xref: /honee/problems/newtonian.c (revision e3db12f8fd36c2c636163113c7ff57d59e00b06c)
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, CeedOperatorCompositeGetSubList(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;
105   CeedQFunctionContext newtonian_qfctx = NULL;
106 
107   PetscFunctionBeginUser;
108   // -- Get Pre-requisite things
109   PetscCall(DMGetDimension(projection->dm, &dim));
110   PetscCallCeed(ceed, CeedBasisGetNumComponents(honee->basis_q, &num_comp_q));
111 
112   {  // Get newtonian QF context
113     CeedOperator *sub_ops, main_op = honee->op_ifunction ? honee->op_ifunction : honee->op_rhs_ctx->op;
114     PetscInt      sub_op_index = 0;  // will be 0 for the volume op
115 
116     PetscCallCeed(ceed, CeedOperatorCompositeGetSubList(main_op, &sub_ops));
117     PetscCallCeed(ceed, CeedOperatorGetContext(sub_ops[sub_op_index], &newtonian_qfctx));
118   }
119   PetscCallCeed(ceed, CeedOperatorCreateComposite(ceed, op_rhs));
120   {  // Add the volume integral CeedOperator
121     CeedQFunction       qf_rhs_volume;
122     CeedOperator        op_rhs_volume;
123     CeedVector          q_data;
124     CeedElemRestriction elem_restr_qd, elem_restr_diff_flux_volume = NULL;
125     CeedBasis           basis_diff_flux = NULL;
126     CeedInt             q_data_size;
127 
128     PetscCall(DivDiffFluxProjectionGetOperatorFieldData(diff_flux_proj, &elem_restr_diff_flux_volume, &basis_diff_flux, NULL, NULL));
129     PetscCall(QDataGet(ceed, projection->dm, DMLABEL_DEFAULT, DMLABEL_DEFAULT_VALUE, honee->elem_restr_x, honee->basis_x, honee->x_coord,
130                        &elem_restr_qd, &q_data, &q_data_size));
131     switch (honee->phys->state_var) {
132       case STATEVAR_PRIMITIVE:
133         PetscCallCeed(ceed,
134                       CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxVolumeRHS_NS_Prim, DivDiffusiveFluxVolumeRHS_NS_Prim_loc, &qf_rhs_volume));
135         break;
136       case STATEVAR_CONSERVATIVE:
137         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxVolumeRHS_NS_Conserv, DivDiffusiveFluxVolumeRHS_NS_Conserv_loc,
138                                                         &qf_rhs_volume));
139         break;
140       case STATEVAR_ENTROPY:
141         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxVolumeRHS_NS_Entropy, DivDiffusiveFluxVolumeRHS_NS_Entropy_loc,
142                                                         &qf_rhs_volume));
143         break;
144     }
145 
146     PetscCallCeed(ceed, CeedQFunctionSetContext(qf_rhs_volume, newtonian_qfctx));
147     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_volume, "q", num_comp_q, CEED_EVAL_INTERP));
148     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_volume, "Grad_q", num_comp_q * dim, CEED_EVAL_GRAD));
149     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_volume, "qdata", q_data_size, CEED_EVAL_NONE));
150     PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_rhs_volume, "diffusive flux RHS", projection->num_comp * dim, CEED_EVAL_GRAD));
151 
152     PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_rhs_volume, NULL, NULL, &op_rhs_volume));
153     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
154     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "Grad_q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
155     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "qdata", elem_restr_qd, CEED_BASIS_NONE, q_data));
156     PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_volume, "diffusive flux RHS", elem_restr_diff_flux_volume, basis_diff_flux, CEED_VECTOR_ACTIVE));
157 
158     PetscCallCeed(ceed, CeedOperatorCompositeAddSub(*op_rhs, op_rhs_volume));
159 
160     PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
161     PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qd));
162     PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_diff_flux_volume));
163     PetscCallCeed(ceed, CeedBasisDestroy(&basis_diff_flux));
164     PetscCallCeed(ceed, CeedOperatorDestroy(&op_rhs_volume));
165     PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_rhs_volume));
166   }
167 
168   {  // Add the boundary integral CeedOperator
169     CeedQFunction qf_rhs_boundary;
170     DMLabel       face_sets_label;
171     PetscInt      num_face_set_values, *face_set_values;
172     CeedInt       q_data_size;
173 
174     // -- Build RHS operator
175     switch (honee->phys->state_var) {
176       case STATEVAR_PRIMITIVE:
177         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxBoundaryRHS_NS_Prim, DivDiffusiveFluxBoundaryRHS_NS_Prim_loc,
178                                                         &qf_rhs_boundary));
179         break;
180       case STATEVAR_CONSERVATIVE:
181         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxBoundaryRHS_NS_Conserv, DivDiffusiveFluxBoundaryRHS_NS_Conserv_loc,
182                                                         &qf_rhs_boundary));
183         break;
184       case STATEVAR_ENTROPY:
