xref: /honee/problems/newtonian.c (revision 0c608af58d6c66f4fcbe6fff5e0f907584234584)
1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors.
2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause
3 
4 /// @file
5 /// Utility functions for setting up problems using the Newtonian Qfunction
6 
7 #include "../qfunctions/newtonian.h"
8 
9 #include <ceed.h>
10 #include <petscdm.h>
11 
12 #include <navierstokes.h>
13 
14 const char *const StateVariables[]     = {"CONSERVATIVE", "PRIMITIVE", "ENTROPY", "StateVariable", "STATEVAR_", NULL};
15 const char *const StabilizationTypes[] = {"NONE", "SU", "SUPG", "StabilizationType", "STAB_", NULL};
16 
17 static PetscErrorCode UnitTests_Newtonian(Honee honee, NewtonianIGProperties gas);
18 
19 static PetscErrorCode PRINT_NEWTONIAN(Honee honee, ProblemData problem, AppCtx app_ctx) {
20   MPI_Comm                 comm = honee->comm;
21   Ceed                     ceed = honee->ceed;
22   NewtonianIdealGasContext newt_ctx;
23 
24   PetscFunctionBeginUser;
25   PetscCallCeed(ceed, CeedQFunctionContextGetData(problem->apply_vol_rhs.qfctx, CEED_MEM_HOST, &newt_ctx));
26   PetscCall(PetscPrintf(comm,
27                         "  Problem:\n"
28                         "    Problem Name                       : %s\n"
29                         "    Stabilization                      : %s\n",
30                         app_ctx->problem_name, StabilizationTypes[newt_ctx->stabilization]));
31   PetscCallCeed(ceed, CeedQFunctionContextRestoreData(problem->apply_vol_rhs.qfctx, &newt_ctx));
32   PetscFunctionReturn(PETSC_SUCCESS);
33 }
34 
35 // @brief Create CeedOperator for stabilized mass KSP for explicit timestepping
36 //
37 // Only used for SUPG stabilization
38 PetscErrorCode CreateKSPMassOperator_NewtonianStabilized(Honee honee, CeedOperator *op_mass) {
39   Ceed                 ceed = honee->ceed;
40   CeedInt              num_comp_q, q_data_size;
41   CeedQFunction        qf_mass;
42   CeedElemRestriction  elem_restr_q, elem_restr_qd;
43   CeedBasis            basis_q;
44   CeedVector           q_data;
45   CeedQFunctionContext qfctx = NULL;
46   PetscInt             dim   = 3;
47 
48   PetscFunctionBeginUser;
49   {  // Get restriction and basis from the RHS function
50     CeedOperator     *sub_ops;
51     CeedOperatorField op_field;
52     PetscInt          sub_op_index = 0;  // will be 0 for the volume op
53 
54     PetscCallCeed(ceed, CeedCompositeOperatorGetSubList(honee->op_rhs_ctx->op, &sub_ops));
55     PetscCallCeed(ceed, CeedOperatorGetFieldByName(sub_ops[sub_op_index], "q", &op_field));
56     PetscCallCeed(ceed, CeedOperatorFieldGetData(op_field, NULL, &elem_restr_q, &basis_q, NULL));
57     PetscCallCeed(ceed, CeedOperatorGetFieldByName(sub_ops[sub_op_index], "qdata", &op_field));
58     PetscCallCeed(ceed, CeedOperatorFieldGetData(op_field, NULL, &elem_restr_qd, NULL, &q_data));
59 
60     PetscCallCeed(ceed, CeedOperatorGetContext(sub_ops[sub_op_index], &qfctx));
61   }
62 
63   PetscCallCeed(ceed, CeedElemRestrictionGetNumComponents(elem_restr_q, &num_comp_q));
64   PetscCallCeed(ceed, CeedElemRestrictionGetNumComponents(elem_restr_qd, &q_data_size));
65 
66   PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, MassFunction_Newtonian_Conserv, MassFunction_Newtonian_Conserv_loc, &qf_mass));
67 
68   PetscCallCeed(ceed, CeedQFunctionSetContext(qf_mass, qfctx));
69   PetscCallCeed(ceed, CeedQFunctionSetUserFlopsEstimate(qf_mass, 0));
70   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_mass, "q_dot", 5, CEED_EVAL_INTERP));
71   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_mass, "q", 5, CEED_EVAL_INTERP));
72   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_mass, "qdata", q_data_size, CEED_EVAL_NONE));
73   PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_mass, "v", 5, CEED_EVAL_INTERP));
74   PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_mass, "Grad_v", 5 * dim, CEED_EVAL_GRAD));
75 
76   PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_mass, NULL, NULL, op_mass));
77   PetscCallCeed(ceed, CeedOperatorSetName(*op_mass, "RHS Mass Operator, Newtonian Stabilized"));
78   PetscCallCeed(ceed, CeedOperatorSetField(*op_mass, "q_dot", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
79   PetscCallCeed(ceed, CeedOperatorSetField(*op_mass, "q", elem_restr_q, basis_q, honee->q_ceed));
80   PetscCallCeed(ceed, CeedOperatorSetField(*op_mass, "qdata", elem_restr_qd, CEED_BASIS_NONE, q_data));
81   PetscCallCeed(ceed, CeedOperatorSetField(*op_mass, "v", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
82   PetscCallCeed(ceed, CeedOperatorSetField(*op_mass, "Grad_v", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
83 
84   PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_q));
85   PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qd));
86   PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
87   PetscCallCeed(ceed, CeedBasisDestroy(&basis_q));
88   PetscCallCeed(ceed, CeedQFunctionContextDestroy(&qfctx));
89   PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_mass));
90   PetscFunctionReturn(PETSC_SUCCESS);
91 }
92 
93 /**
94   @brief Create RHS CeedOperator for direct projection of divergence of diffusive flux
95 
96   @param[in]  honee          `Honee` context
97   @param[in]  diff_flux_proj `DivDiffFluxProjectionData` object
98   @param[out] op_rhs         Operator to calculate the RHS of the L^2 projection
99 **/
100 static PetscErrorCode DivDiffFluxProjectionCreateRHS_Direct_NS(Honee honee, DivDiffFluxProjectionData diff_flux_proj, CeedOperator *op_rhs) {
101   Ceed                 ceed       = honee->ceed;
102   NodalProjectionData  projection = diff_flux_proj->projection;
103   CeedInt              num_comp_q;
104   PetscInt             dim, label_value = 0;
