xref: /honee/qfunctions/stg_shur14.h (revision 8a8cb6e06ce4728cc6d80ca92f8de31da49852e5)
1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors.
2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause
3 
4 /// @file
5 /// Implementation of the Synthetic Turbulence Generation (STG) algorithm
6 /// presented in Shur et al. 2014
7 //
8 /// SetupSTG_Rand reads in the input files and fills in STGShur14Context.
9 /// Then STGShur14_CalcQF is run over quadrature points.
10 /// Before the program exits, TearDownSTG is run to free the memory of the allocated arrays.
11 #include <ceed.h>
12 #include <math.h>
13 #include <stdlib.h>
14 
15 #include "newtonian_state.h"
16 #include "setupgeo_helpers.h"
17 #include "stg_shur14_type.h"
18 #include "utils.h"
19 
20 #define STG_NMODES_MAX 1024
21 
22 /*
23  * @brief Interpolate quantities from input profile to given location
24  *
25  * Assumed that prof_wd[i+1] > prof_wd[i] and prof_wd[0] = 0
26  * If wall_dist > prof_wd[-1], then the interpolation takes the values at prof_wd[-1]
27  *
28  * @param[in]  wall_dist Distance to the nearest wall
29  * @param[out] ubar      Mean velocity at wall_dist
30  * @param[out] cij       Cholesky decomposition at wall_dist
31  * @param[out] eps       Turbulent dissipation at wall_dist
32  * @param[out] lt        Turbulent length scale at wall_dist
33  * @param[in]  stg_ctx   STGShur14Context for the problem
34  */
35 CEED_QFUNCTION_HELPER void InterpolateProfile(const CeedScalar wall_dist, CeedScalar ubar[3], CeedScalar cij[6], CeedScalar *eps, CeedScalar *lt,
36                                               const StgShur14Context stg_ctx) {
37   const CeedInt     nprofs    = stg_ctx->nprofs;
38   const CeedScalar *prof_wd   = &stg_ctx->data[stg_ctx->offsets.wall_dist];
39   const CeedScalar *prof_eps  = &stg_ctx->data[stg_ctx->offsets.eps];
40   const CeedScalar *prof_lt   = &stg_ctx->data[stg_ctx->offsets.lt];
41   const CeedScalar *prof_ubar = &stg_ctx->data[stg_ctx->offsets.ubar];
42   const CeedScalar *prof_cij  = &stg_ctx->data[stg_ctx->offsets.cij];
43   CeedInt           idx       = -1;
44 
45   for (CeedInt i = 0; i < nprofs; i++) {
46     if (wall_dist < prof_wd[i]) {
47       idx = i;
48       break;
49     }
50   }
51 
52   if (idx > 0) {  // y within the bounds of prof_wd
53     CeedScalar coeff = (wall_dist - prof_wd[idx - 1]) / (prof_wd[idx] - prof_wd[idx - 1]);
54 
55     ubar[0] = prof_ubar[0 * nprofs + idx - 1] + coeff * (prof_ubar[0 * nprofs + idx] - prof_ubar[0 * nprofs + idx - 1]);
56     ubar[1] = prof_ubar[1 * nprofs + idx - 1] + coeff * (prof_ubar[1 * nprofs + idx] - prof_ubar[1 * nprofs + idx - 1]);
57     ubar[2] = prof_ubar[2 * nprofs + idx - 1] + coeff * (prof_ubar[2 * nprofs + idx] - prof_ubar[2 * nprofs + idx - 1]);
58     cij[0]  = prof_cij[0 * nprofs + idx - 1] + coeff * (prof_cij[0 * nprofs + idx] - prof_cij[0 * nprofs + idx - 1]);
59     cij[1]  = prof_cij[1 * nprofs + idx - 1] + coeff * (prof_cij[1 * nprofs + idx] - prof_cij[1 * nprofs + idx - 1]);
60     cij[2]  = prof_cij[2 * nprofs + idx - 1] + coeff * (prof_cij[2 * nprofs + idx] - prof_cij[2 * nprofs + idx - 1]);
61     cij[3]  = prof_cij[3 * nprofs + idx - 1] + coeff * (prof_cij[3 * nprofs + idx] - prof_cij[3 * nprofs + idx - 1]);
62     cij[4]  = prof_cij[4 * nprofs + idx - 1] + coeff * (prof_cij[4 * nprofs + idx] - prof_cij[4 * nprofs + idx - 1]);
63     cij[5]  = prof_cij[5 * nprofs + idx - 1] + coeff * (prof_cij[5 * nprofs + idx] - prof_cij[5 * nprofs + idx - 1]);
64     *eps    = prof_eps[idx - 1] + coeff * (prof_eps[idx] - prof_eps[idx - 1]);
65     *lt     = prof_lt[idx - 1] + coeff * (prof_lt[idx] - prof_lt[idx - 1]);
66   } else {  // y outside bounds of prof_wd
67     ubar[0] = prof_ubar[1 * nprofs - 1];
68     ubar[1] = prof_ubar[2 * nprofs - 1];
69     ubar[2] = prof_ubar[3 * nprofs - 1];
70     cij[0]  = prof_cij[1 * nprofs - 1];
71     cij[1]  = prof_cij[2 * nprofs - 1];
72     cij[2]  = prof_cij[3 * nprofs - 1];
73     cij[3]  = prof_cij[4 * nprofs - 1];
74     cij[4]  = prof_cij[5 * nprofs - 1];
75     cij[5]  = prof_cij[6 * nprofs - 1];
76     *eps    = prof_eps[nprofs - 1];
77     *lt     = prof_lt[nprofs - 1];