185         PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DivDiffusiveFluxBoundaryRHS_NS_Entropy, DivDiffusiveFluxBoundaryRHS_NS_Entropy_loc,
186                                                         &qf_rhs_boundary));
187         break;
188     }
189 
190     PetscCall(QDataBoundaryGradientGetNumComponents(honee->dm, &q_data_size));
191     PetscCallCeed(ceed, CeedQFunctionSetContext(qf_rhs_boundary, newtonian_qfctx));
192     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_boundary, "q", num_comp_q, CEED_EVAL_INTERP));
193     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_boundary, "Grad_q", num_comp_q * dim, CEED_EVAL_GRAD));
194     PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs_boundary, "qdata", q_data_size, CEED_EVAL_NONE));
195     PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_rhs_boundary, "diffusive flux RHS", projection->num_comp, CEED_EVAL_INTERP));
196 
197     PetscCall(DMGetLabel(projection->dm, "Face Sets", &face_sets_label));
198     PetscCall(DMLabelCreateGlobalValueArray(projection->dm, face_sets_label, &num_face_set_values, &face_set_values));
199     for (PetscInt f = 0; f < num_face_set_values; f++) {
200       DMLabel  face_orientation_label;
201       PetscInt num_orientations_values, *orientation_values;
202 
203       {
204         char *face_orientation_label_name;
205 
206         PetscCall(DMPlexCreateFaceLabel(projection->dm, face_set_values[f], &face_orientation_label_name));
207         PetscCall(DMGetLabel(projection->dm, face_orientation_label_name, &face_orientation_label));
208         PetscCall(PetscFree(face_orientation_label_name));
209       }
210       PetscCall(DMLabelCreateGlobalValueArray(projection->dm, face_orientation_label, &num_orientations_values, &orientation_values));
211       for (PetscInt o = 0; o < num_orientations_values; o++) {
212         CeedOperator        op_rhs_boundary;
213         CeedBasis           basis_q, basis_diff_flux_boundary;
214         CeedElemRestriction elem_restr_qdata, elem_restr_q, elem_restr_diff_flux_boundary;
215         CeedVector          q_data;
216         CeedInt             q_data_size;
217         PetscInt            orientation = orientation_values[o], dm_field_q = 0, height_cell = 0, height_face = 1;
218 
219         PetscCall(DMPlexCeedElemRestrictionCreate(ceed, honee->dm, face_orientation_label, orientation, height_cell, dm_field_q, &elem_restr_q));
220         PetscCall(DMPlexCeedBasisCellToFaceCreate(ceed, honee->dm, face_orientation_label, orientation, orientation, dm_field_q, &basis_q));
221         PetscCall(DMPlexCeedElemRestrictionCreate(ceed, projection->dm, face_orientation_label, orientation, height_face, 0,
222                                                   &elem_restr_diff_flux_boundary));
223         PetscCall(DMPlexCeedBasisCreate(ceed, projection->dm, face_orientation_label, orientation, height_face, 0, &basis_diff_flux_boundary));
224         PetscCall(QDataBoundaryGradientGet(ceed, honee->dm, face_orientation_label, orientation, honee->x_coord, &elem_restr_qdata, &q_data,
225                                            &q_data_size));
226 
227         PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_rhs_boundary, NULL, NULL, &op_rhs_boundary));
228         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "q", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
229         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "Grad_q", elem_restr_q, basis_q, CEED_VECTOR_ACTIVE));
230         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "qdata", elem_restr_qdata, CEED_BASIS_NONE, q_data));
231         PetscCallCeed(ceed, CeedOperatorSetField(op_rhs_boundary, "diffusive flux RHS", elem_restr_diff_flux_boundary, basis_diff_flux_boundary,
232                                                  CEED_VECTOR_ACTIVE));
233 
234         PetscCallCeed(ceed, CeedOperatorCompositeAddSub(*op_rhs, op_rhs_boundary));
235 
236         PetscCallCeed(ceed, CeedOperatorDestroy(&op_rhs_boundary));
237         PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qdata));
238         PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_q));
239         PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_diff_flux_boundary));
240         PetscCallCeed(ceed, CeedBasisDestroy(&basis_q));
241         PetscCallCeed(ceed, CeedBasisDestroy(&basis_diff_flux_boundary));
242         PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
243       }
244       PetscCall(PetscFree(orientation_values));
245     }
246     PetscCall(PetscFree(face_set_values));
247     PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_rhs_boundary));
248   }
249 
250   PetscCallCeed(ceed, CeedQFunctionContextDestroy(&newtonian_qfctx));
251   PetscFunctionReturn(PETSC_SUCCESS);
252 }
253 
254 /**
255   @brief Create RHS CeedOperator for indirect projection of divergence of diffusive flux
256 
257   @param[in]  honee          `Honee` context
258   @param[in]  diff_flux_proj `DivDiffFluxProjectionData` object
259   @param[out] op_rhs         Operator to calculate the RHS of the L^2 projection
260 **/
