xref: /honee/problems/bc_freestream.c (revision e171caa68043cdab94d9ff3802f1bff2fefaf340) !
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 Freestream boundary condition
6 
7 #include "../qfunctions/bc_freestream.h"
8 
9 #include <ceed.h>
10 #include <petscdm.h>
11 
12 #include <navierstokes.h>
13 #include "../qfunctions/newtonian_types.h"
14 
15 static const char *const RiemannSolverTypes[] = {"HLL", "HLLC", "RiemannSolverTypes", "RIEMANN_", NULL};
16 
17 static PetscErrorCode RiemannSolverUnitTests(NewtonianIdealGasContext gas, CeedScalar rtol);
18 
19 typedef struct {
20   RiemannFluxType flux_type;
21 } *FreestreamHoneeBCCtx;
22 
23 static PetscErrorCode FreestreamBCSetup_CreateIFunctionQF(BCDefinition bc_def, CeedQFunction *qf) {
24   Honee         honee;
25   HoneeBCStruct honee_bc;
26 
27   PetscFunctionBeginUser;
28   PetscCall(BCDefinitionGetContext(bc_def, &honee_bc));
29   honee                                    = honee_bc->honee;
30   FreestreamHoneeBCCtx freestream_honee_bc = (FreestreamHoneeBCCtx)honee_bc->ctx;
31 
32   switch (honee->phys->state_var) {
33     case STATEVAR_CONSERVATIVE:
34       switch (freestream_honee_bc->flux_type) {
35         case RIEMANN_HLL:
36           PetscCall(HoneeBCCreateIFunctionQF(bc_def, Freestream_Conserv_HLL, Freestream_Conserv_HLL_loc, honee_bc->qfctx, qf));
37           break;
38         case RIEMANN_HLLC:
39           PetscCall(HoneeBCCreateIFunctionQF(bc_def, Freestream_Conserv_HLLC, Freestream_Conserv_HLLC_loc, honee_bc->qfctx, qf));
40           break;
41       }
42       break;
43     case STATEVAR_PRIMITIVE:
44       switch (freestream_honee_bc->flux_type) {
45         case RIEMANN_HLL:
46           PetscCall(HoneeBCCreateIFunctionQF(bc_def, Freestream_Prim_HLL, Freestream_Prim_HLL_loc, honee_bc->qfctx, qf));
47           break;
48         case RIEMANN_HLLC:
49           PetscCall(HoneeBCCreateIFunctionQF(bc_def, Freestream_Prim_HLLC, Freestream_Prim_HLLC_loc, honee_bc->qfctx, qf));
50           break;
51       }
52       break;
53     case STATEVAR_ENTROPY:
54       switch (freestream_honee_bc->flux_type) {
55         case RIEMANN_HLL:
56           PetscCall(HoneeBCCreateIFunctionQF(bc_def, Freestream_Entropy_HLL, Freestream_Entropy_HLL_loc, honee_bc->qfctx, qf));
57           break;
58         case RIEMANN_HLLC:
59           PetscCall(HoneeBCCreateIFunctionQF(bc_def, Freestream_Entropy_HLLC, Freestream_Entropy_HLLC_loc, honee_bc->qfctx, qf));
60           break;
61       }
62       break;
63   }
64   PetscFunctionReturn(PETSC_SUCCESS);
65 }
66 
67 static PetscErrorCode FreestreamBCSetup_CreateIJacobianQF(BCDefinition bc_def, CeedQFunction *qf) {
68   Honee         honee;
69   HoneeBCStruct honee_bc;
70 
71   PetscFunctionBeginUser;
72   PetscCall(BCDefinitionGetContext(bc_def, &honee_bc));
73   honee                                    = honee_bc->honee;
74   FreestreamHoneeBCCtx freestream_honee_bc = (FreestreamHoneeBCCtx)honee_bc->ctx;
75 
76   switch (honee->phys->state_var) {
77     case STATEVAR_CONSERVATIVE:
78       switch (freestream_honee_bc->flux_type) {
79         case RIEMANN_HLL:
80           PetscCall(HoneeBCCreateIJacobianQF(bc_def, Freestream_Jacobian_Conserv_HLL, Freestream_Jacobian_Conserv_HLL_loc, honee_bc->qfctx, qf));
81           break;
82         case RIEMANN_HLLC:
83           PetscCall(HoneeBCCreateIJacobianQF(bc_def, Freestream_Jacobian_Conserv_HLLC, Freestream_Jacobian_Conserv_HLLC_loc, honee_bc->qfctx, qf));
