xref: /honee/problems/newtonian.c (revision bff204bcbef0cb2ac109c0e2b33a4eb8a241421f)
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, NewtonianIdealGasContext 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 newtonian_ctx;
23 
24   PetscFunctionBeginUser;
25   PetscCallCeed(ceed, CeedQFunctionContextGetData(problem->apply_vol_rhs.qfctx, CEED_MEM_HOST, &newtonian_ctx));
26   PetscCall(PetscPrintf(comm,
27                         "  Problem:\n"
28                         "    Problem Name                       : %s\n"
29                         "    Stabilization                      : %s\n",
30                         app_ctx->problem_name, StabilizationTypes[newtonian_ctx->stabilization]));
31   PetscCallCeed(ceed, CeedQFunctionContextRestoreData(problem->apply_vol_rhs.qfctx, &newtonian_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   CeedQFunctionContext     newtonian_ig_qfctx;
378 
379   PetscFunctionBeginUser;
380   // Option Defaults
381   StatePrimitive reference      = {.pressure = 1.01e5, .velocity = {0}, .temperature = 288.15};
382   CeedScalar     idl_decay_time = -1;
383   {
384     PetscCall(PetscNew(&newtonian_ig_ctx));
385     const CeedScalar                 Cv_func[3]                = {36, 60, 128};
386     struct NewtonianIdealGasContext_ newtonian_ig_ctx_defaults = {
387         .cv           = 717., // J/(kg K)
388         .cp           = 1004., // J/(kg K)
389         .g            = {0, 0, 0}, // m/s^2
390         .lambda       = -2. / 3., // -
391         .mu           = 1.8e-5, // Pa s, dynamic viscosity
392         .k            = 0.02638, // W/(m K)
393         .c_tau        = 0.5 / degree, // -
394         .Ctau_t       = 1.0, // -
395         .Ctau_v       = Cv_func[(CeedInt)Min(3, degree) - 1],
396         .Ctau_C       = 0.25 / degree,
397         .Ctau_M       = 0.25 / degree,
398         .Ctau_E       = 0.125,
399         .idl_start    = 0,
400         .idl_length   = 0,
401         .idl_pressure = reference.pressure,
402         .idl_enable   = PETSC_FALSE,
403     };
404     *newtonian_ig_ctx = newtonian_ig_ctx_defaults;
405   }
406 
407   PetscOptionsBegin(comm, NULL, "Options for Newtonian Ideal Gas based problem", NULL);
408   PetscCall(PetscOptionsEnum("-state_var", "State variables used", NULL, StateVariables, (PetscEnum)(state_var = STATEVAR_CONSERVATIVE),
409                              (PetscEnum *)&state_var, NULL));
410 
411   // Newtonian fluid properties
412   PetscCall(PetscOptionsScalar("-cv", "Heat capacity at constant volume", NULL, newtonian_ig_ctx->cv, &newtonian_ig_ctx->cv, NULL));
413   PetscCall(PetscOptionsScalar("-cp", "Heat capacity at constant pressure", NULL, newtonian_ig_ctx->cp, &newtonian_ig_ctx->cp, NULL));
414   PetscCall(PetscOptionsScalar("-lambda", "Stokes hypothesis second viscosity coefficient", NULL, newtonian_ig_ctx->lambda, &newtonian_ig_ctx->lambda,
415                                NULL));
416   PetscCall(PetscOptionsScalar("-mu", "Shear dynamic viscosity coefficient", NULL, newtonian_ig_ctx->mu, &newtonian_ig_ctx->mu, NULL));
417   PetscCall(PetscOptionsScalar("-k", "Thermal conductivity", NULL, newtonian_ig_ctx->k, &newtonian_ig_ctx->k, NULL));
418 
419   PetscInt  dim          = 3;
420   PetscBool given_option = PETSC_FALSE;
421   PetscCall(PetscOptionsDeprecated("-g", "-gravity", "libCEED 0.11.1", NULL));
422   PetscCall(PetscOptionsRealArray("-gravity", "Gravitational acceleration vector", NULL, newtonian_ig_ctx->g, &dim, &given_option));
423   if (given_option) PetscCheck(dim == 3, comm, PETSC_ERR_ARG_SIZ, "Gravity vector must be size 3, %" PetscInt_FMT " values given", dim);