261 static PetscErrorCode DivDiffFluxProjectionCreateRHS_Indirect_NS(Honee honee, DivDiffFluxProjectionData diff_flux_proj, CeedOperator *op_rhs) {
262   Ceed                 ceed       = honee->ceed;
263   NodalProjectionData  projection = diff_flux_proj->projection;
264   CeedBasis            basis_diff_flux;
265   CeedElemRestriction  elem_restr_diff_flux, elem_restr_qd;
266   CeedVector           q_data;
267   CeedInt              num_comp_q, q_data_size;
268   PetscInt             dim;
269   PetscInt             height = 0, dm_field = 0;
270   CeedQFunction        qf_rhs;
271   CeedQFunctionContext newtonian_qfctx = NULL;
272 
273   PetscFunctionBeginUser;
274   PetscCall(DMGetDimension(projection->dm, &dim));
275   PetscCallCeed(ceed, CeedBasisGetNumComponents(honee->basis_q, &num_comp_q));
276 
277   {  // Get newtonian QF context
278     CeedOperator *sub_ops, main_op = honee->op_ifunction ? honee->op_ifunction : honee->op_rhs_ctx->op;
279     PetscInt      sub_op_index = 0;  // will be 0 for the volume op
280 
281     PetscCallCeed(ceed, CeedOperatorCompositeGetSubList(main_op, &sub_ops));
282     PetscCallCeed(ceed, CeedOperatorGetContext(sub_ops[sub_op_index], &newtonian_qfctx));
283   }
284   PetscCall(DMPlexCeedElemRestrictionCreate(ceed, projection->dm, DMLABEL_DEFAULT, DMLABEL_DEFAULT_VALUE, height, dm_field, &elem_restr_diff_flux));
285   PetscCall(DMPlexCeedBasisCreate(ceed, projection->dm, DMLABEL_DEFAULT, DMLABEL_DEFAULT_VALUE, height, dm_field, &basis_diff_flux));
286   PetscCall(QDataGet(ceed, projection->dm, DMLABEL_DEFAULT, DMLABEL_DEFAULT_VALUE, honee->elem_restr_x, honee->basis_x, honee->x_coord,
287                      &elem_restr_qd, &q_data, &q_data_size));
288 
289   switch (honee->phys->state_var) {
290     case STATEVAR_PRIMITIVE:
291       PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DiffusiveFluxRHS_NS_Prim, DiffusiveFluxRHS_NS_Prim_loc, &qf_rhs));
292       break;
293     case STATEVAR_CONSERVATIVE:
294       PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DiffusiveFluxRHS_NS_Conserv, DiffusiveFluxRHS_NS_Conserv_loc, &qf_rhs));
295       break;
296     case STATEVAR_ENTROPY:
297       PetscCallCeed(ceed, CeedQFunctionCreateInterior(ceed, 1, DiffusiveFluxRHS_NS_Entropy, DiffusiveFluxRHS_NS_Entropy_loc, &qf_rhs));
298       break;
299   }
300 
301   PetscCallCeed(ceed, CeedQFunctionSetContext(qf_rhs, newtonian_qfctx));
302   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs, "q", num_comp_q, CEED_EVAL_INTERP));
303   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs, "Grad_q", num_comp_q * dim, CEED_EVAL_GRAD));
304   PetscCallCeed(ceed, CeedQFunctionAddInput(qf_rhs, "qdata", q_data_size, CEED_EVAL_NONE));
305   PetscCallCeed(ceed, CeedQFunctionAddOutput(qf_rhs, "F_diff RHS", projection->num_comp, CEED_EVAL_INTERP));
306 
307   PetscCallCeed(ceed, CeedOperatorCreate(ceed, qf_rhs, NULL, NULL, op_rhs));
308   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
309   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "Grad_q", honee->elem_restr_q, honee->basis_q, CEED_VECTOR_ACTIVE));
310   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "qdata", elem_restr_qd, CEED_BASIS_NONE, q_data));
311   PetscCallCeed(ceed, CeedOperatorSetField(*op_rhs, "F_diff RHS", elem_restr_diff_flux, basis_diff_flux, CEED_VECTOR_ACTIVE));
312 
313   PetscCallCeed(ceed, CeedQFunctionDestroy(&qf_rhs));
314   PetscCallCeed(ceed, CeedQFunctionContextDestroy(&newtonian_qfctx));
315   PetscCallCeed(ceed, CeedBasisDestroy(&basis_diff_flux));
316   PetscCallCeed(ceed, CeedVectorDestroy(&q_data));
317   PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_qd));
318   PetscCallCeed(ceed, CeedElemRestrictionDestroy(&elem_restr_diff_flux));
319   PetscFunctionReturn(PETSC_SUCCESS);
320 }
321 
322 static PetscErrorCode BoundaryIntegralBCSetup_CreateIFunctionQF(BCDefinition bc_def, CeedQFunction *qf) {
323   HoneeBCStruct honee_bc;
324 
325   PetscFunctionBeginUser;
326   PetscCall(BCDefinitionGetContext(bc_def, &honee_bc));
327   Honee honee = honee_bc->honee;
328 
329   switch (honee->phys->state_var) {
330     case STATEVAR_CONSERVATIVE:
331       PetscCall(HoneeBCCreateIFunctionQF(bc_def, BoundaryIntegral_Conserv, BoundaryIntegral_Conserv_loc, honee_bc->qfctx, qf));
332       break;
333     case STATEVAR_PRIMITIVE:
334       PetscCall(HoneeBCCreateIFunctionQF(bc_def, BoundaryIntegral_Prim, BoundaryIntegral_Prim_loc, honee_bc->qfctx, qf));
335       break;
336     case STATEVAR_ENTROPY:
337       PetscCall(HoneeBCCreateIFunctionQF(bc_def, BoundaryIntegral_Entropy, BoundaryIntegral_Entropy_loc, honee_bc->qfctx, qf));
338       break;
339   }
340   PetscFunctionReturn(PETSC_SUCCESS);
341 }
342 
343 static PetscErrorCode BoundaryIntegralBCSetup_CreateIJacobianQF(BCDefinition bc_def, CeedQFunction *qf) {
344   HoneeBCStruct honee_bc;
345 
346   PetscFunctionBeginUser;
347   PetscCall(BCDefinitionGetContext(bc_def, &honee_bc));
348   Honee honee = honee_bc->honee;
349 
350   switch (honee->phys->state_var) {
351     case STATEVAR_CONSERVATIVE:
352       PetscCall(HoneeBCCreateIJacobianQF(bc_def, BoundaryIntegral_Jacobian_Conserv, BoundaryIntegral_Jacobian_Conserv_loc, honee_bc->qfctx, qf));
353       break;
354     case STATEVAR_PRIMITIVE:
355       PetscCall(HoneeBCCreateIJacobianQF(bc_def, BoundaryIntegral_Jacobian_Prim, BoundaryIntegral_Jacobian_Prim_loc, honee_bc->qfctx, qf));
356       break;
357     case STATEVAR_ENTROPY:
358       PetscCall(HoneeBCCreateIJacobianQF(bc_def, BoundaryIntegral_Jacobian_Entropy, BoundaryIntegral_Jacobian_Entropy_loc, honee_bc->qfctx, qf));
359       break;
360   }
361   PetscFunctionReturn(PETSC_SUCCESS);
362 }
363 
364 PetscErrorCode NS_NEWTONIAN_IG(ProblemData problem, DM dm, void *ctx) {
365   SetupContext             setup_context;
366   Honee                    honee  = *(Honee *)ctx;
367   CeedInt                  degree = honee->app_ctx->degree;
368   StabilizationType        stab;
369   StateVariable            state_var;
370   MPI_Comm                 comm = honee->comm;
371   Ceed                     ceed = honee->ceed;
372   PetscBool                implicit;
373   PetscBool                unit_tests;
374   NewtonianIdealGasContext newtonian_ig_ctx;
375 
376   PetscFunctionBeginUser;
377   // Option Defaults
378   const CeedScalar Cv_func[3]     = {36, 60, 128};
379   StatePrimitive   reference      = {.pressure = 1.01e5, .velocity = {0}, .temperature = 288.15};
380   CeedScalar       idl_decay_time = -1;
381   PetscCall(PetscNew(&newtonian_ig_ctx));
382   *newtonian_ig_ctx = (struct NewtonianIdealGasContext_){
383       .gas =
384           {
385                 .cv     = 717.,
386                 .cp     = 1004.,
387                 .lambda = -2. / 3.,
388                 .mu     = 1.8e-5,
389                 .k      = 0.02638,
390                 },
391       .tau_coeffs =
392           {
393                 .Ctau_t = 1.0,
394                 .Ctau_v = Cv_func[(CeedInt)Min(3, degree) - 1],
395                 .Ctau_C = 0.25 / degree,
396                 .Ctau_M = 0.25 / degree,
397                 .Ctau_E = 0.125,
398                 },
399       .g            = {0, 0, 0}, // m/s^2
400       .idl_start    = 0,
401       .idl_length   = 0,
402       .idl_pressure = reference.pressure,
403       .idl_enable   = PETSC_FALSE,
404   };
405 
406   PetscOptionsBegin(comm, NULL, "Options for Newtonian Ideal Gas based problem", NULL);
407   PetscCall(PetscOptionsEnum("-state_var", "State variables used", NULL, StateVariables, (PetscEnum)(state_var = STATEVAR_CONSERVATIVE),
408                              (PetscEnum *)&state_var, NULL));
409 
410   // Newtonian fluid properties
411   PetscCall(PetscOptionsScalar("-cv", "Heat capacity at constant volume", NULL, newtonian_ig_ctx->gas.cv, &newtonian_ig_ctx->gas.cv, NULL));
412   PetscCall(PetscOptionsScalar("-cp", "Heat capacity at constant pressure", NULL, newtonian_ig_ctx->gas.cp, &newtonian_ig_ctx->gas.cp, NULL));
413   PetscCall(PetscOptionsScalar("-lambda", "Stokes hypothesis second viscosity coefficient", NULL, newtonian_ig_ctx->gas.lambda,
414                                &newtonian_ig_ctx->gas.lambda, NULL));
415   PetscCall(PetscOptionsScalar("-mu", "Shear dynamic viscosity coefficient", NULL, newtonian_ig_ctx->gas.mu, &newtonian_ig_ctx->gas.mu, NULL));
416   PetscCall(PetscOptionsScalar("-k", "Thermal conductivity", NULL, newtonian_ig_ctx->gas.k, &newtonian_ig_ctx->gas.k, NULL));
417 
418   PetscInt  dim          = 3;
419   PetscBool given_option = PETSC_FALSE;
420   PetscCall(PetscOptionsDeprecated("-g", "-gravity", "libCEED 0.11.1", NULL));
421   PetscCall(PetscOptionsRealArray("-gravity", "Gravitational acceleration vector", NULL, newtonian_ig_ctx->g, &dim, &given_option));
422   if (given_option) PetscCheck(dim == 3, comm, PETSC_ERR_ARG_SIZ, "Gravity vector must be size 3, %" PetscInt_FMT " values given", dim);
423 
424   // Stabilization parameters
425   PetscCall(PetscOptionsEnum("-stab", "Stabilization method", NULL, StabilizationTypes, (PetscEnum)(stab = STAB_NONE), (PetscEnum *)&stab, NULL));
426   PetscCall(PetscOptionsScalar("-Ctau_t", "Stabilization time constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_t,
427                                &newtonian_ig_ctx->tau_coeffs.Ctau_t, NULL));
428   PetscCall(PetscOptionsScalar("-Ctau_v", "Stabilization viscous constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_v,
429                                &newtonian_ig_ctx->tau_coeffs.Ctau_v, NULL));
430   PetscCall(PetscOptionsScalar("-Ctau_C", "Stabilization continuity constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_C,
431                                &newtonian_ig_ctx->tau_coeffs.Ctau_C, NULL));
432   PetscCall(PetscOptionsScalar("-Ctau_M", "Stabilization momentum constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_M,
433                                &newtonian_ig_ctx->tau_coeffs.Ctau_M, NULL));
434   PetscCall(PetscOptionsScalar("-Ctau_E", "Stabilization energy constant", NULL, newtonian_ig_ctx->tau_coeffs.Ctau_E,
435                                &newtonian_ig_ctx->tau_coeffs.Ctau_E, NULL));
436 
437   dim = 3;