105   DMLabel              domain_label    = NULL;
106   CeedQFunctionContext newtonian_qfctx = NULL;
107 
108   PetscFunctionBeginUser;
109   // -- Get Pre-requisite things
110   PetscCall(DMGetDimension(projection->dm, &dim));
111   PetscCallCeed(ceed, CeedBasisGetNumComponents(honee->basis_q, &num_comp_q));
112 
113   {  // Get newtonian QF context
114     CeedOperator *sub_ops, main_op = honee->op_ifunction ? honee->op_ifunction : honee->op_rhs_ctx->op;
115     PetscInt      sub_op_index = 0;  // will be 0 for the volume op
116 
117     PetscCallCeed(ceed, CeedCompositeOperatorGetSubList(main_op, &sub_ops));
118     PetscCallCeed(ceed, CeedOperatorGetContext(sub_ops[sub_op_index], &newtonian_qfctx));
119   }
120   PetscCallCeed(ceed, CeedCompositeOperatorCreate(ceed, op_rhs));
121   {  // Add the volume integral CeedOperator
122     CeedQFunction       qf_rhs_volume;
123     CeedOperator        op_rhs_volume;
124     CeedVector          q_data;
125     CeedElemRestriction elem_restr_qd, elem_restr_diff_flux_volume = NULL;
126     CeedBasis           basis_diff_flux = NULL;
127     CeedInt             q_data_size;
128 
129     PetscCall(DivDiffFluxProjectionGetOperatorFieldData(diff_flux_proj, &elem_restr_diff_flux_volume, &basis_diff_flux, NULL, NULL));
130     PetscCall(QDataGet(ceed, projection->dm, domain_label, label_value, honee->elem_restr_x, honee->basis_x, honee->x_coord, &elem_restr_qd, &q_data,
131                        &q_data_size));
132     switch (honee->phys->state_var) {
133       case STATEVAR_PRIMITIVE:
134         PetscCallCeed(ceed,
135                       CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxVolumeRHS_NS_Prim, DivDiffusiveFluxVolumeRHS_NS_Prim_loc, &qf_rhs_volume));
136         break;
137       case STATEVAR_CONSERVATIVE:
138         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxVolumeRHS_NS_Conserv, DivDiffusiveFluxVolumeRHS_NS_Conserv_loc,
139                                                         &qf_rhs_volume));
140         break;
141       case STATEVAR_ENTROPY:
142         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxVolumeRHS_NS_Entropy, DivDiffusiveFluxVolumeRHS_NS_Entropy_loc,
143                                                         &qf_rhs_volume));
144         break;
145     }
146 
147     PetscCallCeed(ceed, CeedQFunctionSetContext(qf_rhs_volume, newtonian_qfctx));
148     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_volume, "q", num_comp_q, CEED_EVAL_INTERP));
149     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_volume, "Grad_q", num_comp_q * dim, CEED_EVAL_GRAD));
150     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_volume, "qdata", q_data_size, CEED_EVAL_NONE));
151     PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_rhs_volume, "diffusive flux RHS", projection->num_comp * dim, CEED_EVAL_GRAD));
152 
153     PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_rhs_volume, NULL, NULL, &op_rhs_volume));
154     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
155     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "Grad_q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
156     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "qdata", elem_restr_qd, CEED_BASIS_NONE, q_data));
157     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "diffusive flux RHS", elem_restr_diff_flux_volume, basis_diff_flux, CEED_VECTOR_ACTIVE));
158 
159     PetscCallCeed(ceed, CeedCompositeOperatorAddSub(*op_rhs, op_rhs_volume));
160 
161     PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
162     PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qd));
163     PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_diff_flux_volume));
164     PetscCallCeed(ceed, CeedBasisDestroy(&basis_diff_flux));
165     PetscCallCeed(ceed, CeedOperatorDestroy(&op_rhs_volume));
166     PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_rhs_volume));
167   }
168 
169   {  // Add the boundary integral CeedOperator
170     CeedQFunction qf_rhs_boundary;
171     DMLabel       face_sets_label;
172     PetscInt      num_face_set_values, *face_set_values;
173     CeedInt       q_data_size;
174 
175     // -- Build RHS operator
176     switch (honee->phys->state_var) {
177       case STATEVAR_PRIMITIVE:
178         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxBoundaryRHS_NS_Prim, DivDiffusiveFluxBoundaryRHS_NS_Prim_loc,
179                                                         &qf_rhs_boundary));
180         break;
181       case STATEVAR_CONSERVATIVE:
182         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxBoundaryRHS_NS_Conserv, DivDiffusiveFluxBoundaryRHS_NS_Conserv_loc,
183                                                         &qf_rhs_boundary));
184         break;
185       case STATEVAR_ENTROPY:
186         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxBoundaryRHS_NS_Entropy, DivDiffusiveFluxBoundaryRHS_NS_Entropy_loc,
187                                                         &qf_rhs_boundary));
188         break;
189     }
190 
191     PetscCall(QDataBoundaryGradientGetNumComponents(honee->dm, &q_data_size));
192     PetscCallCeed(ceed, CeedQFunctionSetContext(qf_rhs_boundary, newtonian_qfctx));
193     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_boundary, "q", num_comp_q, CEED_EVAL_INTERP));
194     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_boundary, "Grad_q", num_comp_q * dim, CEED_EVAL_GRAD));
195     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_boundary, "qdata", q_data_size, CEED_EVAL_NONE));
196     PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_rhs_boundary, "diffusive flux RHS", projection->num_comp, CEED_EVAL_INTERP));
197 
198     PetscCall(DMGetLabel(projection->dm, "Face Sets", &face_sets_label));
