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 <optional>
9 : #include <type_traits>
10 :
11 : #include "DataStructures/DataBox/AsAccess.hpp"
12 : #include "DataStructures/DataBox/DataBox.hpp"
13 : #include "DataStructures/DataBox/PrefixHelpers.hpp"
14 : #include "DataStructures/DataBox/Prefixes.hpp"
15 : #include "DataStructures/DataVector.hpp"
16 : #include "DataStructures/TaggedContainers.hpp"
17 : #include "DataStructures/Tensor/Tensor.hpp"
18 : #include "DataStructures/Variables.hpp"
19 : #include "DataStructures/VectorImpl.hpp"
20 : #include "Domain/Structure/Element.hpp"
21 : #include "Domain/Tags.hpp"
22 : #include "Domain/TagsTimeDependent.hpp"
23 : #include "Evolution/BoundaryCorrection.hpp"
24 : #include "Evolution/BoundaryCorrectionTags.hpp"
25 : #include "Evolution/DgSubcell/CartesianFluxDivergence.hpp"
26 : #include "Evolution/DgSubcell/ComputeBoundaryTerms.hpp"
27 : #include "Evolution/DgSubcell/CorrectPackagedData.hpp"
28 : #include "Evolution/DgSubcell/Projection.hpp"
29 : #include "Evolution/DgSubcell/ReconstructionOrder.hpp"
30 : #include "Evolution/DgSubcell/Tags/Coordinates.hpp"
31 : #include "Evolution/DgSubcell/Tags/GhostDataForReconstruction.hpp"
32 : #include "Evolution/DgSubcell/Tags/Jacobians.hpp"
33 : #include "Evolution/DgSubcell/Tags/Mesh.hpp"
34 : #include "Evolution/DgSubcell/Tags/OnSubcellFaces.hpp"
35 : #include "Evolution/DiscontinuousGalerkin/Actions/NormalCovectorAndMagnitude.hpp"
36 : #include "Evolution/DiscontinuousGalerkin/Actions/PackageDataImpl.hpp"
37 : #include "Evolution/DiscontinuousGalerkin/MortarTags.hpp"
38 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/AllSolutions.hpp"
39 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/FiniteDifference/BoundaryConditionGhostData.hpp"
40 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/FiniteDifference/Derivatives.hpp"
41 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/FiniteDifference/FilterOptions.hpp"
42 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/FiniteDifference/Filters.hpp"
43 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/FiniteDifference/Reconstructor.hpp"
44 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/FiniteDifference/Tag.hpp"
45 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/StressEnergy.hpp"
46 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/System.hpp"
47 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/Tags.hpp"
48 : #include "Evolution/Systems/GrMhd/GhValenciaDivClean/TimeDerivativeTerms.hpp"
49 : #include "Evolution/Systems/GrMhd/ValenciaDivClean/Fluxes.hpp"
50 : #include "Evolution/Systems/GrMhd/ValenciaDivClean/Sources.hpp"
51 : #include "Evolution/Systems/GrMhd/ValenciaDivClean/Subcell/ComputeFluxes.hpp"
52 : #include "Evolution/Systems/GrMhd/ValenciaDivClean/TimeDerivativeTerms.hpp"
53 : #include "NumericalAlgorithms/FiniteDifference/PartialDerivatives.hpp"
54 : #include "NumericalAlgorithms/Spectral/Mesh.hpp"
55 : #include "PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic/DerivSpatialMetric.hpp"
56 : #include "PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic/ExtrinsicCurvature.hpp"
57 : #include "PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic/SpatialDerivOfLapse.hpp"
58 : #include "PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic/SpatialDerivOfShift.hpp"
59 : #include "PointwiseFunctions/Hydro/Tags.hpp"
60 : #include "Utilities/CallWithDynamicType.hpp"
61 : #include "Utilities/ErrorHandling/Assert.hpp"
62 : #include "Utilities/Gsl.hpp"
63 : #include "Utilities/TMPL.hpp"
64 :
65 : /// \cond
66 : namespace Tags {
67 : struct Time;
68 : } // namespace Tags
69 : /// \endcond
70 :
71 : namespace grmhd::GhValenciaDivClean::subcell {
72 : namespace detail {
73 : template <class GhDtTagsList, class GhTemporariesList, class GhGradientTagsList,
74 : class GhExtraTagsList, class GrmhdDtTagsList,
75 : class GrmhdSourceTagsList, class GrmhdArgumentSourceTagsList,
76 : typename System>
77 : struct ComputeTimeDerivImpl;
78 :
79 : template <class... GhDtTags, class... GhTemporaries, class... GhGradientTags,
80 : class... GhExtraTags, class... GrmhdDtTags, class... GrmhdSourceTags,
81 : class... GrmhdArgumentSourceTags, typename System>
82 : struct ComputeTimeDerivImpl<
83 : tmpl::list<GhDtTags...>, tmpl::list<GhTemporaries...>,
84 : tmpl::list<GhGradientTags...>, tmpl::list<GhExtraTags...>,
85 : tmpl::list<GrmhdDtTags...>, tmpl::list<GrmhdSourceTags...>,
86 : tmpl::list<GrmhdArgumentSourceTags...>, System> {
87 : template <class DbTagsList>
88 : static void apply(
89 : const gsl::not_null<db::DataBox<DbTagsList>*> box,
90 : const tnsr::I<DataVector, 3, Frame::Inertial>& inertial_coords,
91 : const Scalar<DataVector>& cell_centered_det_inv_jacobian,
92 : const InverseJacobian<DataVector, 3, Frame::ElementLogical,
93 : Frame::Inertial>&
94 : cell_centered_logical_to_inertial_inv_jacobian,
95 : const std::array<double, 3>& one_over_delta_xi,
96 : const std::array<Variables<tmpl::list<GrmhdDtTags...>>, 3>&
97 : boundary_corrections,
98 : const Variables<
99 : db::wrap_tags_in<::Tags::deriv, typename System::gradients_tags,
100 : tmpl::size_t<3>, Frame::Inertial>>& gh_derivs) {
101 : const Mesh<3>& subcell_mesh =
102 : db::get<evolution::dg::subcell::Tags::Mesh<3>>(*box);