84           break;
85       }
86       break;
87     case STATEVAR_PRIMITIVE:
88       switch (freestream_honee_bc->flux_type) {
89         case RIEMANN_HLL:
90           PetscCall(HoneeBCCreateIJacobianQF(bc_def, Freestream_Jacobian_Prim_HLL, Freestream_Jacobian_Prim_HLL_loc, honee_bc->qfctx, qf));
91           break;
92         case RIEMANN_HLLC:
93           PetscCall(HoneeBCCreateIJacobianQF(bc_def, Freestream_Jacobian_Prim_HLLC, Freestream_Jacobian_Prim_HLLC_loc, honee_bc->qfctx, qf));
94           break;
95       }
96       break;
97     case STATEVAR_ENTROPY:
98       switch (freestream_honee_bc->flux_type) {
99         case RIEMANN_HLL:
100           PetscCall(HoneeBCCreateIJacobianQF(bc_def, Freestream_Jacobian_Entropy_HLL, Freestream_Jacobian_Entropy_HLL_loc, honee_bc->qfctx, qf));
101           break;
102         case RIEMANN_HLLC:
103           PetscCall(HoneeBCCreateIJacobianQF(bc_def, Freestream_Jacobian_Entropy_HLLC, Freestream_Jacobian_Entropy_HLLC_loc, honee_bc->qfctx, qf));
104           break;
105       }
106       break;
107   }
108   PetscFunctionReturn(PETSC_SUCCESS);
109 }
110 
111 PetscErrorCode FreestreamBCSetup(BCDefinition bc_def, ProblemData problem, DM dm, void *ctx, NewtonianIdealGasContext newtonian_ig_ctx,
112                                  const StatePrimitive *reference) {
113   Honee                honee = *(Honee *)ctx;
114   MPI_Comm             comm  = honee->comm;
115   Ceed                 ceed  = honee->ceed;
116   FreestreamContext    freestream_ctx;
117   CeedQFunctionContext freestream_qfctx;
118   RiemannFluxType      flux_type = RIEMANN_HLLC;
119   Units                units     = honee->units;
120   FreestreamHoneeBCCtx freestream_honee_bc;
121   HoneeBCStruct        honee_bc;
122 
123   PetscFunctionBeginUser;
124   // Freestream inherits reference state. We re-dimensionalize so the defaults in -help will be visible in SI units.
125   StatePrimitive Y_inf = {.pressure = reference->pressure / units->Pascal, .velocity = {0}, .temperature = reference->temperature / units->Kelvin};
126   for (int i = 0; i < 3; i++) Y_inf.velocity[i] = reference->velocity[i] * units->second / units->meter;
127 
128   PetscOptionsBegin(comm, NULL, "Options for Freestream boundary condition", NULL);
129   PetscCall(PetscOptionsEnum("-freestream_riemann", "Riemann solver to use in freestream boundary condition", NULL, RiemannSolverTypes,
130                              (PetscEnum)flux_type, (PetscEnum *)&flux_type, NULL));
131   PetscCall(PetscOptionsScalar("-freestream_pressure", "Pressure at freestream condition", NULL, Y_inf.pressure, &Y_inf.pressure, NULL));
132   PetscInt narray = 3;
133   PetscCall(PetscOptionsScalarArray("-freestream_velocity", "Velocity at freestream condition", NULL, Y_inf.velocity, &narray, NULL));
134   PetscCall(PetscOptionsScalar("-freestream_temperature", "Temperature at freestream condition", NULL, Y_inf.temperature, &Y_inf.temperature, NULL));
135   PetscOptionsEnd();
136 
137   Y_inf.pressure *= units->Pascal;
138   for (int i = 0; i < 3; i++) Y_inf.velocity[i] *= units->meter / units->second;
139   Y_inf.temperature *= units->Kelvin;
140 
141   State S_infty = StateFromPrimitive(newtonian_ig_ctx, Y_inf);
142 
143   // -- Set freestream_ctx struct values
144   PetscCall(PetscCalloc1(1, &freestream_ctx));