199     PetscCall(DMLabelCreateGlobalValueArray(projection->dm, face_sets_label, &num_face_set_values, &face_set_values));
200     for (PetscInt f = 0; f < num_face_set_values; f++) {
201       DMLabel  face_orientation_label;
202       PetscInt num_orientations_values, *orientation_values;
203 
204       {
205         char *face_orientation_label_name;
206 
207         PetscCall(DMPlexCreateFaceLabel(projection->dm, face_set_values[f], &face_orientation_label_name));
208         PetscCall(DMGetLabel(projection->dm, face_orientation_label_name, &face_orientation_label));
209         PetscCall(PetscFree(face_orientation_label_name));
210       }
211       PetscCall(DMLabelCreateGlobalValueArray(projection->dm, face_orientation_label, &num_orientations_values, &orientation_values));
212       for (PetscInt o = 0; o < num_orientations_values; o++) {
213         CeedOperator        op_rhs_boundary;
214         CeedBasis           basis_q, basis_diff_flux_boundary;
215         CeedElemRestriction elem_restr_qdata, elem_restr_q, elem_restr_diff_flux_boundary;
216         CeedVector          q_data;
217         CeedInt             q_data_size;
218         PetscInt            orientation = orientation_values[o], dm_field_q = 0, height_cell = 0, height_face = 1;
219 
220         PetscCall(DMPlexCeedElemRestrictionCreate(ceed, honee->dm, face_orientation_label, orientation, height_cell, dm_field_q, &elem_restr_q));
221         PetscCall(DMPlexCeedBasisCellToFaceCreate(ceed, honee->dm, face_orientation_label, orientation, orientation, dm_field_q, &basis_q));
222         PetscCall(DMPlexCeedElemRestrictionCreate(ceed, projection->dm, face_orientation_label, orientation, height_face, 0,
223                                                   &elem_restr_diff_flux_boundary));
224         PetscCall(CreateBasisFromPlex(ceed, projection->dm, face_orientation_label, orientation, height_face, 0, &basis_diff_flux_boundary));
225         PetscCall(
226             QDataBoundaryGradientGet(ceed, honee->dm, face_orientation_label, orientation, honee->x_coord, &elem_restr_qdata, &q_data, &q_data_size));
227 
228         PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_rhs_boundary, NULL, NULL, &op_rhs_boundary));
229         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "q", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
230         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "Grad_q", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
231         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "qdata", elem_restr_qdata, CEED_BASIS_NONE, q_data));
232         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "diffusive flux RHS", elem_restr_diff_flux_boundary, basis_diff_flux_boundary,
233                                                  CEED_VECTOR_ACTIVE));
234 
235         PetscCallCeed(ceed, CeedCompositeOperatorAddSub(*op_rhs, op_rhs_boundary));
236 
237         PetscCallCeed(ceed, CeedOperatorDestroy(&op_rhs_boundary));
238         PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qdata));
239         PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_q));
240         PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_diff_flux_boundary));
241         PetscCallCeed(ceed, CeedBasisDestroy(&basis_q));
242         PetscCallCeed(ceed, CeedBasisDestroy(&basis_diff_flux_boundary));
243         PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
244       }
245       PetscCall(PetscFree(orientation_values));
246     }
247     PetscCall(PetscFree(face_set_values));
248     PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_rhs_boundary));
249   }
250 
251   PetscCallCeed(ceed, CeedQFunctionContextDestroy(&newtonian_qfctx));
252   PetscFunctionReturn(PETSC_SUCCESS);
253 }
254 
255 /**
256   @brief Create RHS CeedOperator for indirect projection of divergence of diffusive flux
257 
258   @param[in]  honee          `Honee` context
259   @param[in]  diff_flux_proj `DivDiffFluxProjectionData` object
260   @param[out] op_rhs         Operator to calculate the RHS of the L^2 projection
261 **/
262 static PetscErrorCode DivDiffFluxProjectionCreateRHS_Indirect_NS(Honee honee, DivDiffFluxProjectionData diff_flux_proj, CeedOperator *op_rhs) {
263   Ceed                 ceed       = honee->ceed;
264   NodalProjectionData  projection = diff_flux_proj->projection;
265   CeedBasis            basis_diff_flux;
266   CeedElemRestriction  elem_restr_diff_flux, elem_restr_qd;
267   CeedVector           q_data;
268   CeedInt              num_comp_q, q_data_size;
269   PetscInt             dim;
270   PetscInt             label_value = 0, height = 0, dm_field = 0;
271   DMLabel              domain_label = NULL;
272   CeedQFunction        qf_rhs;
273   CeedQFunctionContext newtonian_qfctx = NULL;
274 
275   PetscFunctionBeginUser;
276   PetscCall(DMGetDimension(projection->dm, &dim));
277   PetscCallCeed(ceed, CeedBasisGetNumComponents(honee->basis_q, &num_comp_q));
278 
279   {  // Get newtonian QF context
280     CeedOperator *sub_ops, main_op = honee->op_ifunction ? honee->op_ifunction : honee->op_rhs_ctx->op;
281     PetscInt      sub_op_index = 0;  // will be 0 for the volume op
282 
283     PetscCallCeed(ceed, CeedCompositeOperatorGetSubList(main_op, &sub_ops));
284     PetscCallCeed(ceed, CeedOperatorGetContext(sub_ops[sub_op_index], &newtonian_qfctx));
285   }
286   PetscCall(DMPlexCeedElemRestrictionCreate(ceed, projection->dm, domain_label, label_value, height, dm_field, &elem_restr_diff_flux));
287   PetscCall(CreateBasisFromPlex(ceed, projection->dm, domain_label, label_value, height, dm_field, &basis_diff_flux));
288   PetscCall(QDataGet(ceed, projection->dm, domain_label, label_value, honee->elem_restr_x, honee->basis_x, honee->x_coord, &elem_restr_qd, &q_data,