438   PetscCall(PetscOptionsScalar("-reference_pressure", "Reference/initial pressure", NULL, reference.pressure, &reference.pressure, NULL));
439   PetscCall(PetscOptionsScalarArray("-reference_velocity", "Reference/initial velocity", NULL, reference.velocity, &dim, NULL));
440   PetscCall(PetscOptionsScalar("-reference_temperature", "Reference/initial temperature", NULL, reference.temperature, &reference.temperature, NULL));
441 
442   PetscCall(PetscOptionsBool("-implicit", "Use implicit (IFunction) formulation", NULL, implicit = PETSC_FALSE, &implicit, NULL));
443   PetscCall(PetscOptionsBool("-newtonian_unit_tests", "Run Newtonian unit tests", NULL, unit_tests = PETSC_FALSE, &unit_tests, NULL));
444   PetscCheck(!(state_var == STATEVAR_PRIMITIVE && !implicit), comm, PETSC_ERR_SUP,
445              "RHSFunction is not provided for primitive variables (use -state_var primitive only with -implicit)\n");
446 
447   // IDL Settings
448   {
449     PetscBool idl_enable = (PetscBool)newtonian_ig_ctx->idl_enable;  // Need PetscBool variable to read in from PetscOptionsScalar()
450     PetscCall(PetscOptionsScalar("-idl_decay_time", "Characteristic timescale of the pressure deviance decay. The timestep is good starting point",
451                                  NULL, idl_decay_time, &idl_decay_time, &idl_enable));
452     PetscCheck(!(idl_enable && idl_decay_time == 0), comm, PETSC_ERR_SUP, "idl_decay_time may not be equal to zero.");
453     if (idl_decay_time < 0) idl_enable = PETSC_FALSE;
454     newtonian_ig_ctx->idl_enable = idl_enable;
455 
456     PetscCall(PetscOptionsScalar("-idl_start", "Start of IDL in the x direction", NULL, newtonian_ig_ctx->idl_start, &newtonian_ig_ctx->idl_start,
457                                  NULL));
458     PetscCall(PetscOptionsScalar("-idl_length", "Length of IDL in the positive x direction", NULL, newtonian_ig_ctx->idl_length,
459                                  &newtonian_ig_ctx->idl_length, NULL));
460     newtonian_ig_ctx->idl_pressure = reference.pressure;
461     PetscCall(PetscOptionsScalar("-idl_pressure", "Pressure IDL uses as reference (default is `-reference_pressure`)", NULL,
462                                  newtonian_ig_ctx->idl_pressure, &newtonian_ig_ctx->idl_pressure, NULL));
463   }
464   PetscOptionsEnd();
465 
466   // ------------------------------------------------------
467   //           Set up the QFunction context
468   // ------------------------------------------------------
469   // -- Scale variables to desired units
470   Units units = honee->units;
471   newtonian_ig_ctx->gas.cv *= units->J_per_kg_K;
472   newtonian_ig_ctx->gas.cp *= units->J_per_kg_K;
473   newtonian_ig_ctx->gas.mu *= units->Pascal * units->second;
474   newtonian_ig_ctx->gas.k *= units->W_per_m_K;
475   for (PetscInt i = 0; i < 3; i++) newtonian_ig_ctx->g[i] *= units->m_per_squared_s;
476   reference.pressure *= units->Pascal;
477   for (PetscInt i = 0; i < 3; i++) reference.velocity[i] *= units->meter / units->second;
478   reference.temperature *= units->Kelvin;
479 
480   PetscReal domain_min[3], domain_max[3], domain_size[3];
481   PetscCall(DMGetBoundingBox(dm, domain_min, domain_max));
482   for (PetscInt i = 0; i < 3; i++) domain_size[i] = (domain_max[i] - domain_min[i]) * units->meter;
483 
484   // -- Solver Settings
485   honee->phys->implicit  = implicit;
486   honee->phys->state_var = state_var;
487 
488   // -- QFunction Context
489   newtonian_ig_ctx->stabilization   = stab;
490   newtonian_ig_ctx->is_implicit     = implicit;
491   newtonian_ig_ctx->state_var       = state_var;
492   newtonian_ig_ctx->idl_amplitude   = 1 / (idl_decay_time * units->second);
493   newtonian_ig_ctx->divFdiff_method = honee->app_ctx->divFdiffproj_method;
494 
495   // -- Setup Context
496   PetscCall(PetscNew(&setup_context));
497   *setup_context = (struct SetupContext_){
498       .reference = reference,
499       .newt_ctx  = *newtonian_ig_ctx,
500       .lx        = domain_size[0],
501       .ly        = domain_size[1],
502       .lz        = domain_size[2],
503       .time      = 0,
504   };
505 
506   CeedQFunctionContext ics_qfctx, newtonian_ig_qfctx;
507 
508   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &ics_qfctx));
509   PetscCallCeed(ceed, CeedQFunctionContextSetData(ics_qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*setup_context), setup_context));
510   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(ics_qfctx, CEED_MEM_HOST, FreeContextPetsc));
511   PetscCallCeed(ceed,
512                 CeedQFunctionContextRegisterDouble(ics_qfctx, "evaluation time", offsetof(struct SetupContext_, time), 1, "Time of evaluation"));
513 
514   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &newtonian_ig_qfctx));
515   PetscCallCeed(ceed, CeedQFunctionContextSetData(newtonian_ig_qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*newtonian_ig_ctx), newtonian_ig_ctx));
516   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(newtonian_ig_qfctx, CEED_MEM_HOST, FreeContextPetsc));
517   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "timestep size", offsetof(struct NewtonianIdealGasContext_, dt), 1,