145   freestream_ctx->newtonian_ctx = *newtonian_ig_ctx;
146   freestream_ctx->S_infty       = S_infty;
147 
148   PetscCallCeed(ceed, CeedQFunctionContextCreate(honee->ceed, &freestream_qfctx));
149   PetscCallCeed(ceed, CeedQFunctionContextSetData(freestream_qfctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(*freestream_ctx), freestream_ctx));
150   PetscCallCeed(ceed, CeedQFunctionContextSetDataDestroy(freestream_qfctx, CEED_MEM_HOST, FreeContextPetsc));
151 
152   PetscCall(PetscNew(&honee_bc));
153   PetscCall(PetscNew(&freestream_honee_bc));
154   freestream_honee_bc->flux_type = flux_type;
155   honee_bc->ctx                  = freestream_honee_bc;
156   honee_bc->DestroyCtx           = PetscCtxDestroyDefault;
157   honee_bc->honee                = honee;
158   honee_bc->num_comps_jac_data   = honee->phys->implicit ? 5 : 0;
159   honee_bc->qfctx                = freestream_qfctx;
160   PetscCall(BCDefinitionSetContext(bc_def, HoneeBCDestroy, honee_bc));
161 
162   PetscCall(BCDefinitionSetIFunction(bc_def, FreestreamBCSetup_CreateIFunctionQF, HoneeBCAddIFunctionOp));
163   PetscCall(BCDefinitionSetIJacobian(bc_def, FreestreamBCSetup_CreateIJacobianQF, HoneeBCAddIJacobianOp));
164 
165   {
166     PetscBool run_unit_tests = PETSC_FALSE;
167 
168     PetscCall(PetscOptionsGetBool(NULL, NULL, "-riemann_solver_unit_tests", &run_unit_tests, NULL));
169     if (run_unit_tests) PetscCall(RiemannSolverUnitTests(newtonian_ig_ctx, 5e-7));
170   }
171   PetscFunctionReturn(PETSC_SUCCESS);
172 }
173 
174 // *****************************************************************************
175 // Code for verifying the Riemann solver and Riemann Jacobian functions
176 // *****************************************************************************
177 
178 // @brief Calculate relative error, (A - B) / S
179 // If S < threshold, then set S=1
180 static inline CeedScalar RelativeError(CeedScalar S, CeedScalar A, CeedScalar B, CeedScalar threshold) {
181   return (A - B) / (fabs(S) > threshold ? S : 1);
182 }
183 
184 // @brief Check errors of a State vector and print if above tolerance
185 static PetscErrorCode CheckQWithTolerance(const CeedScalar Q_s[5], const CeedScalar Q_a[5], const CeedScalar Q_b[5], const char *name,
186                                           PetscReal rtol_0, PetscReal rtol_u, PetscReal rtol_4) {
187   CeedScalar relative_error[5];  // relative error
188   CeedScalar divisor_threshold = 10 * CEED_EPSILON;
189 
190   PetscFunctionBeginUser;
191   relative_error[0] = RelativeError(Q_s[0], Q_a[0], Q_b[0], divisor_threshold);
192   relative_error[4] = RelativeError(Q_s[4], Q_a[4], Q_b[4], divisor_threshold);
193 
194   CeedScalar u_magnitude = sqrt(Square(Q_s[1]) + Square(Q_s[2]) + Square(Q_s[3]));
195   for (int i = 1; i < 4; i++) {
196     relative_error[i] = RelativeError(u_magnitude, Q_a[i], Q_b[i], divisor_threshold);
197   }
198 
199   if (fabs(relative_error[0]) >= rtol_0) {
200     printf("%s[0] error %g (expected %.10e, got %.10e)\n", name, relative_error[0], Q_s[0], Q_a[0]);
201   }
202   for (int i = 1; i < 4; i++) {
203     if (fabs(relative_error[i]) >= rtol_u) {
204       printf("%s[%d] error %g (expected %.10e, got %.10e)\n", name, i, relative_error[i], Q_s[i], Q_a[i]);
205     }
206   }
207   if (fabs(relative_error[4]) >= rtol_4) {
208     printf("%s[4] error %g (expected %.10e, got %.10e)\n", name, relative_error[4], Q_s[4], Q_a[4]);