103 : const size_t number_of_points = subcell_mesh.number_of_grid_points();
104 : // Note: GH+GRMHD tags are always GH,GRMHD
105 : using deriv_lapse = ::Tags::deriv<gr::Tags::Lapse<DataVector>,
106 : tmpl::size_t<3>, Frame::Inertial>;
107 : using deriv_shift = ::Tags::deriv<gr::Tags::Shift<DataVector, 3>,
108 : tmpl::size_t<3>, Frame::Inertial>;
109 : using deriv_spatial_metric =
110 : ::Tags::deriv<gr::Tags::SpatialMetric<DataVector, 3>, tmpl::size_t<3>,
111 : Frame::Inertial>;
112 : using extra_tags_for_grmhd =
113 : tmpl::list<deriv_lapse, deriv_shift, deriv_spatial_metric,
114 : gr::Tags::ExtrinsicCurvature<DataVector, 3>>;
115 : using temporary_tags = tmpl::remove_duplicates<tmpl::append<
116 : typename gh::TimeDerivative<ghmhd::GhValenciaDivClean::InitialData::
117 : analytic_solutions_and_data_list,
118 : 3_st>::temporary_tags,
119 : tmpl::push_front<typename grmhd::ValenciaDivClean::TimeDerivativeTerms::
120 : temporary_tags,
121 : ::gh::Tags::ConstraintGamma0>,
122 : extra_tags_for_grmhd,
123 : tmpl::list<
124 : Tags::TraceReversedStressEnergy, Tags::FourVelocityOneForm,
125 : grmhd::ValenciaDivClean::Tags::ComovingMagneticFieldOneForm>>>;
126 : Variables<temporary_tags> temp_tags{subcell_mesh.number_of_grid_points()};
127 : const auto temp_tags_ptr = make_not_null(&temp_tags);
128 :
129 : // Compute constraint damping terms.
130 : const double time = db::get<::Tags::Time>(*box);
131 : const auto& functions_of_time =
132 : db::get<::domain::Tags::FunctionsOfTime>(*box);
133 : const auto& grid_coords =
134 : db::get<evolution::dg::subcell::Tags::Coordinates<3, Frame::Grid>>(
135 : *box);
136 : db::get<gh::Tags::DampingFunctionGamma0<3, Frame::Grid>> (*box)(
137 : get<gh::Tags::ConstraintGamma0>(temp_tags_ptr), grid_coords, time,
138 : functions_of_time);
139 : db::get<gh::Tags::DampingFunctionGamma1<3, Frame::Grid>> (*box)(
140 : get<gh::Tags::ConstraintGamma1>(temp_tags_ptr), grid_coords, time,
141 : functions_of_time);
142 : db::get<gh::Tags::DampingFunctionGamma2<3, Frame::Grid>> (*box)(
143 : get<gh::Tags::ConstraintGamma2>(temp_tags_ptr), grid_coords, time,
144 : functions_of_time);
145 :
146 : using variables_tag = typename System::variables_tag;
147 : using dt_variables_tag = db::add_tag_prefix<::Tags::dt, variables_tag>;
148 : const gsl::not_null<typename dt_variables_tag::type*> dt_vars_ptr =
149 : db::mutate<dt_variables_tag>(
150 : [](const auto local_dt_vars_ptr) { return local_dt_vars_ptr; },
151 : box);
152 : dt_vars_ptr->initialize(subcell_mesh.number_of_grid_points());
153 :
154 : using primitives_tag = typename System::primitive_variables_tag;
155 : using evolved_vars_tag = typename System::variables_tag;
156 :
157 : const auto& primitive_vars = db::get<primitives_tag>(*box);
158 : const auto& evolved_vars = db::get<evolved_vars_tag>(*box);
159 :
160 : // Velocity of the moving mesh, if applicable. We project the value
161 : // stored on the DG grid onto the subcell grid.
162 : const Mesh<3>& dg_mesh = db::get<domain::Tags::Mesh<3>>(*box);
163 : const std::optional<tnsr::I<DataVector, 3, Frame::Inertial>>&
164 : mesh_velocity_dg = db::get<domain::Tags::MeshVelocity<3>>(*box);
165 : const std::optional<Scalar<DataVector>>& div_mesh_velocity_dg =
166 : db::get<domain::Tags::DivMeshVelocity>(*box);
167 : std::optional<tnsr::I<DataVector, 3, Frame::Inertial>>
168 : mesh_velocity_subcell = {};
169 : if (mesh_velocity_dg.has_value()) {
170 : mesh_velocity_subcell = tnsr::I<DataVector, 3, Frame::Inertial>{
171 : subcell_mesh.number_of_grid_points()};
172 : for (size_t i = 0; i < 3; i++) {
173 : mesh_velocity_subcell.value().get(i) =
174 : evolution::dg::subcell::fd::project(mesh_velocity_dg.value().get(i),
175 : dg_mesh,
176 : subcell_mesh.extents());
177 : }
178 : }
179 :
180 : gh::TimeDerivative<
181 : ghmhd::GhValenciaDivClean::InitialData::
182 : analytic_solutions_and_data_list,
183 : 3_st>::apply(get<::Tags::dt<GhDtTags>>(dt_vars_ptr)...,
184 : get<GhTemporaries>(temp_tags_ptr)...,
185 : get<::Tags::deriv<GhGradientTags, tmpl::size_t<3>,
186 : Frame::Inertial>>(gh_derivs)...,
187 : get<GhExtraTags>(evolved_vars, temp_tags)...,
188 :
189 : db::get<::gh::gauges::Tags::GaugeCondition>(*box),
190 : db::get<evolution::dg::subcell::Tags::Mesh<3>>(*box), time,
191 : inertial_coords,
192 : cell_centered_logical_to_inertial_inv_jacobian,
193 : mesh_velocity_subcell);
194 : if (get<gh::gauges::Tags::GaugeCondition>(*box).is_harmonic()) {
195 : get(get<gr::Tags::SqrtDetSpatialMetric<DataVector>>(*temp_tags_ptr)) =
196 : sqrt(
197 : get(get<gr::Tags::DetSpatialMetric<DataVector>>(*temp_tags_ptr)));
198 : }
199 :
200 : // Add source terms from moving mesh
201 : if (mesh_velocity_dg.has_value()) {
202 : tmpl::for_each<tmpl::list<GhDtTags...>>([&dt_vars_ptr,
203 : &mesh_velocity_subcell,
204 : &gh_derivs](
205 : auto evolved_var_tag_v) {
206 : using evolved_var_tag = tmpl::type_from<decltype(evolved_var_tag_v)>;
207 : using dt_tag = ::Tags::dt<evolved_var_tag>;
208 : using grad_tag =
209 : ::Tags::deriv<evolved_var_tag, tmpl::size_t<3>, Frame::Inertial>;
210 : // Flux and gradients use the same indexing conventions,
211 : // replacing the direction of the face with the direction
212 : // of the derivative.