78   }
79 }
80 
81 /*
82  * @brief Calculate spectrum coefficient, qn
83  *
84  * Calculates q_n at a given distance to the wall
85  *
86  * @param[in]  kappa     nth wavenumber
87  * @param[in]  dkappa    Difference between wavenumbers
88  * @param[in]  keta      Dissipation wavenumber
89  * @param[in]  kcut      Mesh-induced cutoff wavenumber
90  * @param[in]  ke        Energy-containing wavenumber
91  * @param[in]  Ektot_inv Inverse of total turbulent kinetic energy of spectrum
92  * @returns    qn        Spectrum coefficient
93  */
94 CEED_QFUNCTION_HELPER CeedScalar Calc_qn(const CeedScalar kappa, const CeedScalar dkappa, const CeedScalar keta, const CeedScalar kcut,
95                                          const CeedScalar ke, const CeedScalar Ektot_inv) {
96   const CeedScalar feta_x_fcut = exp(-Square(12 * kappa / keta) - Cube(4 * Max(kappa - 0.9 * kcut, 0) / kcut));
97   return pow(kappa / ke, 4.) * pow(1 + 2.4 * Square(kappa / ke), -17. / 6) * feta_x_fcut * dkappa * Ektot_inv;
98 }
99 
100 // Calculate hmax, ke, keta, and kcut
101 CEED_QFUNCTION_HELPER void SpectrumConstants(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar hNodSep[3],
102                                              const CeedScalar nu, CeedScalar *hmax, CeedScalar *ke, CeedScalar *keta, CeedScalar *kcut) {
103   *hmax = Max(Max(hNodSep[0], hNodSep[1]), hNodSep[2]);
104   *ke   = wall_dist == 0 ? 1e16 : 2 * M_PI / Min(2 * wall_dist, 3 * lt);
105   *keta = 2 * M_PI * pow(Cube(nu) / eps, -0.25);
106   *kcut = M_PI / Min(Max(Max(hNodSep[1], hNodSep[2]), 0.3 * (*hmax)) + 0.1 * wall_dist, *hmax);
107 }
108 
109 /*
110  * @brief Calculate spectrum coefficients for STG
111  *
112  * Calculates q_n at a given distance to the wall
113  *
114  * @param[in]  wall_dist  Distance to the nearest wall
115  * @param[in]  eps        Turbulent dissipation w/rt wall_dist
116  * @param[in]  lt         Turbulent length scale w/rt wall_dist
117  * @param[in]  h_node_sep Element lengths in coordinate directions
118  * @param[in]  nu         Dynamic Viscosity;
119  * @param[in]  stg_ctx    STGShur14Context for the problem
120  * @param[out] qn         Spectrum coefficients, [nmodes]
121  */
122 CEED_QFUNCTION_HELPER void CalcSpectrum(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h_node_sep[3],
123                                         const CeedScalar nu, CeedScalar qn[], const StgShur14Context stg_ctx) {
124   const CeedInt     nmodes = stg_ctx->nmodes;
125   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
126   CeedScalar        hmax, ke, keta, kcut, Ektot = 0.0;
127 
128   SpectrumConstants(wall_dist, eps, lt, h_node_sep, nu, &hmax, &ke, &keta, &kcut);
129 
130   for (CeedInt n = 0; n < nmodes; n++) {
131     const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
132     qn[n]                   = Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
133     Ektot += qn[n];
134   }
135 
136   if (Ektot == 0) return;
137   for (CeedInt n = 0; n < nmodes; n++) qn[n] /= Ektot;
138 }
139 
140 /******************************************************
141  * @brief Calculate u(x,t) for STG inflow condition
142  *
143  * @param[in]  X       Location to evaluate u(X,t)
144  * @param[in]  t       Time to evaluate u(X,t)
145  * @param[in]  ubar    Mean velocity at X
146  * @param[in]  cij     Cholesky decomposition at X
147  * @param[in]  qn      Wavemode amplitudes at X, [nmodes]
148  * @param[out] u       Velocity at X and t
149  * @param[in]  stg_ctx STGShur14Context for the problem
150  */
151 CEED_QFUNCTION_HELPER void StgShur14Calc(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
152                                          const CeedScalar qn[], CeedScalar u[3], const StgShur14Context stg_ctx) {
153   const CeedInt     nmodes = stg_ctx->nmodes;
154   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
155   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
156   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
157   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
158   CeedScalar        xdotd, vp[3] = {0.};
159   CeedScalar        xhat[] = {0., X[1], X[2]};
160 