289                      &q_data_size));
290 
291   switch (honee->phys->state_var) {
292     case STATEVAR_PRIMITIVE:
293       PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DiffusiveFluxRHS_NS_Prim, DiffusiveFluxRHS_NS_Prim_loc, &qf_rhs));
294       break;
295     case STATEVAR_CONSERVATIVE:
296       PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DiffusiveFluxRHS_NS_Conserv, DiffusiveFluxRHS_NS_Conserv_loc, &qf_rhs));
297       break;
298     case STATEVAR_ENTROPY:
299       PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DiffusiveFluxRHS_NS_Entropy, DiffusiveFluxRHS_NS_Entropy_loc, &qf_rhs));
300       break;
301   }
302 
303   PetscCallCeed(ceed, CeedQFunctionSetContext(qf_rhs, newtonian_qfctx));
304   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs, "q", num_comp_q, CEED_EVAL_INTERP));
305   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs, "Grad_q", num_comp_q * dim, CEED_EVAL_GRAD));
306   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs, "qdata", q_data_size, CEED_EVAL_NONE));
307   PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_rhs, "F_diff RHS", projection->num_comp, CEED_EVAL_INTERP));
308 
309   PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_rhs, NULL, NULL, op_rhs));
310   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
311   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "Grad_q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
312   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "qdata", elem_restr_qd, CEED_BASIS_NONE, q_data));
313   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "F_diff RHS", elem_restr_diff_flux, basis_diff_flux, CEED_VECTOR_ACTIVE));
314 
315   PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_rhs));
316   PetscCallCeed(ceed, CeedQFunctionContextDestroy(&newtonian_qfctx));
317   PetscCallCeed(ceed, CeedBasisDestroy(&basis_diff_flux));
318   PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
319   PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qd));
320   PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_diff_flux));
321   PetscFunctionReturn(PETSC_SUCCESS);
322 }
323 
324 static PetscErrorCode BoundaryIntegralBCSetup_CreateIFunctionQF(BCDefinition bc_def, CeedQFunction *qf) {
325   HoneeBCStruct honee_bc;
326 
327   PetscFunctionBeginUser;
328   PetscCall(BCDefinitionGetContext(bc_def, &honee_bc));
329   Honee honee = honee_bc->honee;
330 
331   switch (honee->phys->state_var) {
332     case STATEVAR_CONSERVATIVE:
333       PetscCall(HoneeBCCreateIFunctionQF(bc_def, BoundaryIntegral_Conserv, BoundaryIntegral_Conserv_loc, honee_bc->qfctx, qf));
334       break;
335     case STATEVAR_PRIMITIVE:
336       PetscCall(HoneeBCCreateIFunctionQF(bc_def, BoundaryIntegral_Prim, BoundaryIntegral_Prim_loc, honee_bc->qfctx, qf));
337       break;
338     case STATEVAR_ENTROPY:
339       PetscCall(HoneeBCCreateIFunctionQF(bc_def, BoundaryIntegral_Entropy, BoundaryIntegral_Entropy_loc, honee_bc->qfctx, qf));
340       break;
341   }
342   PetscFunctionReturn(PETSC_SUCCESS);
343 }
344 
345 static PetscErrorCode BoundaryIntegralBCSetup_CreateIJacobianQF(BCDefinition bc_def, CeedQFunction *qf) {
346   HoneeBCStruct honee_bc;
347 
348   PetscFunctionBeginUser;
349   PetscCall(BCDefinitionGetContext(bc_def, &honee_bc));
350   Honee honee = honee_bc->honee;
351 
352   switch (honee->phys->state_var) {
353     case STATEVAR_CONSERVATIVE:
354       PetscCall(HoneeBCCreateIJacobianQF(bc_def, BoundaryIntegral_Jacobian_Conserv, BoundaryIntegral_Jacobian_Conserv_loc, honee_bc->qfctx, qf));
355       break;
356     case STATEVAR_PRIMITIVE:
357       PetscCall(HoneeBCCreateIJacobianQF(bc_def, BoundaryIntegral_Jacobian_Prim, BoundaryIntegral_Jacobian_Prim_loc, honee_bc->qfctx, qf));
358       break;
359     case STATEVAR_ENTROPY:
360       PetscCall(HoneeBCCreateIJacobianQF(bc_def, BoundaryIntegral_Jacobian_Entropy, BoundaryIntegral_Jacobian_Entropy_loc, honee_bc->qfctx, qf));
361       break;
362   }
363   PetscFunctionReturn(PETSC_SUCCESS);
364 }
365 
366 PetscErrorCode NS_NEWTONIAN_IG(ProblemData problem, DM dm, void *ctx) {
367   SetupContext             setup_context;
368   Honee                    honee  = *(Honee *)ctx;
369   CeedInt                  degree = honee->app_ctx->degree;
370   StabilizationType        stab;
371   StateVariable            state_var;
372   MPI_Comm                 comm = honee->comm;
373   Ceed                     ceed = honee->ceed;
374   PetscBool                implicit;
375   PetscBool                unit_tests;
376   NewtonianIdealGasContext newtonian_ig_ctx;
377 
378   PetscFunctionBeginUser;
379   // Option Defaults
380   const CeedScalar Cv_func[3]     = {36, 60, 128};
381   StatePrimitive   reference      = {.pressure = 1.01e5, .velocity = {0}, .temperature = 288.15};
382   CeedScalar       idl_decay_time = -1;
383   PetscCall(PetscNew(&newtonian_ig_ctx));
384   *newtonian_ig_ctx = (struct NewtonianIdealGasContext_){
385       .gas =
386           {
387                 .cv     = 717.,
388                 .cp     = 1004.,
389                 .lambda = -2. / 3.,
390                 .mu     = 1.8e-5,
391                 .k      = 0.02638,
392                 },
393       .tau_coeffs =
394           {
395                 .Ctau_t = 1.0,
396                 .Ctau_v = Cv_func[(CeedInt)Min(3, degree) - 1],
397                 .Ctau_C = 0.25 / degree,
398                 .Ctau_M = 0.25 / degree,
399                 .Ctau_E = 0.125,
400                 },
401       .g            = {0, 0, 0}, // m/s^2
402       .idl_start    = 0,
403       .idl_length   = 0,
404       .idl_pressure = reference.pressure,
405       .idl_enable   = PETSC_FALSE,
406   };
407 
408   PetscOptionsBegin(comm, NULL, "Options for Newtonian Ideal Gas based problem", NULL);