213 : using FluxTensor = typename grad_tag::type;
214 : auto& dt_var = get<dt_tag>(*dt_vars_ptr);
215 : const auto& grad_var = get<grad_tag>(gh_derivs);
216 : for (size_t i = 0; i < dt_var.size(); ++i) {
217 : const auto tensor_index = dt_var.get_tensor_index(i);
218 : for (size_t j = 0; j < 3; j++) {
219 : const auto grad_index =
220 : FluxTensor::get_storage_index(prepend(tensor_index, j));
221 : // Add (mesh_velocity)^j grad_j (var[i])
222 : dt_var[i] +=
223 : mesh_velocity_subcell.value().get(j) * grad_var[grad_index];
224 : }
225 : }
226 : });
227 : }
228 :
229 : {
230 : // Set extra tags needed for GRMHD source terms. We compute these from
231 : // quantities already computed inside the GH RHS computation to minimize
232 : // FLOPs.
233 : const auto& lapse = get<gr::Tags::Lapse<DataVector>>(temp_tags);
234 : const auto& half_phi_two_normals =
235 : get<gh::Tags::HalfPhiTwoNormals<3>>(temp_tags);
236 : const auto& phi = get<gh::Tags::Phi<DataVector, 3>>(evolved_vars);
237 : const auto& phi_one_normal = get<gh::Tags::PhiOneNormal<3>>(temp_tags);
238 : const auto& spacetime_normal_vector =
239 : get<gr::Tags::SpacetimeNormalVector<DataVector, 3>>(temp_tags);
240 : const auto& inverse_spacetime_metric =
241 : get<gr::Tags::InverseSpacetimeMetric<DataVector, 3>>(temp_tags);
242 :
243 : auto& spatial_deriv_lapse = get<deriv_lapse>(temp_tags);
244 : auto& spatial_deriv_shift = get<deriv_shift>(temp_tags);
245 : // Compute d_i beta^i
246 : for (size_t i = 0; i < 3; ++i) {
247 : // Use spatial_deriv_lapse as temp buffer to reduce number of 2*
248 : // operations.
249 : const auto& phi_two_normals_i = spatial_deriv_lapse.get(i) =
250 : 2.0 * half_phi_two_normals.get(i);
251 : for (size_t j = 0; j < 3; ++j) {
252 : spatial_deriv_shift.get(i, j) =
253 : spacetime_normal_vector.get(j + 1) * phi_two_normals_i;
254 : for (size_t a = 0; a < 4; ++a) {
255 : spatial_deriv_shift.get(i, j) +=
256 : inverse_spacetime_metric.get(j + 1, a) *
257 : phi_one_normal.get(i, a);
258 : }
259 : spatial_deriv_shift.get(i, j) *= get(lapse);
260 : }
261 : }
262 :
263 : // Compute d_i lapse
264 : for (size_t i = 0; i < 3; ++i) {
265 : spatial_deriv_lapse.get(i) = -get(lapse) * half_phi_two_normals.get(i);
266 : }
267 : // Extract d_i \gamma_{ij}
268 : for (size_t k = 0; k < 3; ++k) {
269 : for (size_t i = 0; i < 3; ++i) {
270 : for (size_t j = i; j < 3; ++j) {
271 : get<deriv_spatial_metric>(temp_tags).get(k, i, j) =
272 : phi.get(k, i + 1, j + 1);
273 : }
274 : }
275 : }
276 :
277 : // Compute extrinsic curvature
278 : const auto& pi = get<gh::Tags::Pi<DataVector, 3>>(evolved_vars);
279 : for (size_t i = 0; i < 3; ++i) {
280 : for (size_t j = i; j < 3; ++j) {
281 : get<gr::Tags::ExtrinsicCurvature<DataVector, 3>>(temp_tags).get(i,
282 : j) =
283 : 0.5 * (pi.get(i + 1, j + 1) + phi_one_normal.get(i, j + 1) +
284 : phi_one_normal.get(j, i + 1));
285 : }
286 : }
287 : } // End scope for computing metric terms in GRMHD source terms.
288 :
289 : grmhd::ValenciaDivClean::ComputeSources::apply(
290 : get<::Tags::dt<GrmhdSourceTags>>(dt_vars_ptr)...,
291 : get<GrmhdArgumentSourceTags>(temp_tags, primitive_vars, evolved_vars,
292 : *box)...);
293 :
294 : // Zero GRMHD tags that don't have sources.