161   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
162     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
163     xdotd   = 0.;
164     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
165     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
166     vp[0] += sqrt(qn[n]) * sigma[0 * nmodes + n] * cos_kxdp;
167     vp[1] += sqrt(qn[n]) * sigma[1 * nmodes + n] * cos_kxdp;
168     vp[2] += sqrt(qn[n]) * sigma[2 * nmodes + n] * cos_kxdp;
169   }
170   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
171 
172   u[0] = ubar[0] + cij[0] * vp[0];
173   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
174   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
175 }
176 
177 /******************************************************
178  * @brief Calculate u(x,t) for STG inflow condition
179  *
180  * @param[in]  X          Location to evaluate u(X,t)
181  * @param[in]  t          Time to evaluate u(X,t)
182  * @param[in]  ubar       Mean velocity at X
183  * @param[in]  cij        Cholesky decomposition at X
184  * @param[in]  Ektot      Total spectrum energy at this location
185  * @param[in]  h_node_sep Element size in 3 directions
186  * @param[in]  wall_dist  Distance to closest wall
187  * @param[in]  eps        Turbulent dissipation
188  * @param[in]  lt         Turbulent length scale
189  * @param[out] u          Velocity at X and t
190  * @param[in]  stg_ctx    STGShur14Context for the problem
191  */
192 CEED_QFUNCTION_HELPER void StgShur14Calc_PrecompEktot(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
193                                                       const CeedScalar Ektot, const CeedScalar h_node_sep[3], const CeedScalar wall_dist,
194                                                       const CeedScalar eps, const CeedScalar lt, const CeedScalar nu, CeedScalar u[3],
195                                                       const StgShur14Context stg_ctx) {
196   const CeedInt     nmodes = stg_ctx->nmodes;
197   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
198   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
199   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
200   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
201   CeedScalar        hmax, ke, keta, kcut;
202   SpectrumConstants(wall_dist, eps, lt, h_node_sep, nu, &hmax, &ke, &keta, &kcut);
203   CeedScalar xdotd, vp[3] = {0.};
204   CeedScalar xhat[] = {0., X[1], X[2]};
205 
206   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
207     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
208     xdotd   = 0.;
209     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
210     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
211     const CeedScalar dkappa   = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
212     const CeedScalar qn       = Calc_qn(kappa[n], dkappa, keta, kcut, ke, Ektot);
213     vp[0] += sqrt(qn) * sigma[0 * nmodes + n] * cos_kxdp;
214     vp[1] += sqrt(qn) * sigma[1 * nmodes + n] * cos_kxdp;
215     vp[2] += sqrt(qn) * sigma[2 * nmodes + n] * cos_kxdp;
216   }
217   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
218 
219   u[0] = ubar[0] + cij[0] * vp[0];
220   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
221   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
222 }
223 
224 /**
225    @brief Calculate the element length scales based on dXdx
226 
227    WARNING: This assumes the reference domain is [-1,1], which is not true for tetrahedral elements
228 
229    @param[in]  dXdx    Inverse mapping Jacobian, d\xi/dx
230    @param[in]  scale   Scale factor for the element lengths
231    @param[out] lengths The element lengths in each cartesian direction
232 **/
233 CEED_QFUNCTION_HELPER void CalculateElementLengths(CeedScalar dXdx[3][3], CeedScalar scale, CeedScalar lengths[3]) {
234   for (CeedInt j = 0; j < 3; j++) lengths[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j]));
235   ScaleN(lengths, scale, 3);
236 }
237 
238 // Create preprocessed input for the stg calculation
239 //
240 // stg_data[0] = 1 / Ektot (inverse of total spectrum energy)
241 CEED_QFUNCTION(StgShur14Preprocess)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