409   PetscCall(PetscOptionsEnum("-state_var", "State variables used", NULL, StateVariables, (PetscEnum)(state_var = STATEVAR_CONSERVATIVE),
410                              (PetscEnum *)&state_var, NULL));
411 
412   // Newtonian fluid properties
413   PetscCall(PetscOptionsScalar("-cv", "Heat capacity at constant volume", NULL, newtonian_ig_ctx->gas.cv, &newtonian_ig_ctx->gas.cv, NULL));
414   PetscCall(PetscOptionsScalar("-cp", "Heat capacity at constant pressure", NULL, newtonian_ig_ctx->gas.cp, &newtonian_ig_ctx->gas.cp, NULL));
415   PetscCall(PetscOptionsScalar("-lambda", "Stokes hypothesis second viscosity coefficient", NULL, newtonian_ig_ctx->gas.lambda,
416                                &newtonian_ig_ctx->gas.lambda, NULL));
417   PetscCall(PetscOptionsScalar("-mu", "Shear dynamic viscosity coefficient", NULL, newtonian_ig_ctx->gas.mu, &newtonian_ig_ctx->gas.mu, NULL));
418   PetscCall(PetscOptionsScalar("-k", "Thermal conductivity", NULL, newtonian_ig_ctx->gas.k, &newtonian_ig_ctx->gas.k, NULL));
419 
420   PetscInt  dim          = 3;
421   PetscBool given_option = PETSC_FALSE;
422   PetscCall(PetscOptionsDeprecated("-g", "-gravity", "libCEED 0.11.1", NULL));
423   PetscCall(PetscOptionsRealArray("-gravity", "Gravitational acceleration vector", NULL, newtonian_ig_ctx->g, &dim, &given_option));
424   if (given_option) PetscCheck(dim == 3, comm, PETSC_ERR_ARG_SIZ, "Gravity vector must be size 3, %" PetscInt_FMT " values given", dim);
425 
426   // Stabilization parameters
427   PetscCall(PetscOptionsEnum("-stab", "Stabilization method", NULL, StabilizationTypes, (PetscEnum)(stab = STAB_NONE), (PetscEnum *)&stab, NULL));
428   PetscCall(PetscOptionsScalar("-Ctau_t", "Stabilization time constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_t,
429                                &newtonian_ig_ctx->tau_coeffs.Ctau_t, NULL));
430   PetscCall(PetscOptionsScalar("-Ctau_v", "Stabilization viscous constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_v,
431                                &newtonian_ig_ctx->tau_coeffs.Ctau_v, NULL));
432   PetscCall(PetscOptionsScalar("-Ctau_C", "Stabilization continuity constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_C,
433                                &newtonian_ig_ctx->tau_coeffs.Ctau_C, NULL));
434   PetscCall(PetscOptionsScalar("-Ctau_M", "Stabilization momentum constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_M,
435                                &newtonian_ig_ctx->tau_coeffs.Ctau_M, NULL));
436   PetscCall(PetscOptionsScalar("-Ctau_E", "Stabilization energy constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_E,
437                                &newtonian_ig_ctx->tau_coeffs.Ctau_E, NULL));
438 
439   dim = 3;
440   PetscCall(PetscOptionsScalar("-reference_pressure", "Reference/initial pressure", NULL, reference.pressure, &reference.pressure, NULL));
441   PetscCall(PetscOptionsScalarArray("-reference_velocity", "Reference/initial velocity", NULL, reference.velocity, &dim, NULL));
442   PetscCall(PetscOptionsScalar("-reference_temperature", "Reference/initial temperature", NULL, reference.temperature, &reference.temperature, NULL));
443 
444   PetscCall(PetscOptionsBool("-implicit", "Use implicit (IFunction) formulation", NULL, implicit = PETSC_FALSE, &implicit, NULL));
445   PetscCall(PetscOptionsBool("-newtonian_unit_tests", "Run Newtonian unit tests", NULL, unit_tests = PETSC_FALSE, &unit_tests, NULL));
446   PetscCheck(!(state_var == STATEVAR_PRIMITIVE && !implicit), comm, PETSC_ERR_SUP,
447              "RHSFunction is not provided for primitive variables (use -state_var primitive only with -implicit)\n");
448 
449   // IDL Settings
450   {
451     PetscBool idl_enable = (PetscBool)newtonian_ig_ctx->idl_enable;  // Need PetscBool variable to read in from PetscOptionsScalar()
452     PetscCall(PetscOptionsScalar("-idl_decay_time", "Characteristic timescale of the pressure deviance decay. The timestep is good starting point",
453                                  NULL, idl_decay_time, &idl_decay_time, &idl_enable));
454     PetscCheck(!(idl_enable && idl_decay_time == 0), comm, PETSC_ERR_SUP, "idl_decay_time may not be equal to zero.");
455     if (idl_decay_time < 0) idl_enable = PETSC_FALSE;
456     newtonian_ig_ctx->idl_enable = idl_enable;
457 
458     PetscCall(
459         PetscOptionsScalar("-idl_start", "Start of IDL in the x direction", NULL, newtonian_ig_ctx->idl_start, &newtonian_ig_ctx->idl_start, NULL));
460     PetscCall(PetscOptionsScalar("-idl_length", "Length of IDL in the positive x direction", NULL, newtonian_ig_ctx->idl_length,
461                                  &newtonian_ig_ctx->idl_length, NULL));
462     newtonian_ig_ctx->idl_pressure = reference.pressure;
463     PetscCall(PetscOptionsScalar("-idl_pressure", "Pressure IDL uses as reference (default is `-reference_pressure`)", NULL,
464                                  newtonian_ig_ctx->idl_pressure, &newtonian_ig_ctx->idl_pressure, NULL));
465   }
466   PetscOptionsEnd();
467 
468   // ------------------------------------------------------
469   //           Set up the QFunction context
470   // ------------------------------------------------------
471   // -- Scale variables to desired units
472   Units units = honee->units;
473   newtonian_ig_ctx->gas.cv *= units->J_per_kg_K;
474   newtonian_ig_ctx->gas.cp *= units->J_per_kg_K;
475   newtonian_ig_ctx->gas.mu *= units->Pascal * units->second;
476   newtonian_ig_ctx->gas.k *= units->W_per_m_K;
477   for (PetscInt i = 0; i < 3; i++) newtonian_ig_ctx->g[i] *= units->m_per_squared_s;
478   reference.pressure *= units->Pascal;
479   for (PetscInt i = 0; i < 3; i++) reference.velocity[i] *= units->meter / units->second;
480   reference.temperature *= units->Kelvin;
481 