424 
425   // Stabilization parameters
426   PetscCall(PetscOptionsEnum("-stab", "Stabilization method", NULL, StabilizationTypes, (PetscEnum)(stab = STAB_NONE), (PetscEnum *)&stab, NULL));
427   PetscCall(PetscOptionsScalar("-c_tau", "Stabilization constant", NULL, newtonian_ig_ctx->c_tau, &newtonian_ig_ctx->c_tau, NULL));
428   PetscCall(PetscOptionsScalar("-Ctau_t", "Stabilization time constant", NULL, newtonian_ig_ctx->Ctau_t, &newtonian_ig_ctx->Ctau_t, NULL));
429   PetscCall(PetscOptionsScalar("-Ctau_v", "Stabilization viscous constant", NULL, newtonian_ig_ctx->Ctau_v, &newtonian_ig_ctx->Ctau_v, NULL));
430   PetscCall(PetscOptionsScalar("-Ctau_C", "Stabilization continuity constant", NULL, newtonian_ig_ctx->Ctau_C, &newtonian_ig_ctx->Ctau_C, NULL));
431   PetscCall(PetscOptionsScalar("-Ctau_M", "Stabilization momentum constant", NULL, newtonian_ig_ctx->Ctau_M, &newtonian_ig_ctx->Ctau_M, NULL));
432   PetscCall(PetscOptionsScalar("-Ctau_E", "Stabilization energy constant", NULL, newtonian_ig_ctx->Ctau_E, &newtonian_ig_ctx->Ctau_E, NULL));
433 
434   dim = 3;
435   PetscCall(PetscOptionsScalar("-reference_pressure", "Reference/initial pressure", NULL, reference.pressure, &reference.pressure, NULL));
436   PetscCall(PetscOptionsScalarArray("-reference_velocity", "Reference/initial velocity", NULL, reference.velocity, &dim, NULL));
437   PetscCall(PetscOptionsScalar("-reference_temperature", "Reference/initial temperature", NULL, reference.temperature, &reference.temperature, NULL));
438 
439   PetscCall(PetscOptionsBool("-implicit", "Use implicit (IFunction) formulation", NULL, implicit = PETSC_FALSE, &implicit, NULL));
440   PetscCall(PetscOptionsBool("-newtonian_unit_tests", "Run Newtonian unit tests", NULL, unit_tests = PETSC_FALSE, &unit_tests, NULL));
441   PetscCheck(!(state_var == STATEVAR_PRIMITIVE && !implicit), comm, PETSC_ERR_SUP,
442              "RHSFunction is not provided for primitive variables (use -state_var primitive only with -implicit)\n");
443 
444   // IDL Settings
445   {
446     PetscBool idl_enable = (PetscBool)newtonian_ig_ctx->idl_enable;  // Need PetscBool variable to read in from PetscOptionsScalar()
447     PetscCall(PetscOptionsScalar("-idl_decay_time", "Characteristic timescale of the pressure deviance decay. The timestep is good starting point",
448                                  NULL, idl_decay_time, &idl_decay_time, &idl_enable));
449     PetscCheck(!(idl_enable && idl_decay_time == 0), comm, PETSC_ERR_SUP, "idl_decay_time may not be equal to zero.");
450     if (idl_decay_time < 0) idl_enable = PETSC_FALSE;
451     newtonian_ig_ctx->idl_enable = idl_enable;
452 
453     PetscCall(
454         PetscOptionsScalar("-idl_start", "Start of IDL in the x direction", NULL, newtonian_ig_ctx->idl_start, &newtonian_ig_ctx->idl_start, NULL));
455     PetscCall(PetscOptionsScalar("-idl_length", "Length of IDL in the positive x direction", NULL, newtonian_ig_ctx->idl_length,
456                                  &newtonian_ig_ctx->idl_length, NULL));
457     newtonian_ig_ctx->idl_pressure = reference.pressure;
458     PetscCall(PetscOptionsScalar("-idl_pressure", "Pressure IDL uses as reference (default is `-reference_pressure`)", NULL,
459                                  newtonian_ig_ctx->idl_pressure, &newtonian_ig_ctx->idl_pressure, NULL));
460   }
461   PetscOptionsEnd();
462 
463   // Set problem information
464   problem->num_comps_jac_data = 14;
465   if (newtonian_ig_ctx->idl_enable) problem->num_comps_jac_data += 1;
466   problem->compute_exact_solution_error = PETSC_FALSE;