242   const CeedScalar *dXdx_q         = in[0];
243   const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1];
244 
245   CeedScalar(*stg_data) = (CeedScalar(*))out[0];
246 
247   CeedScalar             ubar[3], cij[6], eps, lt;
248   const StgShur14Context stg_ctx = (StgShur14Context)ctx;
249   const CeedScalar       mu      = stg_ctx->newtonian_ctx.mu;
250   const CeedScalar       theta0  = stg_ctx->theta0;
251   const CeedScalar       P0      = stg_ctx->P0;
252   const CeedScalar       Rd      = GasConstant(&stg_ctx->newtonian_ctx);
253   const CeedScalar       rho     = P0 / (Rd * theta0);
254   const CeedScalar       nu      = mu / rho;
255 
256   const CeedInt     nmodes = stg_ctx->nmodes;
257   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
258   CeedScalar        hmax, ke, keta, kcut;
259 
260   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
261     const CeedScalar wall_dist = x[1][i];
262     CeedScalar       dXdx[3][3], h_node_sep[3];
263     StoredValuesUnpack(Q, i, 0, 9, dXdx_q, (CeedScalar *)dXdx);
264 
265     CalculateElementLengths(dXdx, stg_ctx->h_scale_factor, h_node_sep);
266     InterpolateProfile(wall_dist, ubar, cij, &eps, &lt, stg_ctx);
267     SpectrumConstants(wall_dist, eps, lt, h_node_sep, nu, &hmax, &ke, &keta, &kcut);
268 
269     // Calculate total TKE per spectrum
270     CeedScalar Ek_tot = 0;
271     CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
272       const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
273       Ek_tot += Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
274     }
275     // avoid underflowed and poorly defined spectrum coefficients
276     stg_data[i] = Ek_tot != 0 ? 1 / Ek_tot : 0;
277   }
278   return 0;
279 }
280 
281 // Extrude the STGInflow profile through out the domain for an initial condition
282 CEED_QFUNCTION(ICsStg)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
283   const CeedScalar(*x)[CEED_Q_VLA]    = (const CeedScalar(*)[CEED_Q_VLA])in[0];
284   const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[1];
285   CeedScalar(*q0)[CEED_Q_VLA]         = (CeedScalar(*)[CEED_Q_VLA])out[0];
286 
287   const StgShur14Context         stg_ctx = (StgShur14Context)ctx;
288   const NewtonianIdealGasContext gas     = &stg_ctx->newtonian_ctx;
289   CeedScalar                     qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
290   const CeedScalar               dx     = stg_ctx->dx;
291   const CeedScalar               time   = stg_ctx->time;
292   const CeedScalar               theta0 = stg_ctx->theta0;
293   const CeedScalar               P0     = stg_ctx->P0;
294   const CeedScalar               rho    = P0 / (GasConstant(gas) * theta0);
295   const CeedScalar               nu     = gas->mu / rho;
296 
297   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
298     const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]};
299     CeedScalar       dXdx[3][3];
300     InvertMappingJacobian_3D(Q, i, J, dXdx, NULL);
301     CeedScalar h_node_sep[3];
302     h_node_sep[0] = dx;
303     for (CeedInt j = 1; j < 3; j++) h_node_sep[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j]));
304     ScaleN(h_node_sep, stg_ctx->h_scale_factor, 3);
305 
306     InterpolateProfile(x_i[1], ubar, cij, &eps, &lt, stg_ctx);
307     if (stg_ctx->use_fluctuating_IC) {
308       CalcSpectrum(x_i[1], eps, lt, h_node_sep, nu, qn, stg_ctx);
309       StgShur14Calc(x_i, time, ubar, cij, qn, u, stg_ctx);
310     } else {
311       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
312     }
313 
314     CeedScalar Y[5] = {P0, u[0], u[1], u[2], theta0}, q[5];
315     State      s    = StateFromY(gas, Y);
316     StateToQ(gas, s, q, gas->state_var);
317     for (CeedInt j = 0; j < 5; j++) {
318       q0[j][i] = q[j];
319     }
320   }
321   return 0;
322 }
323 
324 /********************************************************************
325  * @brief QFunction to calculate the inflow boundary condition
326  *
327  * This will loop through quadrature points, calculate the wavemode amplitudes
328  * at each location, then calculate the actual velocity.