482   PetscReal domain_min[3], domain_max[3], domain_size[3];
483   PetscCall(DMGetBoundingBox(dm, domain_min, domain_max));
484   for (PetscInt i = 0; i < 3; i++) domain_size[i] = (domain_max[i] - domain_min[i]) * units->meter;
485 
486   // -- Solver Settings
487   honee->phys->implicit  = implicit;
488   honee->phys->state_var = state_var;
489 
490   // -- QFunction Context
491   newtonian_ig_ctx->stabilization   = stab;
492   newtonian_ig_ctx->is_implicit     = implicit;
493   newtonian_ig_ctx->state_var       = state_var;
494   newtonian_ig_ctx->idl_amplitude   = 1 / (idl_decay_time * units->second);
495   newtonian_ig_ctx->divFdiff_method = honee->app_ctx->divFdiffproj_method;
496 
497   // -- Setup Context
498   PetscCall(PetscNew(&setup_context));
499   *setup_context = (struct SetupContext_){
500       .reference = reference,
501       .newt_ctx  = *newtonian_ig_ctx,
502       .lx        = domain_size[0],
503       .ly        = domain_size[1],
504       .lz        = domain_size[2],
505       .time      = 0,
506   };
507 
508   CeedQFunctionContext ics_qfctx, newtonian_ig_qfctx;
509 
510   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &ics_qfctx));
511   PetscCallCeed(ceed, CeedQFunctionContextSetData(ics_qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*setup_context), setup_context));
512   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(ics_qfctx, CEED_MEM_HOST, FreeContextPetsc));
513   PetscCallCeed(ceed,
514                 CeedQFunctionContextRegisterDouble(ics_qfctx, "evaluation time", offsetof(struct SetupContext_, time), 1, "Time of evaluation"));
515 
516   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &newtonian_ig_qfctx));
517   PetscCallCeed(ceed, CeedQFunctionContextSetData(newtonian_ig_qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*newtonian_ig_ctx), newtonian_ig_ctx));
518   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(newtonian_ig_qfctx, CEED_MEM_HOST, FreeContextPetsc));
519   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "timestep size", offsetof(struct NewtonianIdealGasContext_, dt), 1,
520                                                          "Size of timestep, delta t"));
521   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "ijacobian time shift",
522                                                          offsetof(struct NewtonianIdealGasContext_, ijacobian_time_shift), 1,
523                                                          "Shift for mass matrix in IJacobian"));
524   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "solution time", offsetof(struct NewtonianIdealGasContext_, time), 1,
525                                                          "Current solution time"));
526 
527   // Set problem information
528   problem->num_comps_jac_data = 14;
529   if (newtonian_ig_ctx->idl_enable) problem->num_comps_jac_data += 1;
530   problem->compute_exact_solution_error = PETSC_FALSE;
531   problem->print_info                   = PRINT_NEWTONIAN;
532   problem->num_components               = 5;
533   PetscCall(PetscMalloc1(problem->num_components, &problem->component_names));
534   static const char *const conserv_component_names[] = {"Density", "MomentumX", "MomentumY", "MomentumZ", "TotalEnergy"};
535   static const char *const prim_component_names[]    = {"Pressure", "VelocityX", "VelocityY", "VelocityZ", "Temperature"};
536   static const char *const entropy_component_names[] = {"EntropyDensity", "EntropyMomentumX", "EntropyMomentumY", "EntropyMomentumZ",
537                                                         "EntropyTotalEnergy"};
538 
539   switch (state_var) {
540     case STATEVAR_CONSERVATIVE:
541       problem->ics                 = (HoneeQFSpec){.qf_func_ptr = ICsNewtonianIG_Conserv, .qf_loc = ICsNewtonianIG_Conserv_loc};
542       problem->apply_vol_rhs       = (HoneeQFSpec){.qf_func_ptr = RHSFunction_Newtonian, .qf_loc = RHSFunction_Newtonian_loc};
543       problem->apply_vol_ifunction = (HoneeQFSpec){.qf_func_ptr = IFunction_Newtonian_Conserv, .qf_loc = IFunction_Newtonian_Conserv_loc};
544       problem->apply_vol_ijacobian = (HoneeQFSpec){.qf_func_ptr = IJacobian_Newtonian_Conserv, .qf_loc = IJacobian_Newtonian_Conserv_loc};
545       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(conserv_component_names[i], &problem->component_names[i]));
546       break;
547     case STATEVAR_PRIMITIVE:
548       problem->ics                 = (HoneeQFSpec){.qf_func_ptr = ICsNewtonianIG_Prim, .qf_loc = ICsNewtonianIG_Prim_loc};
549       problem->apply_vol_ifunction = (HoneeQFSpec){.qf_func_ptr = IFunction_Newtonian_Prim, .qf_loc = IFunction_Newtonian_Prim_loc};
550       problem->apply_vol_ijacobian = (HoneeQFSpec){.qf_func_ptr = IJacobian_Newtonian_Prim, .qf_loc = IJacobian_Newtonian_Prim_loc};
551       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(prim_component_names[i], &problem->component_names[i]));
552       break;
553     case STATEVAR_ENTROPY:
554       problem->ics                 = (HoneeQFSpec){.qf_func_ptr = ICsNewtonianIG_Entropy, .qf_loc = ICsNewtonianIG_Entropy_loc};
555       problem->apply_vol_ifunction = (HoneeQFSpec){.qf_func_ptr = IFunction_Newtonian_Entropy, .qf_loc = IFunction_Newtonian_Entropy_loc};
556       problem->apply_vol_ijacobian = (HoneeQFSpec){.qf_func_ptr = IJacobian_Newtonian_Entropy, .qf_loc = IJacobian_Newtonian_Entropy_loc};
557       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(entropy_component_names[i], &problem->component_names[i]));
558       break;
559   }
560   // All QFunctions get the same QFunctionContext regardless of state variable
561   problem->ics.qfctx           = ics_qfctx;
562   problem->apply_vol_rhs.qfctx = newtonian_ig_qfctx;
563   PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &problem->apply_vol_ifunction.qfctx));