518                                                          "Size of timestep, delta t"));
519   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "ijacobian time shift",
520                                                          offsetof(struct NewtonianIdealGasContext_, ijacobian_time_shift), 1,
521                                                          "Shift for mass matrix in IJacobian"));
522   PetscCallCeed(ceed, CeedQFunctionContextRegisterDouble(newtonian_ig_qfctx, "solution time", offsetof(struct NewtonianIdealGasContext_, time), 1,
523                                                          "Current solution time"));
524 
525   // Set problem information
526   problem->num_comps_jac_data = 14;
527   if (newtonian_ig_ctx->idl_enable) problem->num_comps_jac_data += 1;
528   problem->compute_exact_solution_error = PETSC_FALSE;
529   problem->print_info                   = PRINT_NEWTONIAN;
530   problem->num_components               = 5;
531   PetscCall(PetscMalloc1(problem->num_components, &problem->component_names));
532   static const char *const conserv_component_names[] = {"Density", "MomentumX", "MomentumY", "MomentumZ", "TotalEnergy"};
533   static const char *const prim_component_names[]    = {"Pressure", "VelocityX", "VelocityY", "VelocityZ", "Temperature"};
534   static const char *const entropy_component_names[] = {"EntropyDensity", "EntropyMomentumX", "EntropyMomentumY", "EntropyMomentumZ",
535                                                         "EntropyTotalEnergy"};
536 
537   switch (state_var) {
538     case STATEVAR_CONSERVATIVE:
539       problem->ics                 = (HoneeQFSpec){.qf_func_ptr = ICsNewtonianIG_Conserv, .qf_loc = ICsNewtonianIG_Conserv_loc};
540       problem->apply_vol_rhs       = (HoneeQFSpec){.qf_func_ptr = RHSFunction_Newtonian, .qf_loc = RHSFunction_Newtonian_loc};
541       problem->apply_vol_ifunction = (HoneeQFSpec){.qf_func_ptr = IFunction_Newtonian_Conserv, .qf_loc = IFunction_Newtonian_Conserv_loc};
542       problem->apply_vol_ijacobian = (HoneeQFSpec){.qf_func_ptr = IJacobian_Newtonian_Conserv, .qf_loc = IJacobian_Newtonian_Conserv_loc};
543       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(conserv_component_names[i], &problem->component_names[i]));
544       break;
545     case STATEVAR_PRIMITIVE:
546       problem->ics                 = (HoneeQFSpec){.qf_func_ptr = ICsNewtonianIG_Prim, .qf_loc = ICsNewtonianIG_Prim_loc};
547       problem->apply_vol_ifunction = (HoneeQFSpec){.qf_func_ptr = IFunction_Newtonian_Prim, .qf_loc = IFunction_Newtonian_Prim_loc};
548       problem->apply_vol_ijacobian = (HoneeQFSpec){.qf_func_ptr = IJacobian_Newtonian_Prim, .qf_loc = IJacobian_Newtonian_Prim_loc};
549       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(prim_component_names[i], &problem->component_names[i]));
550       break;
551     case STATEVAR_ENTROPY:
552       problem->ics                 = (HoneeQFSpec){.qf_func_ptr = ICsNewtonianIG_Entropy, .qf_loc = ICsNewtonianIG_Entropy_loc};
553       problem->apply_vol_ifunction = (HoneeQFSpec){.qf_func_ptr = IFunction_Newtonian_Entropy, .qf_loc = IFunction_Newtonian_Entropy_loc};
554       problem->apply_vol_ijacobian = (HoneeQFSpec){.qf_func_ptr = IJacobian_Newtonian_Entropy, .qf_loc = IJacobian_Newtonian_Entropy_loc};
555       for (PetscInt i = 0; i < 5; i++) PetscCall(PetscStrallocpy(entropy_component_names[i], &problem->component_names[i]));
556       break;
557   }
558   // All QFunctions get the same QFunctionContext regardless of state variable
559   problem->ics.qfctx           = ics_qfctx;
560   problem->apply_vol_rhs.qfctx = newtonian_ig_qfctx;
561   PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &problem->apply_vol_ifunction.qfctx));
562   PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &problem->apply_vol_ijacobian.qfctx));
563 
564   if (stab == STAB_SUPG && !implicit) problem->create_mass_operator = CreateKSPMassOperator_NewtonianStabilized;
565 
566   PetscCall(DivDiffFluxProjectionCreate(honee, honee->app_ctx->divFdiffproj_method, 4, &honee->diff_flux_proj));
567   if (honee->diff_flux_proj) {
568     DivDiffFluxProjectionData diff_flux_proj = honee->diff_flux_proj;
569     NodalProjectionData       projection     = diff_flux_proj->projection;
570     PetscSection              section;
571 
572     diff_flux_proj->CreateRHSOperator_Direct   = DivDiffFluxProjectionCreateRHS_Direct_NS;
573     diff_flux_proj->CreateRHSOperator_Indirect = DivDiffFluxProjectionCreateRHS_Indirect_NS;
574     PetscCall(DMGetLocalSection(projection->dm, &section));
575     switch (honee->diff_flux_proj->method) {
576       case DIV_DIFF_FLUX_PROJ_DIRECT: {
577         PetscCall(PetscSectionSetFieldName(section, 0, ""));
578         PetscCall(PetscSectionSetComponentName(section, 0, 0, "DivDiffusiveFlux_MomentumX"));
579         PetscCall(PetscSectionSetComponentName(section, 0, 1, "DivDiffusiveFlux_MomentumY"));
580         PetscCall(PetscSectionSetComponentName(section, 0, 2, "DivDiffusiveFlux_MomentumZ"));