467   problem->print_info                   = PRINT_NEWTONIAN;
468   problem->num_components               = 5;
469   PetscCall(PetscMalloc1(problem->num_components, &problem->component_names));
470   static const char *const conservative_component_names[] = {"Density", "MomentumX", "MomentumY", "MomentumZ", "TotalEnergy"};
471   static const char *const primitive_component_names[]    = {"Pressure", "VelocityX", "VelocityY", "VelocityZ", "Temperature"};
472   static const char *const entropy_component_names[]      = {"EntropyDensity", "EntropyMomentumX", "EntropyMomentumY", "EntropyMomentumZ",
473                                                              "EntropyTotalEnergy"};
474 
475   switch (state_var) {
476     case STATEVAR_CONSERVATIVE:
477       problem->ics.qf_func_ptr                 = ICsNewtonianIG_Conserv;
478       problem->ics.qf_loc                      = ICsNewtonianIG_Conserv_loc;
479       problem->apply_vol_rhs.qf_func_ptr       = RHSFunction_Newtonian;
480       problem->apply_vol_rhs.qf_loc            = RHSFunction_Newtonian_loc;
481       problem->apply_vol_ifunction.qf_func_ptr = IFunction_Newtonian_Conserv;
482       problem->apply_vol_ifunction.qf_loc      = IFunction_Newtonian_Conserv_loc;
483       problem->apply_vol_ijacobian.qf_func_ptr = IJacobian_Newtonian_Conserv;
484       problem->apply_vol_ijacobian.qf_loc      = IJacobian_Newtonian_Conserv_loc;
485       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(conservative_component_names[i], &problem->component_names[i]));
486       break;
487     case STATEVAR_PRIMITIVE:
488       problem->ics.qf_func_ptr                 = ICsNewtonianIG_Prim;
489       problem->ics.qf_loc                      = ICsNewtonianIG_Prim_loc;
490       problem->apply_vol_ifunction.qf_func_ptr = IFunction_Newtonian_Prim;
491       problem->apply_vol_ifunction.qf_loc      = IFunction_Newtonian_Prim_loc;
492       problem->apply_vol_ijacobian.qf_func_ptr = IJacobian_Newtonian_Prim;
493       problem->apply_vol_ijacobian.qf_loc      = IJacobian_Newtonian_Prim_loc;
494       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(primitive_component_names[i], &problem->component_names[i]));
495       break;
496     case STATEVAR_ENTROPY:
497       problem->ics.qf_func_ptr                 = ICsNewtonianIG_Entropy;
498       problem->ics.qf_loc                      = ICsNewtonianIG_Entropy_loc;
499       problem->apply_vol_ifunction.qf_func_ptr = IFunction_Newtonian_Entropy;
500       problem->apply_vol_ifunction.qf_loc      = IFunction_Newtonian_Entropy_loc;
501       problem->apply_vol_ijacobian.qf_func_ptr = IJacobian_Newtonian_Entropy;
502       problem->apply_vol_ijacobian.qf_loc      = IJacobian_Newtonian_Entropy_loc;
503       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(entropy_component_names[i], &problem->component_names[i]));
504       break;
505   }
506 
507   if (stab == STAB_SUPG && !implicit) problem->create_mass_operator = CreateKSPMassOperator_NewtonianStabilized;
508 
509   PetscCall(DivDiffFluxProjectionCreate(honee, 4, &honee->diff_flux_proj));
510   if (honee->diff_flux_proj) {
511     DivDiffFluxProjectionData diff_flux_proj = honee->diff_flux_proj;
512     NodalProjectionData       projection     = diff_flux_proj->projection;
513 
514     diff_flux_proj->CreateRHSOperator_Direct   = DivDiffFluxProjectionCreateRHS_Direct_NS;
515     diff_flux_proj->CreateRHSOperator_Indirect = DivDiffFluxProjectionCreateRHS_Indirect_NS;
516 
517     switch (honee->diff_flux_proj->method) {
518       case DIV_DIFF_FLUX_PROJ_DIRECT: {
519         PetscSection section;