209   }
210   PetscFunctionReturn(PETSC_SUCCESS);
211 }
212 
213 // @brief Verify RiemannFlux_HLL_fwd function against finite-difference approximation
214 static PetscErrorCode TestRiemannHLL_fwd(NewtonianIdealGasContext gas, CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
215   CeedScalar       eps = 4e-7;  // Finite difference step
216   char             buf[128];
217   const CeedScalar T           = 200;
218   const CeedScalar rho         = 1.2;
219   const CeedScalar p           = (HeatCapacityRatio(gas) - 1) * rho * gas->cv * T;
220   const CeedScalar u_base      = 40;
221   const CeedScalar u[3]        = {u_base, u_base * 1.1, u_base * 1.2};
222   const CeedScalar Y0_left[5]  = {p, u[0], u[1], u[2], T};
223   const CeedScalar Y0_right[5] = {1.2 * p, 1.2 * u[0], 1.2 * u[1], 1.2 * u[2], 1.2 * T};
224   CeedScalar       normal[3]   = {1, 2, 3};
225 
226   PetscFunctionBeginUser;
227   State left0  = StateFromY(gas, Y0_left);
228   State right0 = StateFromY(gas, Y0_right);
229   ScaleN(normal, 1 / Norm3(normal), 3);
230 
231   for (int i = 0; i < 10; i++) {
232     CeedScalar dFlux[5] = {0.}, dFlux_fd[5] = {0.};
233     {  // Calculate dFlux using *_fwd function
234       CeedScalar dY_right[5] = {0};
235       CeedScalar dY_left[5]  = {0};
236 
237       if (i < 5) {
238         dY_left[i] = Y0_left[i];
239       } else {
240         dY_right[i % 5] = Y0_right[i % 5];
241       }
242       State dleft0  = StateFromY_fwd(gas, left0, dY_left);
243       State dright0 = StateFromY_fwd(gas, right0, dY_right);
244 
245       StateConservative dFlux_state = RiemannFlux_HLL_fwd(gas, left0, dleft0, right0, dright0, normal);
246       UnpackState_U(dFlux_state, dFlux);
247     }
248 
249     {  // Calculate dFlux_fd via finite difference approximation
250       CeedScalar Y1_left[5]  = {Y0_left[0], Y0_left[1], Y0_left[2], Y0_left[3], Y0_left[4]};
251       CeedScalar Y1_right[5] = {Y0_right[0], Y0_right[1], Y0_right[2], Y0_right[3], Y0_right[4]};
252       CeedScalar Flux0[5], Flux1[5];
253 
254       if (i < 5) {
255         Y1_left[i] *= 1 + eps;
256       } else {
257         Y1_right[i % 5] *= 1 + eps;
258       }
259       State left1  = StateFromY(gas, Y1_left);
260       State right1 = StateFromY(gas, Y1_right);
261 
262       StateConservative Flux0_state = RiemannFlux_HLL(gas, left0, right0, normal);
263       StateConservative Flux1_state = RiemannFlux_HLL(gas, left1, right1, normal);
264       UnpackState_U(Flux0_state, Flux0);
265       UnpackState_U(Flux1_state, Flux1);
266       for (int j = 0; j < 5; j++) dFlux_fd[j] = (Flux1[j] - Flux0[j]) / eps;
267     }
268 
269     snprintf(buf, sizeof buf, "RiemannFlux_HLL i=%d: Flux", i);
270     PetscCall(CheckQWithTolerance(dFlux_fd, dFlux, dFlux_fd, buf, rtol_0, rtol_u, rtol_4));
271   }
272   PetscFunctionReturn(PETSC_SUCCESS);
273 }
274 
275 // @brief Verify RiemannFlux_HLLC_fwd function against finite-difference approximation
276 static PetscErrorCode TestRiemannHLLC_fwd(NewtonianIdealGasContext gas, CeedScalar rtol_0, CeedScalar rtol_u, CeedScalar rtol_4) {
277   CeedScalar       eps = 4e-7;  // Finite difference step
278   char             buf[128];
279   const CeedScalar T           = 200;
280   const CeedScalar rho         = 1.2;
281   const CeedScalar p           = (HeatCapacityRatio(gas) - 1) * rho * gas->cv * T;