581         PetscCall(PetscSectionSetComponentName(section, 0, 3, "DivDiffusiveFlux_Energy"));
582       } break;
583       case DIV_DIFF_FLUX_PROJ_INDIRECT: {
584         PetscCall(PetscSectionSetFieldName(section, 0, ""));
585         PetscCall(PetscSectionSetComponentName(section, 0, 0, "DiffusiveFlux_MomentumXX"));
586         PetscCall(PetscSectionSetComponentName(section, 0, 1, "DiffusiveFlux_MomentumXY"));
587         PetscCall(PetscSectionSetComponentName(section, 0, 2, "DiffusiveFlux_MomentumXZ"));
588         PetscCall(PetscSectionSetComponentName(section, 0, 3, "DiffusiveFlux_MomentumYX"));
589         PetscCall(PetscSectionSetComponentName(section, 0, 4, "DiffusiveFlux_MomentumYY"));
590         PetscCall(PetscSectionSetComponentName(section, 0, 5, "DiffusiveFlux_MomentumYZ"));
591         PetscCall(PetscSectionSetComponentName(section, 0, 6, "DiffusiveFlux_MomentumZX"));
592         PetscCall(PetscSectionSetComponentName(section, 0, 7, "DiffusiveFlux_MomentumZY"));
593         PetscCall(PetscSectionSetComponentName(section, 0, 8, "DiffusiveFlux_MomentumZZ"));
594         PetscCall(PetscSectionSetComponentName(section, 0, 9, "DiffusiveFlux_EnergyX"));
595         PetscCall(PetscSectionSetComponentName(section, 0, 10, "DiffusiveFlux_EnergyY"));
596         PetscCall(PetscSectionSetComponentName(section, 0, 11, "DiffusiveFlux_EnergyZ"));
597       } break;
598       case DIV_DIFF_FLUX_PROJ_NONE:
599         SETERRQ(PetscObjectComm((PetscObject)honee->dm), PETSC_ERR_ARG_WRONG, "Should not reach here with div_diff_flux_projection_method %s",
600                 DivDiffFluxProjectionMethods[honee->app_ctx->divFdiffproj_method]);
601         break;
602     }
603   }
604 
605   for (PetscCount b = 0; b < problem->num_bc_defs; b++) {
606     BCDefinition bc_def = problem->bc_defs[b];
607     const char  *name;
608 
609     PetscCall(BCDefinitionGetInfo(bc_def, &name, NULL, NULL));
610     if (!strcmp(name, "slip")) {
611       PetscCall(SlipBCSetup(bc_def, problem, dm, ctx, newtonian_ig_qfctx));
612     } else if (!strcmp(name, "freestream")) {
613       PetscCall(FreestreamBCSetup(bc_def, problem, dm, ctx, newtonian_ig_ctx, &reference));
614     } else if (!strcmp(name, "outflow")) {
615       PetscCall(OutflowBCSetup(bc_def, problem, dm, ctx, newtonian_ig_ctx, &reference));
616     } else if (!strcmp(name, "inflow")) {
617       HoneeBCStruct honee_bc;
618 
619       PetscCall(PetscNew(&honee_bc));
620       PetscCallCeed(ceed, CeedQFunctionContextReferenceCopy(newtonian_ig_qfctx, &honee_bc->qfctx));
621       honee_bc->honee              = honee;
622       honee_bc->num_comps_jac_data = honee->phys->implicit ? 11 : 0;
623       PetscCall(BCDefinitionSetContext(bc_def, HoneeBCDestroy, honee_bc));
624 
625       PetscCall(BCDefinitionSetIFunction(bc_def, BoundaryIntegralBCSetup_CreateIFunctionQF, HoneeBCAddIFunctionOp));
626       PetscCall(BCDefinitionSetIJacobian(bc_def, BoundaryIntegralBCSetup_CreateIJacobianQF, HoneeBCAddIJacobianOp));
627     }
628   }
629 
630   if (unit_tests) PetscCall(UnitTests_Newtonian(honee, newtonian_ig_ctx->gas));
631   PetscFunctionReturn(PETSC_SUCCESS);
632 }
633 
634 //------------------------------------
635 // Unit test functions
636 //------------------------------------
637 
638 static PetscErrorCode CheckQWithTolerance(const CeedScalar Q_s[5], const CeedScalar Q_a[5], const CeedScalar Q_b[5], const char *name,
639                                           PetscReal rtol_0, PetscReal rtol_u, PetscReal rtol_4) {
640   CeedScalar relative_error[5];  // relative error
641   CeedScalar divisor_threshold = 10 * CEED_EPSILON;
642 
643   PetscFunctionBeginUser;
644   relative_error[0] = (Q_a[0] - Q_b[0]) / (fabs(Q_s[0]) > divisor_threshold ? Q_s[0] : 1);
645   relative_error[4] = (Q_a[4] - Q_b[4]) / (fabs(Q_s[4]) > divisor_threshold ? Q_s[4] : 1);
646 
647   CeedScalar u_magnitude = sqrt(Square(Q_s[1]) + Square(Q_s[2]) + Square(Q_s[3]));
648   CeedScalar u_divisor   = u_magnitude > divisor_threshold ? u_magnitude : 1;
649   for (int i = 1; i < 4; i++) {
650     relative_error[i] = (Q_a[i] - Q_b[i]) / u_divisor;
651   }
652 
653   if (fabs(relative_error[0]) >= rtol_0) {
654     printf("%s[0] error %g (expected %.10e, got %.10e)\n", name, relative_error[0], Q_s[0], Q_a[0]);
655   }
656   for (int i = 1; i < 4; i++) {
657     if (fabs(relative_error[i]) >= rtol_u) {
658       printf("%s[%d] error %g (expected %.10e, got %.10e)\n", name, i, relative_error[i], Q_s[i], Q_a[i]);
659     }
660   }
661   if (fabs(relative_error[4]) >= rtol_4) {
662     printf("%s[4] error %g (expected %.10e, got %.10e)\n", name, relative_error[4], Q_s[4], Q_a[4]);
663   }
664   PetscFunctionReturn(PETSC_SUCCESS);
665 }
666 
667 // @brief Verify `StateFromQ` by converting A0 -> B0 -> A0_test, where A0 should equal A0_test
668 static PetscErrorCode TestState(StateVariable state_var_A, StateVariable state_var_B, NewtonianIGProperties gas, const CeedScalar A0[5],
669                                 CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
670   CeedScalar        B0[5], A0_test[5];
671   char              buf[128];