520 
521         PetscCall(DMGetLocalSection(projection->dm, &section));
522         PetscCall(PetscSectionSetFieldName(section, 0, ""));
523         PetscCall(PetscSectionSetComponentName(section, 0, 0, "DivDiffusiveFlux_MomentumX"));
524         PetscCall(PetscSectionSetComponentName(section, 0, 1, "DivDiffusiveFlux_MomentumY"));
525         PetscCall(PetscSectionSetComponentName(section, 0, 2, "DivDiffusiveFlux_MomentumZ"));
526         PetscCall(PetscSectionSetComponentName(section, 0, 3, "DivDiffusiveFlux_Energy"));
527       } break;
528       case DIV_DIFF_FLUX_PROJ_INDIRECT: {
529         PetscSection section;
530 
531         PetscCall(DMGetLocalSection(projection->dm, &section));
532         PetscCall(PetscSectionSetFieldName(section, 0, ""));
533         PetscCall(PetscSectionSetComponentName(section, 0, 0, "DiffusiveFlux_MomentumXX"));
534         PetscCall(PetscSectionSetComponentName(section, 0, 1, "DiffusiveFlux_MomentumXY"));
535         PetscCall(PetscSectionSetComponentName(section, 0, 2, "DiffusiveFlux_MomentumXZ"));
536         PetscCall(PetscSectionSetComponentName(section, 0, 3, "DiffusiveFlux_MomentumYX"));
537         PetscCall(PetscSectionSetComponentName(section, 0, 4, "DiffusiveFlux_MomentumYY"));
538         PetscCall(PetscSectionSetComponentName(section, 0, 5, "DiffusiveFlux_MomentumYZ"));
539         PetscCall(PetscSectionSetComponentName(section, 0, 6, "DiffusiveFlux_MomentumZX"));
540         PetscCall(PetscSectionSetComponentName(section, 0, 7, "DiffusiveFlux_MomentumZY"));
541         PetscCall(PetscSectionSetComponentName(section, 0, 8, "DiffusiveFlux_MomentumZZ"));
542         PetscCall(PetscSectionSetComponentName(section, 0, 9, "DiffusiveFlux_EnergyX"));
543         PetscCall(PetscSectionSetComponentName(section, 0, 10, "DiffusiveFlux_EnergyY"));
544         PetscCall(PetscSectionSetComponentName(section, 0, 11, "DiffusiveFlux_EnergyZ"));
545       } break;
546       case DIV_DIFF_FLUX_PROJ_NONE:
547         SETERRQ(PetscObjectComm((PetscObject)honee->dm), PETSC_ERR_ARG_WRONG, "Should not reach here with div_diff_flux_projection_method %s",
548                 DivDiffFluxProjectionMethods[honee->app_ctx->divFdiffproj_method]);
549         break;
550     }
551   }
552 
553   // ------------------------------------------------------
554   //           Set up the QFunction context
555   // ------------------------------------------------------
556   // -- Scale variables to desired units
557   Units units = honee->units;
558   newtonian_ig_ctx->cv *= units->J_per_kg_K;
559   newtonian_ig_ctx->cp *= units->J_per_kg_K;
560   newtonian_ig_ctx->mu *= units->Pascal * units->second;
561   newtonian_ig_ctx->k *= units->W_per_m_K;
562   for (PetscInt i = 0; i < 3; i++) newtonian_ig_ctx->g[i] *= units->m_per_squared_s;
563   reference.pressure *= units->Pascal;
564   for (PetscInt i = 0; i < 3; i++) reference.velocity[i] *= units->meter / units->second;
565   reference.temperature *= units->Kelvin;
566 
567   PetscReal domain_min[3], domain_max[3], domain_size[3];
568   PetscCall(DMGetBoundingBox(dm, domain_min, domain_max));
569   for (PetscInt i = 0; i < 3; i++) domain_size[i] = (domain_max[i] - domain_min[i]) * units->meter;
570 
571   // -- Solver Settings
572   honee->phys->implicit  = implicit;
573   honee->phys->state_var = state_var;
574 
575   // -- QFunction Context
576   newtonian_ig_ctx->stabilization   = stab;
577   newtonian_ig_ctx->is_implicit     = implicit;
578   newtonian_ig_ctx->state_var       = state_var;
579   newtonian_ig_ctx->idl_amplitude   = 1 / (idl_decay_time * units->second);