282   const CeedScalar u_base      = 40;
283   const CeedScalar u[3]        = {u_base, u_base * 1.1, u_base * 1.2};
284   const CeedScalar Y0_left[5]  = {p, u[0], u[1], u[2], T};
285   const CeedScalar Y0_right[5] = {1.2 * p, 1.2 * u[0], 1.2 * u[1], 1.2 * u[2], 1.2 * T};
286   CeedScalar       normal[3]   = {1, 2, 3};
287 
288   PetscFunctionBeginUser;
289   State left0  = StateFromY(gas, Y0_left);
290   State right0 = StateFromY(gas, Y0_right);
291   ScaleN(normal, 1 / Norm3(normal), 3);
292 
293   for (int i = 0; i < 10; i++) {
294     CeedScalar dFlux[5] = {0.}, dFlux_fd[5] = {0.};
295     {  // Calculate dFlux using *_fwd function
296       CeedScalar dY_right[5] = {0};
297       CeedScalar dY_left[5]  = {0};
298 
299       if (i < 5) {
300         dY_left[i] = Y0_left[i];
301       } else {
302         dY_right[i % 5] = Y0_right[i % 5];
303       }
304       State dleft0  = StateFromY_fwd(gas, left0, dY_left);
305       State dright0 = StateFromY_fwd(gas, right0, dY_right);
306 
307       StateConservative dFlux_state = RiemannFlux_HLLC_fwd(gas, left0, dleft0, right0, dright0, normal);
308       UnpackState_U(dFlux_state, dFlux);
309     }
310 
311     {  // Calculate dFlux_fd via finite difference approximation
312       CeedScalar Y1_left[5]  = {Y0_left[0], Y0_left[1], Y0_left[2], Y0_left[3], Y0_left[4]};
313       CeedScalar Y1_right[5] = {Y0_right[0], Y0_right[1], Y0_right[2], Y0_right[3], Y0_right[4]};
314       CeedScalar Flux0[5], Flux1[5];
315 
316       if (i < 5) {
317         Y1_left[i] *= 1 + eps;
318       } else {
319         Y1_right[i % 5] *= 1 + eps;
320       }
321       State left1  = StateFromY(gas, Y1_left);
322       State right1 = StateFromY(gas, Y1_right);
323 
324       StateConservative Flux0_state = RiemannFlux_HLLC(gas, left0, right0, normal);
325       StateConservative Flux1_state = RiemannFlux_HLLC(gas, left1, right1, normal);
326       UnpackState_U(Flux0_state, Flux0);
327       UnpackState_U(Flux1_state, Flux1);
328       for (int j = 0; j < 5; j++) dFlux_fd[j] = (Flux1[j] - Flux0[j]) / eps;
329     }
330 
331     snprintf(buf, sizeof buf, "RiemannFlux_HLLC i=%d: Flux", i);
332     PetscCall(CheckQWithTolerance(dFlux_fd, dFlux, dFlux_fd, buf, rtol_0, rtol_u, rtol_4));
333   }
334   PetscFunctionReturn(PETSC_SUCCESS);
335 }
336 
337 // @brief Verify ComputeHLLSpeeds_Roe_fwd function against finite-difference approximation
338 static PetscErrorCode TestComputeHLLSpeeds_Roe_fwd(NewtonianIdealGasContext gas, CeedScalar rtol) {
339   CeedScalar       eps = 4e-7;  // Finite difference step
340   char             buf[128];
341   const CeedScalar T           = 200;
342   const CeedScalar rho         = 1.2;
343   const CeedScalar p           = (HeatCapacityRatio(gas) - 1) * rho * gas->cv * T;
344   const CeedScalar u_base      = 40;
345   const CeedScalar u[3]        = {u_base, u_base * 1.1, u_base * 1.2};
346   const CeedScalar Y0_left[5]  = {p, u[0], u[1], u[2], T};
347   const CeedScalar Y0_right[5] = {1.2 * p, 1.2 * u[0], 1.2 * u[1], 1.2 * u[2], 1.2 * T};
348   CeedScalar       normal[3]   = {1, 2, 3};
349 
350   PetscFunctionBeginUser;
351   State left0  = StateFromY(gas, Y0_left);
352   State right0 = StateFromY(gas, Y0_right);
353   ScaleN(normal, 1 / Norm3(normal), 3);
354   CeedScalar u_left0  = Dot3(left0.Y.velocity, normal);
355   CeedScalar u_right0 = Dot3(right0.Y.velocity, normal);
356 