672   const char *const StateVariables_Initial[] = {"U", "Y", "V"};
673 
674   PetscFunctionBeginUser;
675   const char *A_initial = StateVariables_Initial[state_var_A];
676   const char *B_initial = StateVariables_Initial[state_var_B];
677 
678   State state_A0 = StateFromQ(gas, A0, state_var_A);
679   StateToQ(gas, state_A0, B0, state_var_B);
680   State state_B0 = StateFromQ(gas, B0, state_var_B);
681   StateToQ(gas, state_B0, A0_test, state_var_A);
682 
683   snprintf(buf, sizeof buf, "%s->%s->%s: %s", A_initial, B_initial, A_initial, A_initial);
684   PetscCall(CheckQWithTolerance(A0, A0_test, A0, buf, rtol_0, rtol_u, rtol_4));
685   PetscFunctionReturn(PETSC_SUCCESS);
686 }
687 
688 // @brief Verify `StateFromQ_fwd` via a finite difference approximation
689 static PetscErrorCode TestState_fwd(StateVariable state_var_A, StateVariable state_var_B, NewtonianIGProperties gas, const CeedScalar A0[5],
690                                     CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
691   CeedScalar        eps = 4e-7;  // Finite difference step
692   char              buf[128];
693   const char *const StateVariables_Initial[] = {"U", "Y", "V"};
694 
695   PetscFunctionBeginUser;
696   const char *A_initial = StateVariables_Initial[state_var_A];
697   const char *B_initial = StateVariables_Initial[state_var_B];
698   State       state_0   = StateFromQ(gas, A0, state_var_A);
699 
700   for (int i = 0; i < 5; i++) {
701     CeedScalar dB[5] = {0.}, dB_fd[5] = {0.};
702     {  // Calculate dB using State functions
703       CeedScalar dA[5] = {0};
704 
705       dA[i]          = A0[i];
706       State dstate_0 = StateFromQ_fwd(gas, state_0, dA, state_var_A);
707       StateToQ_fwd(gas, state_0, dstate_0, dB, state_var_B);
708     }
709 
710     {  // Calculate dB_fd via finite difference approximation
711       CeedScalar A1[5], B0[5], B1[5];
712 
713       for (int j = 0; j < 5; j++) A1[j] = (1 + eps * (i == j)) * A0[j];
714       State state_1 = StateFromQ(gas, A1, state_var_A);
715       StateToQ(gas, state_0, B0, state_var_B);
716       StateToQ(gas, state_1, B1, state_var_B);
717       for (int j = 0; j < 5; j++) dB_fd[j] = (B1[j] - B0[j]) / eps;
718     }
719 
720     snprintf(buf, sizeof buf, "d%s->d%s: StateFrom%s_fwd i=%d: d%s", A_initial, B_initial, A_initial, i, B_initial);
721     PetscCall(CheckQWithTolerance(dB_fd, dB, dB_fd, buf, rtol_0, rtol_u, rtol_4));
722   }
723   PetscFunctionReturn(PETSC_SUCCESS);
724 }
725 
726 // @brief Test the Newtonian State transformation functions, `StateFrom*`
727 static PetscErrorCode UnitTests_Newtonian(Honee honee, NewtonianIGProperties gas) {
728   Units            units = honee->units;
729   const CeedScalar kg = units->kilogram, m = units->meter, sec = units->second, K = units->Kelvin;
730   CeedScalar       rtol;
731 
732   PetscFunctionBeginUser;
733   const CeedScalar T          = 200 * K;
734   const CeedScalar rho        = 1.2 * kg / Cube(m);
735   const CeedScalar P          = (HeatCapacityRatio(gas) - 1) * rho * gas.cv * T;
736   const CeedScalar u_base     = 40 * m / sec;
737   const CeedScalar u[3]       = {u_base, u_base * 1.1, u_base * 1.2};
738   const CeedScalar e_kinetic  = 0.5 * Dot3(u, u);
739   const CeedScalar e_internal = gas.cv * T;
740   const CeedScalar e_total    = e_kinetic + e_internal;
741   const CeedScalar gamma      = HeatCapacityRatio(gas);
742   const CeedScalar entropy    = log(P) - gamma * log(rho);
743   const CeedScalar rho_div_p  = rho / P;
744   const CeedScalar Y0[5]      = {P, u[0], u[1], u[2], T};
745   const CeedScalar U0[5]      = {rho, rho * u[0], rho * u[1], rho * u[2], rho * e_total};
746   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],
747                                  -rho_div_p};
748 
749   rtol = 20 * CEED_EPSILON;
750   PetscCall(TestState(STATEVAR_PRIMITIVE, STATEVAR_CONSERVATIVE, gas, Y0, rtol, rtol, rtol));
751   PetscCall(TestState(STATEVAR_PRIMITIVE, STATEVAR_ENTROPY, gas, Y0, rtol, rtol, rtol));
752   PetscCall(TestState(STATEVAR_CONSERVATIVE, STATEVAR_PRIMITIVE, gas, U0, rtol, rtol, rtol));
753   PetscCall(TestState(STATEVAR_CONSERVATIVE, STATEVAR_ENTROPY, gas, U0, rtol, rtol, rtol));
754   PetscCall(TestState(STATEVAR_ENTROPY, STATEVAR_CONSERVATIVE, gas, V0, rtol, rtol, rtol));
755   PetscCall(TestState(STATEVAR_ENTROPY, STATEVAR_PRIMITIVE, gas, V0, rtol, rtol, rtol));
756 
757   rtol = 5e-6;
758   PetscCall(TestState_fwd(STATEVAR_PRIMITIVE, STATEVAR_CONSERVATIVE, gas, Y0, rtol, rtol, rtol));
759   PetscCall(TestState_fwd(STATEVAR_PRIMITIVE, STATEVAR_ENTROPY, gas, Y0, rtol, rtol, rtol));
760   PetscCall(TestState_fwd(STATEVAR_CONSERVATIVE, STATEVAR_PRIMITIVE, gas, U0, rtol, rtol, rtol));
761   PetscCall(TestState_fwd(STATEVAR_CONSERVATIVE, STATEVAR_ENTROPY, gas, U0, 10 * rtol, rtol, rtol));
762   PetscCall(TestState_fwd(STATEVAR_ENTROPY, STATEVAR_CONSERVATIVE, gas, V0, 5 * rtol, rtol, rtol));
763   PetscCall(TestState_fwd(STATEVAR_ENTROPY, STATEVAR_PRIMITIVE, gas, V0, 5 * rtol, 5 * rtol, 5 * rtol));
764   PetscFunctionReturn(PETSC_SUCCESS);
765 }
766