295 : tmpl::for_each<tmpl::list<GrmhdDtTags...>>([&dt_vars_ptr](
296 : auto evolved_var_tag_v) {
297 : using evolved_var_tag = tmpl::type_from<decltype(evolved_var_tag_v)>;
298 : using dt_tag = ::Tags::dt<evolved_var_tag>;
299 : auto& dt_var = get<dt_tag>(*dt_vars_ptr);
300 : for (size_t i = 0; i < dt_var.size(); ++i) {
301 : if constexpr (not tmpl::list_contains_v<tmpl::list<GrmhdSourceTags...>,
302 : evolved_var_tag>) {
303 : // Zero the GRMHD dt(u) for variables that do not have a source term .
304 : // This is necessary to avoid `+=` to a `NaN` (debug mode) or random
305 : // garbage (release mode) when adding to dt_var below.
306 : dt_var[i] = 0.0;
307 : }
308 : }
309 : });
310 : // Correction to source terms due to moving mesh
311 : if (div_mesh_velocity_dg.has_value()) {
312 : const DataVector div_mesh_velocity_subcell =
313 : evolution::dg::subcell::fd::project(
314 : div_mesh_velocity_dg.value().get(), dg_mesh,
315 : subcell_mesh.extents());
316 : tmpl::for_each<tmpl::list<GrmhdDtTags...>>(
317 : [&dt_vars_ptr, &div_mesh_velocity_subcell,
318 : &evolved_vars](auto evolved_var_tag_v) {
319 : using evolved_var_tag =
320 : tmpl::type_from<decltype(evolved_var_tag_v)>;
321 : using dt_tag = ::Tags::dt<evolved_var_tag>;
322 : auto& dt_var = get<dt_tag>(*dt_vars_ptr);
323 : const auto& evolved_var = get<evolved_var_tag>(evolved_vars);
324 : for (size_t i = 0; i < dt_var.size(); ++i) {
325 : dt_var[i] -= div_mesh_velocity_subcell * evolved_var[i];
326 : }
327 : });
328 : }
329 :
330 : const tnsr::ii<DataVector, 3> spatial_metric{};
331 : for (size_t i = 0; i < 3; ++i) {
332 : for (size_t j = i; j < 3; ++j) {
333 : make_const_view(
334 : make_not_null(&spatial_metric.get(i, j)),
335 : get<gr::Tags::SpacetimeMetric<DataVector, 3>>(evolved_vars)
336 : .get(i + 1, j + 1),
337 : 0, number_of_points);
338 : }
339 : }
340 :
341 : tenex::evaluate<ti::i>(get<hydro::Tags::SpatialVelocityOneForm<
342 : DataVector, 3, Frame::Inertial>>(temp_tags_ptr),
343 : get<hydro::Tags::SpatialVelocity<DataVector, 3>>(
344 : primitive_vars)(ti::J) *
345 : spatial_metric(ti::i, ti::j));
346 :
347 : tenex::evaluate<ti::i>(
348 : get<hydro::Tags::MagneticFieldOneForm<DataVector, 3, Frame::Inertial>>(
349 : temp_tags_ptr),
350 : get<hydro::Tags::MagneticField<DataVector, 3>>(primitive_vars)(ti::J) *
351 : spatial_metric(ti::i, ti::j));
352 :
353 : tenex::evaluate(
354 : get<hydro::Tags::MagneticFieldSquared<DataVector>>(temp_tags_ptr),
355 : get<hydro::Tags::MagneticField<DataVector, 3>>(primitive_vars)(ti::J) *
356 : get<hydro::Tags::MagneticFieldOneForm<DataVector, 3>>(temp_tags)(
357 : ti::j));
358 :
359 : tenex::evaluate(
360 : get<hydro::Tags::MagneticFieldDotSpatialVelocity<DataVector>>(
361 : temp_tags_ptr),
362 : get<hydro::Tags::SpatialVelocity<DataVector, 3>>(primitive_vars)(
363 : ti::J) *
364 : get<hydro::Tags::MagneticFieldOneForm<DataVector, 3>>(temp_tags)(
365 : ti::j));
366 :
367 : tenex::evaluate(get<typename ValenciaDivClean::TimeDerivativeTerms::
368 : OneOverLorentzFactorSquared>(temp_tags_ptr),
369 : 1.0 / (square(get<hydro::Tags::LorentzFactor<DataVector>>(
370 : primitive_vars)())));
371 :
372 : trace_reversed_stress_energy(
373 : get<Tags::TraceReversedStressEnergy>(temp_tags_ptr),
374 : get<Tags::FourVelocityOneForm>(temp_tags_ptr),
375 : get<grmhd::ValenciaDivClean::Tags::ComovingMagneticFieldOneForm>(
376 : temp_tags_ptr),
377 :
378 : get<hydro::Tags::RestMassDensity<DataVector>>(evolved_vars, temp_tags,
379 : primitive_vars),
380 : get<hydro::Tags::SpatialVelocityOneForm<DataVector, 3,
381 : Frame::Inertial>>(
382 : evolved_vars, temp_tags, primitive_vars),
383 :
384 : get<hydro::Tags::MagneticFieldOneForm<DataVector, 3, Frame::Inertial>>(
385 : evolved_vars, temp_tags, primitive_vars),
386 :
387 : get<hydro::Tags::MagneticFieldSquared<DataVector>>(
388 : evolved_vars, temp_tags, primitive_vars),
389 :
390 : get<hydro::Tags::MagneticFieldDotSpatialVelocity<DataVector>>(
391 : evolved_vars, temp_tags, primitive_vars),
392 : get<hydro::Tags::LorentzFactor<DataVector>>(evolved_vars, temp_tags,
393 : primitive_vars),
394 : get<typename ValenciaDivClean::TimeDerivativeTerms::
395 : OneOverLorentzFactorSquared>(evolved_vars, temp_tags,
396 : primitive_vars),
397 : get<hydro::Tags::Pressure<DataVector>>(evolved_vars, temp_tags,
398 : primitive_vars),
399 : get<hydro::Tags::SpecificInternalEnergy<DataVector>>(
400 : evolved_vars, temp_tags, primitive_vars),
401 : get<gr::Tags::SpacetimeMetric<DataVector, 3>>(evolved_vars, temp_tags,
402 : primitive_vars),