580   newtonian_ig_ctx->divFdiff_method = honee->app_ctx->divFdiffproj_method;
581 
582   // -- Setup Context
583   PetscCall(PetscNew(&setup_context));
584   setup_context->reference = reference;
585   setup_context->gas       = *newtonian_ig_ctx;
586   setup_context->lx        = domain_size[0];
587   setup_context->ly        = domain_size[1];
588   setup_context->lz        = domain_size[2];
589   setup_context->time      = 0;
590 
591   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &problem->ics.qfctx));
592   PetscCallCeed(ceed, CeedQFunctionContextSetData(problem->ics.qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*setup_context), setup_context));
593   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(problem->ics.qfctx, CEED_MEM_HOST, FreeContextPetsc));
594   PetscCallCeed(
595       ceed, CeedQFunctionContextRegisterDouble(problem->ics.qfctx, "evaluation time", offsetof(struct SetupContext_, time), 1, "Time of evaluation"));
596 
597   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &newtonian_ig_qfctx));
598   PetscCallCeed(ceed, CeedQFunctionContextSetData(newtonian_ig_qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*newtonian_ig_ctx), newtonian_ig_ctx));
599   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(newtonian_ig_qfctx, CEED_MEM_HOST, FreeContextPetsc));
600   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "timestep size", offsetof(struct NewtonianIdealGasContext_, dt), 1,
601                                                          "Size of timestep, delta t"));
602   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "ijacobian time shift",
603                                                          offsetof(struct NewtonianIdealGasContext_, ijacobian_time_shift), 1,
604                                                          "Shift for mass matrix in IJacobian"));
605   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "solution time", offsetof(struct NewtonianIdealGasContext_, time), 1,
606                                                          "Current solution time"));
607 
608   problem->apply_vol_rhs.qfctx = newtonian_ig_qfctx;
609   PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &problem->apply_vol_ifunction.qfctx));
610   PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &problem->apply_vol_ijacobian.qfctx));
611 
612   for (PetscCount b = 0; b < problem->num_bc_defs; b++) {
613     BCDefinition bc_def = problem->bc_defs[b];
614     const char  *name;
615 
616     PetscCall(BCDefinitionGetInfo(bc_def, &name, NULL, NULL));
617     if (!strcmp(name, "slip")) {
618       PetscCall(SlipBCSetup(bc_def, problem, dm, ctx, newtonian_ig_qfctx));
619     } else if (!strcmp(name, "freestream")) {
620       PetscCall(FreestreamBCSetup(bc_def, problem, dm, ctx, newtonian_ig_ctx, &reference));
621     } else if (!strcmp(name, "outflow")) {
622       PetscCall(OutflowBCSetup(bc_def, problem, dm, ctx, newtonian_ig_ctx, &reference));
623     } else if (!strcmp(name, "inflow")) {
624       HoneeBCStruct honee_bc;
625 
626       PetscCall(PetscNew(&honee_bc));
627       PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &honee_bc->qfctx));
628       honee_bc->honee              = honee;
629       honee_bc->num_comps_jac_data = honee->phys->implicit ? 11 : 0;
630       PetscCall(BCDefinitionSetContext(bc_def, HoneeBCDestroy, honee_bc));
631 
632       PetscCall(BCDefinitionSetIFunction(bc_def, BoundaryIntegralBCSetup_CreateIFunctionQF, HoneeBCAddIFunctionOp));
633       PetscCall(BCDefinitionSetIJacobian(bc_def, BoundaryIntegralBCSetup_CreateIJacobianQF, HoneeBCAddIJacobianOp));