357   for (int i = 0; i < 10; i++) {
358     CeedScalar ds_left, ds_right, ds_left_fd, ds_right_fd;
359     {  // Calculate ds_{left,right} using *_fwd function
360       CeedScalar dY_right[5] = {0};
361       CeedScalar dY_left[5]  = {0};
362 
363       if (i < 5) {
364         dY_left[i] = Y0_left[i];
365       } else {
366         dY_right[i % 5] = Y0_right[i % 5];
367       }
368       State      dleft0   = StateFromY_fwd(gas, left0, dY_left);
369       State      dright0  = StateFromY_fwd(gas, right0, dY_right);
370       CeedScalar du_left  = Dot3(dleft0.Y.velocity, normal);
371       CeedScalar du_right = Dot3(dright0.Y.velocity, normal);
372 
373       CeedScalar s_left, s_right;  // Throw away
374       ComputeHLLSpeeds_Roe_fwd(gas, left0, dleft0, u_left0, du_left, right0, dright0, u_right0, du_right, &s_left, &ds_left, &s_right, &ds_right);
375     }
376 
377     {  // Calculate ds_{left,right}_fd via finite difference approximation
378       CeedScalar Y1_left[5]  = {Y0_left[0], Y0_left[1], Y0_left[2], Y0_left[3], Y0_left[4]};
379       CeedScalar Y1_right[5] = {Y0_right[0], Y0_right[1], Y0_right[2], Y0_right[3], Y0_right[4]};
380 
381       if (i < 5) {
382         Y1_left[i] *= 1 + eps;
383       } else {
384         Y1_right[i % 5] *= 1 + eps;
385       }
386       State      left1    = StateFromY(gas, Y1_left);
387       State      right1   = StateFromY(gas, Y1_right);
388       CeedScalar u_left1  = Dot3(left1.Y.velocity, normal);
389       CeedScalar u_right1 = Dot3(right1.Y.velocity, normal);
390 
391       CeedScalar s_left0, s_right0, s_left1, s_right1;
392       ComputeHLLSpeeds_Roe(gas, left0, u_left0, right0, u_right0, &s_left0, &s_right0);
393       ComputeHLLSpeeds_Roe(gas, left1, u_left1, right1, u_right1, &s_left1, &s_right1);
394       ds_left_fd  = (s_left1 - s_left0) / eps;
395       ds_right_fd = (s_right1 - s_right0) / eps;
396     }
397 
398     snprintf(buf, sizeof buf, "ComputeHLLSpeeds_Roe i=%d:", i);
399     {
400       CeedScalar divisor_threshold = 10 * CEED_EPSILON;
401       CeedScalar ds_left_err, ds_right_err;
402 
403       ds_left_err  = RelativeError(ds_left_fd, ds_left, ds_left_fd, divisor_threshold);
404       ds_right_err = RelativeError(ds_right_fd, ds_right, ds_right_fd, divisor_threshold);
405       if (fabs(ds_left_err) >= rtol) printf("%s ds_left error %g (expected %.10e, got %.10e)\n", buf, ds_left_err, ds_left_fd, ds_left);
406       if (fabs(ds_right_err) >= rtol) printf("%s ds_right error %g (expected %.10e, got %.10e)\n", buf, ds_right_err, ds_right_fd, ds_right);
407     }
408   }
409   PetscFunctionReturn(PETSC_SUCCESS);
410 }
411 
412 // @brief Verify TotalSpecificEnthalpy_fwd function against finite-difference approximation
413 static PetscErrorCode TestTotalSpecificEnthalpy_fwd(NewtonianIdealGasContext gas, CeedScalar rtol) {
414   CeedScalar       eps = 4e-7;  // Finite difference step
415   char             buf[128];
416   const CeedScalar T      = 200;
417   const CeedScalar rho    = 1.2;
418   const CeedScalar p      = (HeatCapacityRatio(gas) - 1) * rho * gas->cv * T;
419   const CeedScalar u_base = 40;
420   const CeedScalar u[3]   = {u_base, u_base * 1.1, u_base * 1.2};
421   const CeedScalar Y0[5]  = {p, u[0], u[1], u[2], T};
422 
423   PetscFunctionBeginUser;
424   State state0 = StateFromY(gas, Y0);
425 
426   for (int i = 0; i < 5; i++) {
427     CeedScalar dH, dH_fd;