403 : get<gr::Tags::Shift<DataVector, 3>>(evolved_vars, temp_tags,
404 : primitive_vars),
405 : get<gr::Tags::Lapse<DataVector>>(evolved_vars, temp_tags,
406 : primitive_vars));
407 :
408 : add_stress_energy_term_to_dt_pi(
409 : get<::Tags::dt<gh::Tags::Pi<DataVector, 3>>>(dt_vars_ptr),
410 : get<Tags::TraceReversedStressEnergy>(temp_tags),
411 : get<gr::Tags::Lapse<DataVector>>(temp_tags));
412 :
413 : for (size_t dim = 0; dim < 3; ++dim) {
414 : const auto& boundary_correction_in_axis =
415 : gsl::at(boundary_corrections, dim);
416 : const double inverse_delta = gsl::at(one_over_delta_xi, dim);
417 : EXPAND_PACK_LEFT_TO_RIGHT([&dt_vars_ptr, &boundary_correction_in_axis,
418 : &cell_centered_det_inv_jacobian, dim,
419 : inverse_delta, &subcell_mesh]() {
420 : auto& dt_var = *get<::Tags::dt<GrmhdDtTags>>(dt_vars_ptr);
421 : const auto& var_correction =
422 : get<GrmhdDtTags>(boundary_correction_in_axis);
423 : for (size_t i = 0; i < dt_var.size(); ++i) {
424 : evolution::dg::subcell::add_cartesian_flux_divergence(
425 : make_not_null(&dt_var[i]), inverse_delta,
426 : get(cell_centered_det_inv_jacobian), var_correction[i],
427 : subcell_mesh.extents(), dim);
428 : }
429 : }());
430 : }
431 : }
432 : };
433 : } // namespace detail
434 :
435 : /*!
436 : * \brief Compute the time derivative on the subcell grid using FD
437 : * reconstruction.
438 : *
439 : * The code makes the following unchecked assumptions:
440 : * - Assumes Cartesian coordinates with a diagonal Jacobian matrix
441 : * from the logical to the inertial frame
442 : */
443 : template <typename System>
444 1 : struct TimeDerivative {
445 : template <typename DbTagsList>
446 0 : static void apply(const gsl::not_null<db::DataBox<DbTagsList>*> box) {
447 : using metavariables =
448 : typename std::decay_t<decltype(db::get<Parallel::Tags::Metavariables>(
449 : *box))>;
450 : using evolved_vars_tag = typename System::variables_tag;
451 : using evolved_vars_tags = typename evolved_vars_tag::tags_list;
452 : using grmhd_evolved_vars_tag =
453 : typename grmhd::ValenciaDivClean::System::variables_tag;
454 : using grmhd_evolved_vars_tags = typename grmhd_evolved_vars_tag::tags_list;
455 : using fluxes_tags =
456 : db::wrap_tags_in<::Tags::Flux, typename System::flux_variables,
457 : tmpl::size_t<3>, Frame::Inertial>;
458 : using prim_tag = typename System::primitive_variables_tag;
459 : using prim_tags = typename prim_tag::tags_list;
460 : using recons_prim_tags = tmpl::push_front<tmpl::push_back<
461 : prim_tags,
462 : hydro::Tags::LorentzFactorTimesSpatialVelocity<DataVector, 3>>>;
463 : using gradients_tags = typename System::gradients_tags;
464 :
465 : const Mesh<3>& dg_mesh = db::get<domain::Tags::Mesh<3>>(*box);
466 : const Mesh<3>& subcell_mesh =
467 : db::get<evolution::dg::subcell::Tags::Mesh<3>>(*box);
468 : ASSERT(
469 : subcell_mesh == Mesh<3>(subcell_mesh.extents(0), subcell_mesh.basis(0),
470 : subcell_mesh.quadrature(0)),
471 : "The subcell/FD mesh must be isotropic for the FD time derivative but "
472 : "got "
473 : << subcell_mesh);
474 : const size_t num_pts = subcell_mesh.number_of_grid_points();
475 : const size_t reconstructed_num_pts =
476 : (subcell_mesh.extents(0) + 1) *
477 : subcell_mesh.extents().slice_away(0).product();
478 :
479 : const tnsr::I<DataVector, 3, Frame::ElementLogical>&
480 : cell_centered_logical_coords =
481 : db::get<evolution::dg::subcell::Tags::Coordinates<
482 : 3, Frame::ElementLogical>>(*box);
483 : std::array<double, 3> one_over_delta_xi{};
484 : for (size_t i = 0; i < 3; ++i) {
485 : // Note: assumes isotropic extents
486 : gsl::at(one_over_delta_xi, i) =
487 : 1.0 / (get<0>(cell_centered_logical_coords)[1] -
488 : get<0>(cell_centered_logical_coords)[0]);
489 : }
490 : const auto& cell_centered_logical_to_inertial_inv_jacobian = db::get<
491 : evolution::dg::subcell::fd::Tags::InverseJacobianLogicalToInertial<3>>(
492 : *box);
493 : const auto& inertial_coords =
494 : db::get<evolution::dg::subcell::Tags::Coordinates<3, Frame::Inertial>>(
495 : *box);
496 :
497 : const Element<3>& element = db::get<domain::Tags::Element<3>>(*box);
498 : const bool element_is_interior = element.external_boundaries().empty();
499 : constexpr bool subcell_enabled_at_external_boundary =
500 : metavariables::SubcellOptions::subcell_enabled_at_external_boundary;
501 :
502 : ASSERT(element_is_interior or subcell_enabled_at_external_boundary,
503 : "Subcell time derivative is called at a boundary element while "
504 : "using subcell is disabled at external boundaries."