564   PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &problem->apply_vol_ijacobian.qfctx));
565 
566   if (stab == STAB_SUPG && !implicit) problem->create_mass_operator = CreateKSPMassOperator_NewtonianStabilized;
567 
568   PetscCall(DivDiffFluxProjectionCreate(honee, honee->app_ctx->divFdiffproj_method, 4, &honee->diff_flux_proj));
569   if (honee->diff_flux_proj) {
570     DivDiffFluxProjectionData diff_flux_proj = honee->diff_flux_proj;
571     NodalProjectionData       projection     = diff_flux_proj->projection;
572     PetscSection              section;
573 
574     diff_flux_proj->CreateRHSOperator_Direct   = DivDiffFluxProjectionCreateRHS_Direct_NS;
575     diff_flux_proj->CreateRHSOperator_Indirect = DivDiffFluxProjectionCreateRHS_Indirect_NS;
576     PetscCall(DMGetLocalSection(projection->dm, &section));
577     switch (honee->diff_flux_proj->method) {
578       case DIV_DIFF_FLUX_PROJ_DIRECT: {
579         PetscCall(PetscSectionSetFieldName(section, 0, ""));
580         PetscCall(PetscSectionSetComponentName(section, 0, 0, "DivDiffusiveFlux_MomentumX"));
581         PetscCall(PetscSectionSetComponentName(section, 0, 1, "DivDiffusiveFlux_MomentumY"));
582         PetscCall(PetscSectionSetComponentName(section, 0, 2, "DivDiffusiveFlux_MomentumZ"));
583         PetscCall(PetscSectionSetComponentName(section, 0, 3, "DivDiffusiveFlux_Energy"));
584       } break;
585       case DIV_DIFF_FLUX_PROJ_INDIRECT: {
586         PetscCall(PetscSectionSetFieldName(section, 0, ""));
587         PetscCall(PetscSectionSetComponentName(section, 0, 0, "DiffusiveFlux_MomentumXX"));
588         PetscCall(PetscSectionSetComponentName(section, 0, 1, "DiffusiveFlux_MomentumXY"));
589         PetscCall(PetscSectionSetComponentName(section, 0, 2, "DiffusiveFlux_MomentumXZ"));
590         PetscCall(PetscSectionSetComponentName(section, 0, 3, "DiffusiveFlux_MomentumYX"));
591         PetscCall(PetscSectionSetComponentName(section, 0, 4, "DiffusiveFlux_MomentumYY"));
592         PetscCall(PetscSectionSetComponentName(section, 0, 5, "DiffusiveFlux_MomentumYZ"));
593         PetscCall(PetscSectionSetComponentName(section, 0, 6, "DiffusiveFlux_MomentumZX"));
594         PetscCall(PetscSectionSetComponentName(section, 0, 7, "DiffusiveFlux_MomentumZY"));
595         PetscCall(PetscSectionSetComponentName(section, 0, 8, "DiffusiveFlux_MomentumZZ"));
596         PetscCall(PetscSectionSetComponentName(section, 0, 9, "DiffusiveFlux_EnergyX"));
597         PetscCall(PetscSectionSetComponentName(section, 0, 10, "DiffusiveFlux_EnergyY"));
598         PetscCall(PetscSectionSetComponentName(section, 0, 11, "DiffusiveFlux_EnergyZ"));
599       } break;
600       case DIV_DIFF_FLUX_PROJ_NONE:
601         SETERRQ(PetscObjectComm((PetscObject)honee->dm), PETSC_ERR_ARG_WRONG, "Should not reach here with div_diff_flux_projection_method %s",
602                 DivDiffFluxProjectionMethods[honee->app_ctx->divFdiffproj_method]);
603         break;
604     }
605   }
606 
607   for (PetscCount b = 0; b < problem->num_bc_defs; b++) {
608     BCDefinition bc_def = problem->bc_defs[b];
609     const char  *name;
610 
611     PetscCall(BCDefinitionGetInfo(bc_def, &name, NULL, NULL));
612     if (!strcmp(name, "slip")) {
613       PetscCall(SlipBCSetup(bc_def, problem, dm, ctx, newtonian_ig_qfctx));
614     } else if (!strcmp(name, "freestream")) {
615       PetscCall(FreestreamBCSetup(bc_def, problem, dm, ctx, newtonian_ig_ctx, &reference));
616     } else if (!strcmp(name, "outflow")) {
617       PetscCall(OutflowBCSetup(bc_def, problem, dm, ctx, newtonian_ig_ctx, &reference));
618     } else if (!strcmp(name, "inflow")) {
619       HoneeBCStruct honee_bc;
620 
621       PetscCall(PetscNew(&honee_bc));
622       PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &honee_bc->qfctx));
623       honee_bc->honee              = honee;
624       honee_bc->num_comps_jac_data = honee->phys->implicit ? 11 : 0;
625       PetscCall(BCDefinitionSetContext(bc_def, HoneeBCDestroy, honee_bc));
626 
627       PetscCall(BCDefinitionSetIFunction(bc_def, BoundaryIntegralBCSetup_CreateIFunctionQF, HoneeBCAddIFunctionOp));
628       PetscCall(BCDefinitionSetIJacobian(bc_def, BoundaryIntegralBCSetup_CreateIJacobianQF, HoneeBCAddIJacobianOp));
629     }
630   }
631 
632   if (unit_tests) PetscCall(UnitTests_Newtonian(honee, newtonian_ig_ctx->gas));
633   PetscFunctionReturn(PETSC_SUCCESS);
634 }
635 
636 //------------------------------------
637 // Unit test functions
638 //------------------------------------
639 
640 static PetscErrorCode CheckQWithTolerance(const CeedScalar Q_s[5], const CeedScalar Q_a[5], const CeedScalar Q_b[5], const char *name,
641                                           PetscReal rtol_0, PetscReal rtol_u, PetscReal rtol_4) {
642   CeedScalar relative_error[5];  // relative error
643   CeedScalar divisor_threshold = 10 * CEED_EPSILON;
644 
645   PetscFunctionBeginUser;
646   relative_error[0] = (Q_a[0] - Q_b[0]) / (fabs(Q_s[0]) > divisor_threshold ? Q_s[0] : 1);
647   relative_error[4] = (Q_a[4] - Q_b[4]) / (fabs(Q_s[4]) > divisor_threshold ? Q_s[4] : 1);
648 
649   CeedScalar u_magnitude = sqrt(Square(Q_s[1]) + Square(Q_s[2]) + Square(Q_s[3]));
650   CeedScalar u_divisor   = u_magnitude > divisor_threshold ? u_magnitude : 1;
651   for (int i = 1; i < 4; i++) {
652     relative_error[i] = (Q_a[i] - Q_b[i]) / u_divisor;
653   }
654 
655   if (fabs(relative_error[0]) >= rtol_0) {
656     printf("%s[0] error %g (expected %.10e, got %.10e)\n", name, relative_error[0], Q_s[0], Q_a[0]);
657   }
658   for (int i = 1; i < 4; i++) {
659     if (fabs(relative_error[i]) >= rtol_u) {
660       printf("%s[%d] error %g (expected %.10e, got %.10e)\n", name, i, relative_error[i], Q_s[i], Q_a[i]);
661     }