428     {  // Calculate dH using *_fwd function
429       CeedScalar dY[5] = {0};
430 
431       dY[i]         = Y0[i];
432       State dstate0 = StateFromY_fwd(gas, state0, dY);
433       dH            = TotalSpecificEnthalpy_fwd(gas, state0, dstate0);
434     }
435 
436     {  // Calculate dH_fd via finite difference approximation
437       CeedScalar H0, H1;
438       CeedScalar Y1[5] = {Y0[0], Y0[1], Y0[2], Y0[3], Y0[4]};
439       Y1[i] *= 1 + eps;
440       State state1 = StateFromY(gas, Y1);
441 
442       H0    = TotalSpecificEnthalpy(gas, state0);
443       H1    = TotalSpecificEnthalpy(gas, state1);
444       dH_fd = (H1 - H0) / eps;
445     }
446 
447     snprintf(buf, sizeof buf, "TotalSpecificEnthalpy i=%d:", i);
448     {
449       CeedScalar divisor_threshold = 10 * CEED_EPSILON;
450       CeedScalar dH_err;
451 
452       dH_err = RelativeError(dH_fd, dH, dH_fd, divisor_threshold);
453       if (fabs(dH_err) >= rtol) printf("%s dH error %g (expected %.10e, got %.10e)\n", buf, dH_err, dH_fd, dH);
454     }
455   }
456   PetscFunctionReturn(PETSC_SUCCESS);
457 }
458 
459 // @brief Verify RoeSetup_fwd function against finite-difference approximation
460 static PetscErrorCode TestRowSetup_fwd(NewtonianIdealGasContext gas, CeedScalar rtol) {
461   CeedScalar       eps = 4e-7;  // Finite difference step
462   char             buf[128];
463   const CeedScalar rho0[2] = {1.2, 1.4};
464 
465   PetscFunctionBeginUser;
466   for (int i = 0; i < 2; i++) {
467     RoeWeights dR, dR_fd;
468     {  // Calculate using *_fwd function
469       CeedScalar drho[5] = {0};
470 
471       drho[i] = rho0[i];
472       dR      = RoeSetup_fwd(rho0[0], rho0[1], drho[0], drho[1]);
473     }
474 
475     {  // Calculate via finite difference approximation
476       RoeWeights R0, R1;
477       CeedScalar rho1[5] = {rho0[0], rho0[1]};
478       rho1[i] *= 1 + eps;
479 
480       R0          = RoeSetup(rho0[0], rho0[1]);
481       R1          = RoeSetup(rho1[0], rho1[1]);
482       dR_fd.left  = (R1.left - R0.left) / eps;
483       dR_fd.right = (R1.right - R0.right) / eps;
484     }
485 
486     snprintf(buf, sizeof buf, "RoeSetup i=%d:", i);
487     {
488       CeedScalar divisor_threshold = 10 * CEED_EPSILON;
489       RoeWeights dR_err;
490 
491       dR_err.left  = RelativeError(dR_fd.left, dR.left, dR_fd.left, divisor_threshold);
492       dR_err.right = RelativeError(dR_fd.right, dR.right, dR_fd.right, divisor_threshold);
493       if (fabs(dR_err.left) >= rtol) printf("%s dR.left error %g (expected %.10e, got %.10e)\n", buf, dR_err.left, dR_fd.left, dR.left);
494       if (fabs(dR_err.right) >= rtol) printf("%s dR.right error %g (expected %.10e, got %.10e)\n", buf, dR_err.right, dR_fd.right, dR.right);
495     }
496   }
497   PetscFunctionReturn(PETSC_SUCCESS);
498 }
499 
500 // @brief Test Riemann solver related `*_fwd` functions via finite-difference approximation
501 static PetscErrorCode RiemannSolverUnitTests(NewtonianIdealGasContext gas, CeedScalar rtol) {
502   PetscFunctionBeginUser;
503   PetscCall(TestRiemannHLL_fwd(gas, rtol, rtol, rtol));
504   PetscCall(TestRiemannHLLC_fwd(gas, rtol, rtol, rtol));
505   PetscCall(TestComputeHLLSpeeds_Roe_fwd(gas, rtol));
506   PetscCall(TestTotalSpecificEnthalpy_fwd(gas, rtol));
507   PetscCall(TestRowSetup_fwd(gas, rtol));
508   PetscFunctionReturn(PETSC_SUCCESS);
509 }
510