappa1 : db::SimpleTag {
449 0 : using type = double;
450 0 : using option_tags = tmpl::list<OptionTags::Kappa1>;
451 :
452 0 : static constexpr bool pass_metavariables = false;
453 0 : static type create_from_options(const double kappa_1) { return kappa_1; }
454 : };
455 :
456 : /*!
457 : * \brief Free parameter \f$ kappa_2 \f$ related to
458 : * constraint damping
459 : * in eq. 12f of \cite Dumbser2017okk.
460 : */
461 1 : struct Kappa2 : db::SimpleTag {
462 0 : using type = double;
463 0 : using option_tags = tmpl::list<OptionTags::Kappa2>;
464 :
465 0 : static constexpr bool pass_metavariables = false;
466 0 : static type create_from_options(const double kappa_2) { return kappa_2; }
467 : };
468 :
469 : /*!
470 : * \brief Free parameter \f$ kappa_3 \f$ related to
471 : * constraint damping
472 : * in eq. 12h of \cite Dumbser2017okk.
473 : */
474 1 : struct Kappa3 : db::SimpleTag {
475 0 : using type = double;
476 0 : using option_tags = tmpl::list<OptionTags::Kappa3>;
477 :
478 0 : static constexpr bool pass_metavariables = false;
479 0 : static type create_from_options(const double kappa_3) { return kappa_3; }
480 : };
481 :
482 : /*!
483 : * \brief Free parameter \f$ K_0 \f$ in 1+log slicing
484 : * in eq. 12b of \cite Dumbser2017okk.
485 : */
486 : template <typename DataType>
487 1 : struct K0 : db::SimpleTag {
488 0 : using type = Scalar<DataType>;
489 : };
490 :
491 : /*!
492 : * \brief The parameter \f$ \eta \f$ in the gamma-driver
493 : * condition eq. 12i of \cite Dumbser2017okk.
494 : *
495 : */
496 : template <typename DataType>
497 1 : struct Eta : db::SimpleTag {
498 0 : using type = Scalar<DataType>;
499 : };
500 : } // namespace Tags
501 : } // namespace Ccz4
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