505 : "ElementID "
506 : << element.id());
507 :
508 : const fd::Reconstructor<System>& recons =
509 : db::get<fd::Tags::Reconstructor<System>>(*box);
510 : // If the element has external boundaries and subcell is enabled for
511 : // boundary elements, compute FD ghost data with a given boundary condition.
512 : if constexpr (subcell_enabled_at_external_boundary) {
513 : if (not element_is_interior) {
514 : fd::BoundaryConditionGhostData<System>::apply(box, element, recons);
515 : }
516 : }
517 : std::optional<std::array<gsl::span<std::uint8_t>, 3>>
518 : reconstruction_order{};
519 :
520 : if (const auto& filter_options =
521 : db::get<grmhd::GhValenciaDivClean::fd::Tags::FilterOptions>(*box);
522 : filter_options.spacetime_dissipation.has_value()) {
523 : db::mutate<evolved_vars_tag>(
524 : [&filter_options, &recons, &subcell_mesh](const auto evolved_vars_ptr,
525 : const auto& ghost_data) {
526 : typename evolved_vars_tag::type filtered_vars = *evolved_vars_ptr;
527 : // $(recons.ghost_zone_size() - 1) * 2 + 1$ => always use highest
528 : // order dissipation filter possible.
529 : grmhd::GhValenciaDivClean::fd::spacetime_kreiss_oliger_filter(
530 : make_not_null(&filtered_vars), *evolved_vars_ptr, ghost_data,
531 : subcell_mesh, 2 * recons.ghost_zone_size(),
532 : filter_options.spacetime_dissipation.value());
533 : *evolved_vars_ptr = filtered_vars;
534 : },
535 : box,
536 : db::get<evolution::dg::subcell::Tags::GhostDataForReconstruction<3>>(
537 : *box));
538 : }
539 :
540 : // Velocity of the moving mesh on the dg grid, if applicable.
541 : const std::optional<tnsr::I<DataVector, 3, Frame::Inertial>>&
542 : mesh_velocity_dg = db::get<domain::Tags::MeshVelocity<3>>(*box);
543 : // Inverse jacobian, to be projected on faces
544 : const auto& inv_jacobian_dg =
545 : db::get<domain::Tags::InverseJacobian<3, Frame::ElementLogical,
546 : Frame::Inertial>>(*box);
547 : const auto& det_inv_jacobian_dg = db::get<
548 : domain::Tags::DetInvJacobian<Frame::ElementLogical, Frame::Inertial>>(
549 : *box);
550 :
551 : // GH+GRMHD is a bit different.
552 : // 1. Compute GH time derivative, since this will also give us lapse, shift,
553 : // etc. that we need to reconstruct.
554 : // 2. Compute d_t Pi_{ab} source terms from MHD (or do we wait until post
555 : // MHD source terms?)
556 : // 3. Reconstruct MHD+spacetime vars to interfaces
557 : // 4. Compute MHD time derivatives.
558 : //
559 : // Compute FD GH derivatives with neighbor data
560 : // Use highest possible FD order for number of GZ, 2 * (ghost_zone_size)
561 : const auto& evolved_vars = db::get<evolved_vars_tag>(*box);
562 : Variables<db::wrap_tags_in<::Tags::deriv, gradients_tags, tmpl::size_t<3>,
563 : Frame::Inertial>>
564 : cell_centered_gh_derivs{num_pts};
565 : grmhd::GhValenciaDivClean::fd::spacetime_derivatives<System>(
566 : make_not_null(&cell_centered_gh_derivs), evolved_vars,
567 : db::get<evolution::dg::subcell::Tags::GhostDataForReconstruction<3>>(
568 : *box),
569 : recons.ghost_zone_size() * 2, subcell_mesh,
570 : cell_centered_logical_to_inertial_inv_jacobian);
571 :
572 : // Now package the data and compute the correction
573 : //
574 : // Note: Assumes a the GH and GRMHD corrections can be invoked separately.
575 : // This is reasonable since the systems are a tensor product system.
576 : const auto& base_boundary_correction =
577 : db::get<evolution::Tags::BoundaryCorrection>(*box);
578 : using derived_boundary_corrections =
579 : tmpl::at<typename metavariables::factory_creation::factory_classes,
580 : evolution::BoundaryCorrection>;
581 : std::array<Variables<grmhd_evolved_vars_tags>, 3> boundary_corrections{};
582 : call_with_dynamic_type<void, derived_boundary_corrections>(
583 : &base_boundary_correction, [&](const auto* gh_grmhd_correction) {
584 : // Need the GH packaged tags to avoid projecting them.
585 : using gh_dg_package_field_tags = typename std::decay_t<
586 : decltype(gh_grmhd_correction
587 : ->gh_correction())>::dg_package_field_tags;
588 : // Only apply correction to GRMHD variables.