329  */
330 CEED_QFUNCTION(StgShur14Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
331   const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
332   const CeedScalar(*q_data_sur)    = in[2];
333   const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3];
334 
335   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
336   CeedScalar(*jac_data_sur)  = out[1];
337 
338   const StgShur14Context stg_ctx = (StgShur14Context)ctx;
339   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
340   const bool             is_implicit = stg_ctx->is_implicit;
341   const bool             mean_only   = stg_ctx->mean_only;
342   const bool             prescribe_T = stg_ctx->prescribe_T;
343   const CeedScalar       dx          = stg_ctx->dx;
344   const CeedScalar       mu          = stg_ctx->newtonian_ctx.mu;
345   const CeedScalar       time        = stg_ctx->time;
346   const CeedScalar       theta0      = stg_ctx->theta0;
347   const CeedScalar       P0          = stg_ctx->P0;
348   const CeedScalar       cv          = stg_ctx->newtonian_ctx.cv;
349   const CeedScalar       Rd          = GasConstant(&stg_ctx->newtonian_ctx);
350   const CeedScalar       gamma       = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
351 
352   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
353     const CeedScalar rho = prescribe_T ? q[0][i] : P0 / (Rd * theta0);
354     const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]};
355     CeedScalar       wdetJb, dXdx[2][3], norm[3];
356     QdataBoundaryUnpack_3D(Q, i, q_data_sur, &wdetJb, dXdx, norm);
357     wdetJb *= is_implicit ? -1. : 1.;
358 
359     CeedScalar h_node_sep[3];
360     h_node_sep[0] = dx;
361     for (CeedInt j = 1; j < 3; j++) h_node_sep[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
362     ScaleN(h_node_sep, stg_ctx->h_scale_factor, 3);
363 
364     InterpolateProfile(X[1][i], ubar, cij, &eps, &lt, stg_ctx);
365     if (!mean_only) {
366       CalcSpectrum(X[1][i], eps, lt, h_node_sep, mu / rho, qn, stg_ctx);
367       StgShur14Calc(x, time, ubar, cij, qn, u, stg_ctx);
368     } else {
369       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
370     }
371 
372     const CeedScalar E_kinetic = .5 * rho * Dot3(u, u);
373     CeedScalar       E_internal, P;
374     if (prescribe_T) {
375       // Temperature is being set weakly (theta0) and for constant cv this sets E_internal
376       E_internal = rho * cv * theta0;
377       // Find pressure using
378       P = rho * Rd * theta0;  // interior rho with exterior T
379     } else {
380       E_internal = q[4][i] - E_kinetic;  // uses prescribed rho and u, E from solution
381       P          = E_internal * (gamma - 1.);
382     }
383 
384     const CeedScalar E = E_internal + E_kinetic;
385 
386     // Velocity normal to the boundary
387     const CeedScalar u_normal = Dot3(norm, u);
388 
389     // The Physics
390     // Zero v so all future terms can safely sum into it
391     for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.;
392 
393     // The Physics
394     // -- Density
395     v[0][i] -= wdetJb * rho * u_normal;
396 
397     // -- Momentum
398     for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P);
399 
400     // -- Total Energy Density
401     v[4][i] -= wdetJb * u_normal * (E + P);
402 
403     const CeedScalar U[] = {rho, u[0], u[1], u[2], E}, kmstress[6] = {0.};
404     StoredValuesPack(Q, i, 0, 5, U, jac_data_sur);
405     StoredValuesPack(Q, i, 5, 6, kmstress, jac_data_sur);
406   }
407   return 0;
408 }
409 
410 CEED_QFUNCTION(StgShur14Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
411   const CeedScalar(*dq)[CEED_Q_VLA]           = (const CeedScalar(*)[CEED_Q_VLA])in[0];
412   const CeedScalar(*q_data_sur)[CEED_Q_VLA]   = (const CeedScalar(*)[CEED_Q_VLA])in[2];
413   const CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4];