634     }
635   }
636 
637   if (unit_tests) PetscCall(UnitTests_Newtonian(honee, newtonian_ig_ctx));
638   PetscFunctionReturn(PETSC_SUCCESS);
639 }
640 
641 //------------------------------------
642 // Unit test functions
643 //------------------------------------
644 
645 static PetscErrorCode CheckQWithTolerance(const CeedScalar Q_s[5], const CeedScalar Q_a[5], const CeedScalar Q_b[5], const char *name,
646                                           PetscReal rtol_0, PetscReal rtol_u, PetscReal rtol_4) {
647   CeedScalar relative_error[5];  // relative error
648   CeedScalar divisor_threshold = 10 * CEED_EPSILON;
649 
650   PetscFunctionBeginUser;
651   relative_error[0] = (Q_a[0] - Q_b[0]) / (fabs(Q_s[0]) > divisor_threshold ? Q_s[0] : 1);
652   relative_error[4] = (Q_a[4] - Q_b[4]) / (fabs(Q_s[4]) > divisor_threshold ? Q_s[4] : 1);
653 
654   CeedScalar u_magnitude = sqrt(Square(Q_s[1]) + Square(Q_s[2]) + Square(Q_s[3]));
655   CeedScalar u_divisor   = u_magnitude > divisor_threshold ? u_magnitude : 1;
656   for (int i = 1; i < 4; i++) {
657     relative_error[i] = (Q_a[i] - Q_b[i]) / u_divisor;
658   }
659 
660   if (fabs(relative_error[0]) >= rtol_0) {
661     printf("%s[0] error %g (expected %.10e, got %.10e)\n", name, relative_error[0], Q_s[0], Q_a[0]);
662   }
663   for (int i = 1; i < 4; i++) {
664     if (fabs(relative_error[i]) >= rtol_u) {
665       printf("%s[%d] error %g (expected %.10e, got %.10e)\n", name, i, relative_error[i], Q_s[i], Q_a[i]);
666     }
667   }
668   if (fabs(relative_error[4]) >= rtol_4) {
669     printf("%s[4] error %g (expected %.10e, got %.10e)\n", name, relative_error[4], Q_s[4], Q_a[4]);
670   }
671   PetscFunctionReturn(PETSC_SUCCESS);
672 }
673 
674 // @brief Verify `StateFromQ` by converting A0 -> B0 -> A0_test, where A0 should equal A0_test
675 static PetscErrorCode TestState(StateVariable state_var_A, StateVariable state_var_B, NewtonianIdealGasContext gas, const CeedScalar A0[5],
676                                 CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
677   CeedScalar        B0[5], A0_test[5];
678   char              buf[128];
679   const char *const StateVariables_Initial[] = {"U", "Y", "V"};
680 
681   PetscFunctionBeginUser;
682   const char *A_initial = StateVariables_Initial[state_var_A];
683   const char *B_initial = StateVariables_Initial[state_var_B];
684 
685   State state_A0 = StateFromQ(gas, A0, state_var_A);
686   StateToQ(gas, state_A0, B0, state_var_B);
687   State state_B0 = StateFromQ(gas, B0, state_var_B);
688   StateToQ(gas, state_B0, A0_test, state_var_A);
689 
690   snprintf(buf, sizeof buf, "%s->%s->%s: %s", A_initial, B_initial, A_initial, A_initial);
691   PetscCall(CheckQWithTolerance(A0, A0_test, A0, buf, rtol_0, rtol_u, rtol_4));
692   PetscFunctionReturn(PETSC_SUCCESS);
693 }
694 
695 // @brief Verify `StateFromQ_fwd` via a finite difference approximation
696 static PetscErrorCode TestState_fwd(StateVariable state_var_A, StateVariable state_var_B, NewtonianIdealGasContext gas, const CeedScalar A0[5],
697                                     CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
698   CeedScalar        eps = 4e-7;  // Finite difference step
699   char              buf[128];
700   const char *const StateVariables_Initial[] = {"U", "Y", "V"};
701 
702   PetscFunctionBeginUser;
703   const char *A_initial = StateVariables_Initial[state_var_A];
704   const char *B_initial = StateVariables_Initial[state_var_B];
705   State       state_0   = StateFromQ(gas, A0, state_var_A);
706 
707   for (int i = 0; i < 5; i++) {