589 : const auto& boundary_correction =
590 : gh_grmhd_correction->valencia_correction();
591 : using DerivedCorrection = std::decay_t<decltype(boundary_correction)>;
592 : using dg_package_data_temporary_tags =
593 : typename DerivedCorrection::dg_package_data_temporary_tags;
594 :
595 : using dg_package_data_argument_tags = tmpl::append<
596 : evolved_vars_tags, recons_prim_tags, fluxes_tags,
597 : tmpl::remove_duplicates<tmpl::push_back<
598 : dg_package_data_temporary_tags,
599 : gr::Tags::SpatialMetric<DataVector, 3>,
600 : gr::Tags::SqrtDetSpatialMetric<DataVector>,
601 : gr::Tags::InverseSpatialMetric<DataVector, 3>,
602 : evolution::dg::Actions::detail::NormalVector<3>>>>;
603 :
604 : // Computed prims and cons on face via reconstruction
605 : auto package_data_argvars_lower_face = make_array<3>(
606 : Variables<dg_package_data_argument_tags>(reconstructed_num_pts));
607 : auto package_data_argvars_upper_face = make_array<3>(
608 : Variables<dg_package_data_argument_tags>(reconstructed_num_pts));
609 :
610 : // Reconstruct data to the face
611 : call_with_dynamic_type<
612 : void, typename grmhd::GhValenciaDivClean::fd::Reconstructor<
613 : System>::creatable_classes>(
614 : &recons, [&box, &package_data_argvars_lower_face,
615 : &package_data_argvars_upper_face,
616 : &reconstruction_order](const auto& reconstructor) {
617 : using ReconstructorType =
618 : std::decay_t<decltype(*reconstructor)>;
619 : db::apply<
620 : typename ReconstructorType::reconstruction_argument_tags>(
621 : [&package_data_argvars_lower_face,
622 : &package_data_argvars_upper_face, &reconstructor,
623 : &reconstruction_order](const auto&... args) {
624 : if constexpr (ReconstructorType::use_adaptive_order) {
625 : reconstructor->reconstruct(
626 : make_not_null(&package_data_argvars_lower_face),
627 : make_not_null(&package_data_argvars_upper_face),
628 : make_not_null(&reconstruction_order), args...);
629 : } else {
630 : (void)reconstruction_order;
631 : reconstructor->reconstruct(
632 : make_not_null(&package_data_argvars_lower_face),
633 : make_not_null(&package_data_argvars_upper_face),
634 : args...);
635 : }
636 : },
637 : *box);
638 : });
639 :
640 : using dg_package_field_tags =
641 : typename DerivedCorrection::dg_package_field_tags;
642 : // Allocated outside for loop to reduce allocations
643 : Variables<dg_package_field_tags> upper_packaged_data{
644 : reconstructed_num_pts};
645 : Variables<dg_package_field_tags> lower_packaged_data{
646 : reconstructed_num_pts};
647 :
648 : // Compute fluxes on faces
649 : for (size_t i = 0; i < 3; ++i) {
650 : auto& vars_upper_face = gsl::at(package_data_argvars_upper_face, i);
651 : auto& vars_lower_face = gsl::at(package_data_argvars_lower_face, i);
652 : grmhd::ValenciaDivClean::subcell::compute_fluxes(
653 : make_not_null(&vars_upper_face));
654 : grmhd::ValenciaDivClean::subcell::compute_fluxes(
655 : make_not_null(&vars_lower_face));
656 :
657 : // Build extents of mesh shifted by half a grid cell in direction i
658 : const unsigned long& num_subcells_1d = subcell_mesh.extents(0);
659 : Index<3> face_mesh_extents(std::array<size_t, 3>{
660 : num_subcells_1d, num_subcells_1d, num_subcells_1d});
661 : face_mesh_extents[i] = num_subcells_1d + 1;
662 : // Add moving mesh corrections to the fluxes, if needed
663 : std::optional<tnsr::I<DataVector, 3, Frame::Inertial>>
664 : mesh_velocity_on_face = {};
665 : if (mesh_velocity_dg.has_value()) {
666 : // Project mesh velocity on face mesh.
667 : // Can we get away with only doing the normal component? It
668 : // is also used in the packaged data...
669 : mesh_velocity_on_face = tnsr::I<DataVector, 3, Frame::Inertial>{
670 : reconstructed_num_pts};
671 : for (size_t j = 0; j < 3; j++) {
672 : // j^th component of the velocity on the i^th directed face
673 : mesh_velocity_on_face.value().get(j) =
674 : evolution::dg::subcell::fd::project_to_faces(
675 : mesh_velocity_dg.value().get(j), dg_mesh,
676 : face_mesh_extents, i);
677 : }
678 :
679 : tmpl::for_each<grmhd_evolved_vars_tags>(
680 : [&vars_upper_face, &vars_lower_face,
681 : &mesh_velocity_on_face](auto tag_v) {
682 : using tag = tmpl::type_from<decltype(tag_v)>;
683 : using flux_tag =
684 : ::Tags::Flux<tag, tmpl::size_t<3>, Frame::Inertial>;
685 : using FluxTensor = typename flux_tag::type;
686 : const auto& var_upper = get<tag>(vars_upper_face);
687 : const auto& var_lower = get<tag>(vars_lower_face);
688 : auto& flux_upper = get<flux_tag>(vars_upper_face);
689 : auto& flux_lower = get<flux_tag>(vars_lower_face);
690 : for (size_t storage_index = 0;
691 : storage_index < var_upper.size(); ++storage_index) {
692 : const auto tensor_index =
693 : var_upper.get_tensor_index(storage_index);
694 : for (size_t j = 0; j < 3; j++) {
695 : const auto flux_storage_index =
696 : FluxTensor::get_storage_index(
697 : prepend(tensor_index, j));
698 : flux_upper[flux_storage_index] -=
699 : mesh_velocity_on_face.value().get(j) *
700 : var_upper[storage_index];
701 : flux_lower[flux_storage_index] -=
702 : mesh_velocity_on_face.value().get(j) *
703 : var_lower[storage_index];
704 : }
705 : }
706 : });
707 : }
708 :
709 : // Normal vectors in curved spacetime normalized by inverse
710 : // spatial metric. Since we assume a Cartesian grid, this is
711 : // relatively easy. Note that we use the sign convention on
712 : // the normal vectors to be compatible with DG.
713 : //
714 : // Note that these normal vectors are on all faces inside the DG
715 : // element since there are a bunch of subcells. We don't use the
716 : // NormalCovectorAndMagnitude tag in the DataBox right now to avoid
717 : // conflicts with the DG solver. We can explore in the future if
718 : // it's possible to reuse that allocation.
719 : //
720 : // The unnormalized normal vector is
721 : // n_j = d \xi^{\hat i}/dx^j
722 : // with "i" the current face.