662   }
663   if (fabs(relative_error[4]) >= rtol_4) {
664     printf("%s[4] error %g (expected %.10e, got %.10e)\n", name, relative_error[4], Q_s[4], Q_a[4]);
665   }
666   PetscFunctionReturn(PETSC_SUCCESS);
667 }
668 
669 // @brief Verify `StateFromQ` by converting A0 -> B0 -> A0_test, where A0 should equal A0_test
670 static PetscErrorCode TestState(StateVariable state_var_A, StateVariable state_var_B, NewtonianIGProperties gas, const CeedScalar A0[5],
671                                 CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
672   CeedScalar        B0[5], A0_test[5];
673   char              buf[128];
674   const char *const StateVariables_Initial[] = {"U", "Y", "V"};
675 
676   PetscFunctionBeginUser;
677   const char *A_initial = StateVariables_Initial[state_var_A];
678   const char *B_initial = StateVariables_Initial[state_var_B];
679 
680   State state_A0 = StateFromQ(gas, A0, state_var_A);
681   StateToQ(gas, state_A0, B0, state_var_B);
682   State state_B0 = StateFromQ(gas, B0, state_var_B);
683   StateToQ(gas, state_B0, A0_test, state_var_A);
684 
685   snprintf(buf, sizeof buf, "%s->%s->%s: %s", A_initial, B_initial, A_initial, A_initial);
686   PetscCall(CheckQWithTolerance(A0, A0_test, A0, buf, rtol_0, rtol_u, rtol_4));
687   PetscFunctionReturn(PETSC_SUCCESS);
688 }
689 
690 // @brief Verify `StateFromQ_fwd` via a finite difference approximation
691 static PetscErrorCode TestState_fwd(StateVariable state_var_A, StateVariable state_var_B, NewtonianIGProperties gas, const CeedScalar A0[5],
692                                     CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
693   CeedScalar        eps = 4e-7;  // Finite difference step
694   char              buf[128];
695   const char *const StateVariables_Initial[] = {"U", "Y", "V"};
696 
697   PetscFunctionBeginUser;
698   const char *A_initial = StateVariables_Initial[state_var_A];
699   const char *B_initial = StateVariables_Initial[state_var_B];
700   State       state_0   = StateFromQ(gas, A0, state_var_A);
701 
702   for (int i = 0; i < 5; i++) {
703     CeedScalar dB[5] = {0.}, dB_fd[5] = {0.};
704     {  // Calculate dB using State functions
705       CeedScalar dA[5] = {0};
706 
707       dA[i]          = A0[i];
708       State dstate_0 = StateFromQ_fwd(gas, state_0, dA, state_var_A);
709       StateToQ_fwd(gas, state_0, dstate_0, dB, state_var_B);
710     }
711 
712     {  // Calculate dB_fd via finite difference approximation
713       CeedScalar A1[5], B0[5], B1[5];
714 
715       for (int j = 0; j < 5; j++) A1[j] = (1 + eps * (i == j)) * A0[j];
716       State state_1 = StateFromQ(gas, A1, state_var_A);
717       StateToQ(gas, state_0, B0, state_var_B);
718       StateToQ(gas, state_1, B1, state_var_B);
719       for (int j = 0; j < 5; j++) dB_fd[j] = (B1[j] - B0[j]) / eps;
720     }
721 
722     snprintf(buf, sizeof buf, "d%s->d%s: StateFrom%s_fwd i=%d: d%s", A_initial, B_initial, A_initial, i, B_initial);
723     PetscCall(CheckQWithTolerance(dB_fd, dB, dB_fd, buf, rtol_0, rtol_u, rtol_4));
724   }
725   PetscFunctionReturn(PETSC_SUCCESS);
726 }
727 
728 // @brief Test the Newtonian State transformation functions, `StateFrom*`
729 static PetscErrorCode UnitTests_Newtonian(Honee honee, NewtonianIGProperties gas) {
730   Units            units = honee->units;
731   const CeedScalar kg = units->kilogram, m = units->meter, sec = units->second, K = units->Kelvin;
732   CeedScalar       rtol;
733 
734   PetscFunctionBeginUser;
735   const CeedScalar T          = 200 * K;
736   const CeedScalar rho        = 1.2 * kg / Cube(m);
737   const CeedScalar P          = (HeatCapacityRatio(gas) - 1) * rho * gas.cv * T;
738   const CeedScalar u_base     = 40 * m / sec;
739   const CeedScalar u[3]       = {u_base, u_base * 1.1, u_base * 1.2};
740   const CeedScalar e_kinetic  = 0.5 * Dot3(u, u);
741   const CeedScalar e_internal = gas.cv * T;
742   const CeedScalar e_total    = e_kinetic + e_internal;
743   const CeedScalar gamma      = HeatCapacityRatio(gas);
744   const CeedScalar entropy    = log(P) - gamma * log(rho);
745   const CeedScalar rho_div_p  = rho / P;
746   const CeedScalar Y0[5]      = {P, u[0], u[1], u[2], T};
747   const CeedScalar U0[5]      = {rho, rho * u[0], rho * u[1], rho * u[2], rho * e_total};
748   const CeedScalar V0[5]      = {(gamma - entropy) / (gamma - 1) - rho_div_p * (e_kinetic), rho_div_p * u[0], rho_div_p * u[1], rho_div_p * u[2],
749                                  -rho_div_p};
750 
751   rtol = 20 * CEED_EPSILON;
752   PetscCall(TestState(STATEVAR_PRIMITIVE, STATEVAR_CONSERVATIVE, gas, Y0, rtol, rtol, rtol));
753   PetscCall(TestState(STATEVAR_PRIMITIVE, STATEVAR_ENTROPY, gas, Y0, rtol, rtol, rtol));
754   PetscCall(TestState(STATEVAR_CONSERVATIVE, STATEVAR_PRIMITIVE, gas, U0, rtol, rtol, rtol));
755   PetscCall(TestState(STATEVAR_CONSERVATIVE, STATEVAR_ENTROPY, gas, U0, rtol, rtol, rtol));
756   PetscCall(TestState(STATEVAR_ENTROPY, STATEVAR_CONSERVATIVE, gas, V0, rtol, rtol, rtol));
757   PetscCall(TestState(STATEVAR_ENTROPY, STATEVAR_PRIMITIVE, gas, V0, rtol, rtol, rtol));
758 
759   rtol = 5e-6;
760   PetscCall(TestState_fwd(STATEVAR_PRIMITIVE, STATEVAR_CONSERVATIVE, gas, Y0, rtol, rtol, rtol));
761   PetscCall(TestState_fwd(STATEVAR_PRIMITIVE, STATEVAR_ENTROPY, gas, Y0, rtol, rtol, rtol));
762   PetscCall(TestState_fwd(STATEVAR_CONSERVATIVE, STATEVAR_PRIMITIVE, gas, U0, rtol, rtol, rtol));
763   PetscCall(TestState_fwd(STATEVAR_CONSERVATIVE, STATEVAR_ENTROPY, gas, U0, 10 * rtol, rtol, rtol));
764   PetscCall(TestState_fwd(STATEVAR_ENTROPY, STATEVAR_CONSERVATIVE, gas, V0, 5 * rtol, rtol, rtol));
765   PetscCall(TestState_fwd(STATEVAR_ENTROPY, STATEVAR_PRIMITIVE, gas, V0, 5 * rtol, 5 * rtol, 5 * rtol));
766   PetscFunctionReturn(PETSC_SUCCESS);
767 }
768