708     CeedScalar dB[5] = {0.}, dB_fd[5] = {0.};
709     {  // Calculate dB using State functions
710       CeedScalar dA[5] = {0};
711 
712       dA[i]          = A0[i];
713       State dstate_0 = StateFromQ_fwd(gas, state_0, dA, state_var_A);
714       StateToQ_fwd(gas, state_0, dstate_0, dB, state_var_B);
715     }
716 
717     {  // Calculate dB_fd via finite difference approximation
718       CeedScalar A1[5], B0[5], B1[5];
719 
720       for (int j = 0; j < 5; j++) A1[j] = (1 + eps * (i == j)) * A0[j];
721       State state_1 = StateFromQ(gas, A1, state_var_A);
722       StateToQ(gas, state_0, B0, state_var_B);
723       StateToQ(gas, state_1, B1, state_var_B);
724       for (int j = 0; j < 5; j++) dB_fd[j] = (B1[j] - B0[j]) / eps;
725     }
726 
727     snprintf(buf, sizeof buf, "d%s->d%s: StateFrom%s_fwd i=%d: d%s", A_initial, B_initial, A_initial, i, B_initial);
728     PetscCall(CheckQWithTolerance(dB_fd, dB, dB_fd, buf, rtol_0, rtol_u, rtol_4));
729   }
730   PetscFunctionReturn(PETSC_SUCCESS);
731 }
732 
733 // @brief Test the Newtonian State transformation functions, `StateFrom*`
734 static PetscErrorCode UnitTests_Newtonian(Honee honee, NewtonianIdealGasContext gas) {
735   Units            units = honee->units;
736   const CeedScalar kg = units->kilogram, m = units->meter, sec = units->second, K = units->Kelvin;
737   CeedScalar       rtol;
738 
739   PetscFunctionBeginUser;
740   const CeedScalar T          = 200 * K;
741   const CeedScalar rho        = 1.2 * kg / Cube(m);
742   const CeedScalar P          = (HeatCapacityRatio(gas) - 1) * rho * gas->cv * T;
743   const CeedScalar u_base     = 40 * m / sec;
744   const CeedScalar u[3]       = {u_base, u_base * 1.1, u_base * 1.2};
745   const CeedScalar e_kinetic  = 0.5 * Dot3(u, u);
746   const CeedScalar e_internal = gas->cv * T;
747   const CeedScalar e_total    = e_kinetic + e_internal;
748   const CeedScalar gamma      = HeatCapacityRatio(gas);
749   const CeedScalar entropy    = log(P) - gamma * log(rho);
750   const CeedScalar rho_div_p  = rho / P;
751   const CeedScalar Y0[5]      = {P, u[0], u[1], u[2], T};
752   const CeedScalar U0[5]      = {rho, rho * u[0], rho * u[1], rho * u[2], rho * e_total};
753   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],
754                                  -rho_div_p};
755 
756   rtol = 20 * CEED_EPSILON;
757   PetscCall(TestState(STATEVAR_PRIMITIVE, STATEVAR_CONSERVATIVE, gas, Y0, rtol, rtol, rtol));
758   PetscCall(TestState(STATEVAR_PRIMITIVE, STATEVAR_ENTROPY, gas, Y0, rtol, rtol, rtol));
759   PetscCall(TestState(STATEVAR_CONSERVATIVE, STATEVAR_PRIMITIVE, gas, U0, rtol, rtol, rtol));
760   PetscCall(TestState(STATEVAR_CONSERVATIVE, STATEVAR_ENTROPY, gas, U0, rtol, rtol, rtol));
761   PetscCall(TestState(STATEVAR_ENTROPY, STATEVAR_CONSERVATIVE, gas, V0, rtol, rtol, rtol));
762   PetscCall(TestState(STATEVAR_ENTROPY, STATEVAR_PRIMITIVE, gas, V0, rtol, rtol, rtol));
763 
764   rtol = 5e-6;
765   PetscCall(TestState_fwd(STATEVAR_PRIMITIVE, STATEVAR_CONSERVATIVE, gas, Y0, rtol, rtol, rtol));
766   PetscCall(TestState_fwd(STATEVAR_PRIMITIVE, STATEVAR_ENTROPY, gas, Y0, rtol, rtol, rtol));
767   PetscCall(TestState_fwd(STATEVAR_CONSERVATIVE, STATEVAR_PRIMITIVE, gas, U0, rtol, rtol, rtol));
768   PetscCall(TestState_fwd(STATEVAR_CONSERVATIVE, STATEVAR_ENTROPY, gas, U0, 10 * rtol, rtol, rtol));
769   PetscCall(TestState_fwd(STATEVAR_ENTROPY, STATEVAR_CONSERVATIVE, gas, V0, 5 * rtol, rtol, rtol));
770   PetscCall(TestState_fwd(STATEVAR_ENTROPY, STATEVAR_PRIMITIVE, gas, V0, 5 * rtol, 5 * rtol, 5 * rtol));
771   PetscFunctionReturn(PETSC_SUCCESS);
772 }
773