723 : tnsr::i<DataVector, 3, Frame::Inertial> lower_outward_conormal{
724 : reconstructed_num_pts, 0.0};
725 : for (size_t j = 0; j < 3; j++) {
726 : lower_outward_conormal.get(j) =
727 : evolution::dg::subcell::fd::project_to_faces(
728 : inv_jacobian_dg.get(i, j), dg_mesh, face_mesh_extents, i);
729 : }
730 : const auto det_inv_jacobian_face =
731 : evolution::dg::subcell::fd::project_to_faces(
732 : get(det_inv_jacobian_dg), dg_mesh, face_mesh_extents, i);
733 :
734 : const Scalar<DataVector> normalization{sqrt(get(
735 : dot_product(lower_outward_conormal, lower_outward_conormal,
736 : get<gr::Tags::InverseSpatialMetric<DataVector, 3>>(
737 : vars_upper_face))))};
738 : for (size_t j = 0; j < 3; j++) {
739 : lower_outward_conormal.get(j) =
740 : lower_outward_conormal.get(j) / get(normalization);
741 : }
742 :
743 : tnsr::i<DataVector, 3, Frame::Inertial> upper_outward_conormal{
744 : reconstructed_num_pts, 0.0};
745 : for (size_t j = 0; j < 3; j++) {
746 : upper_outward_conormal.get(j) = -lower_outward_conormal.get(j);
747 : }
748 : // Note: we probably should compute the normal vector in addition to
749 : // the co-vector. Not a huge issue since we'll get an FPE right now
750 : // if it's used by a Riemann solver.
751 :
752 : // Compute the packaged data
753 : using dg_package_data_projected_tags = tmpl::append<
754 : grmhd_evolved_vars_tags, fluxes_tags,
755 : dg_package_data_temporary_tags,
756 : typename DerivedCorrection::dg_package_data_primitive_tags>;
757 : evolution::dg::Actions::detail::dg_package_data<System>(
758 : make_not_null(&upper_packaged_data),
759 : dynamic_cast<const DerivedCorrection&>(boundary_correction),
760 : vars_upper_face, upper_outward_conormal, mesh_velocity_on_face,
761 : *box, typename DerivedCorrection::dg_package_data_volume_tags{},
762 : dg_package_data_projected_tags{});
763 :
764 : evolution::dg::Actions::detail::dg_package_data<System>(
765 : make_not_null(&lower_packaged_data),
766 : dynamic_cast<const DerivedCorrection&>(boundary_correction),
767 : vars_lower_face, lower_outward_conormal, mesh_velocity_on_face,
768 : *box, typename DerivedCorrection::dg_package_data_volume_tags{},
769 : dg_package_data_projected_tags{});
770 :
771 : // Now need to check if any of our neighbors are doing DG,
772 : // because if so then we need to use whatever boundary data
773 : // they sent instead of what we computed locally.
774 : //
775 : // Note: We could check this beforehand to avoid the extra
776 : // work of reconstruction and flux computations at the
777 : // boundaries.
778 : evolution::dg::subcell::correct_package_data<true>(
779 : make_not_null(&lower_packaged_data),
780 : make_not_null(&upper_packaged_data), i, element, subcell_mesh,
781 : db::get<evolution::dg::Tags::MortarData<3>>(*box),
782 : Variables<gh_dg_package_field_tags>::
783 : number_of_independent_components);
784 :
785 : // Compute the corrections on the faces. We only need to
786 : // compute this once because we can just flip the normal
787 : // vectors then
788 : gsl::at(boundary_corrections, i).initialize(reconstructed_num_pts);
789 : evolution::dg::subcell::compute_boundary_terms(
790 : make_not_null(&gsl::at(boundary_corrections, i)),
791 : dynamic_cast<const DerivedCorrection&>(boundary_correction),
792 : upper_packaged_data, lower_packaged_data, db::as_access(*box),
793 : typename DerivedCorrection::dg_boundary_terms_volume_tags{});
794 : // We need to multiply by the normal vector normalization
795 : gsl::at(boundary_corrections, i) *= get(normalization);
796 : // Also multiply by determinant of Jacobian, following Eq.(34)
797 : // of 2109.11645
798 : gsl::at(boundary_corrections, i) *= 1.0 / det_inv_jacobian_face;
799 : }
800 : });
801 :
802 : // Now compute the actual time derivatives.
803 : using gh_variables_tags =
804 : typename System::gh_system::variables_tag::tags_list;
805 : using gh_gradient_tags = typename TimeDerivativeTerms::gh_gradient_tags;
806 : using gh_temporary_tags = typename TimeDerivativeTerms::gh_temp_tags;
807 : using gh_extra_tags =
808 : tmpl::list<gr::Tags::SpacetimeMetric<DataVector, 3>,
809 : gh::Tags::Pi<DataVector, 3>, gh::Tags::Phi<DataVector, 3>,
810 : ::gh::Tags::ConstraintGamma0, ::gh::Tags::ConstraintGamma1,
811 : ::gh::Tags::ConstraintGamma2>;
812 : using grmhd_source_tags =
813 : tmpl::transform<ValenciaDivClean::ComputeSources::return_tags,
814 : tmpl::bind<db::remove_tag_prefix, tmpl::_1>>;
815 : using grmhd_source_argument_tags =
816 : ValenciaDivClean::ComputeSources::argument_tags;
817 : detail::ComputeTimeDerivImpl<
818 : gh_variables_tags, gh_temporary_tags, gh_gradient_tags, gh_extra_tags,
819 : grmhd_evolved_vars_tags, grmhd_source_tags, grmhd_source_argument_tags,
820 : System>::apply(box, inertial_coords,
821 : db::get<evolution::dg::subcell::fd::Tags::
822 : DetInverseJacobianLogicalToInertial>(*box),
823 : cell_centered_logical_to_inertial_inv_jacobian,
824 : one_over_delta_xi, boundary_corrections,
825 : cell_centered_gh_derivs);
826 : evolution::dg::subcell::store_reconstruction_order_in_databox(
827 : box, reconstruction_order);
828 : }
829 : };
830 : } // namespace grmhd::GhValenciaDivClean::subcell
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