414   CeedScalar(*v)[CEED_Q_VLA]                  = (CeedScalar(*)[CEED_Q_VLA])out[0];
415 
416   const StgShur14Context stg_ctx  = (StgShur14Context)ctx;
417   const bool             implicit = stg_ctx->is_implicit;
418   const CeedScalar       cv       = stg_ctx->newtonian_ctx.cv;
419   const CeedScalar       Rd       = GasConstant(&stg_ctx->newtonian_ctx);
420   const CeedScalar       gamma    = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
421 
422   const CeedScalar theta0      = stg_ctx->theta0;
423   const bool       prescribe_T = stg_ctx->prescribe_T;
424 
425   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
426     // Setup
427     // -- Interp-to-Interp q_data
428     // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
429     // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
430     // We can effect this by swapping the sign on this weight
431     const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];
432 
433     // Calculate inflow values
434     CeedScalar velocity[3];
435     for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i];
436     // TODO This is almost certainly a bug. Velocity isn't stored here, only 0s.
437 
438     // enabling user to choose between weak T and weak rho inflow
439     CeedScalar drho, dE, dP;
440     if (prescribe_T) {
441       // rho should be from the current solution
442       drho                   = dq[0][i];
443       CeedScalar dE_internal = drho * cv * theta0;
444       CeedScalar dE_kinetic  = .5 * drho * Dot3(velocity, velocity);
445       dE                     = dE_internal + dE_kinetic;
446       dP                     = drho * Rd * theta0;  // interior rho with exterior T
447     } else {                                        // rho specified, E_internal from solution
448       drho = 0;
449       dE   = dq[4][i];
450       dP   = dE * (gamma - 1.);
451     }
452     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
453 
454     const CeedScalar u_normal = Dot3(norm, velocity);
455 
456     v[0][i] = -wdetJb * drho * u_normal;
457     for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP);
458     v[4][i] = -wdetJb * u_normal * (dE + dP);
459   }
460   return 0;
461 }
462 
463 /********************************************************************
464  * @brief QFunction to calculate the strongly enforce inflow BC
465  *
466  * This QF is for the strong application of STG via libCEED (rather than
467  * through the native PETSc `DMAddBoundary` -> `bcFunc` method.
468  */
469 CEED_QFUNCTION(StgShur14InflowStrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
470   const CeedScalar *dXdx_q              = in[0];
471   const CeedScalar(*coords)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1];
472   const CeedScalar(*scale)              = (const CeedScalar(*))in[2];
473   const CeedScalar(*inv_Ektotal)        = (const CeedScalar(*))in[3];
474   CeedScalar(*bcval)[CEED_Q_VLA]        = (CeedScalar(*)[CEED_Q_VLA])out[0];
475 
476   const StgShur14Context         stg_ctx = (StgShur14Context)ctx;
477   const NewtonianIdealGasContext gas     = &stg_ctx->newtonian_ctx;
478   CeedScalar                     u[3], ubar[3], cij[6], eps, lt;
479   const bool                     mean_only = stg_ctx->mean_only;
480   const CeedScalar               time      = stg_ctx->time;
481   const CeedScalar               theta0    = stg_ctx->theta0;
482   const CeedScalar               P0        = stg_ctx->P0;
483   const CeedScalar               rho       = P0 / (GasConstant(gas) * theta0);
484   const CeedScalar               nu        = gas->mu / rho;
485 
486   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
487     const CeedScalar x[] = {coords[0][i], coords[1][i], coords[2][i]};
488     CeedScalar       dXdx[3][3], h_node_sep[3];
489     StoredValuesUnpack(Q, i, 0, 9, dXdx_q, (CeedScalar *)dXdx);
490 
491     CalculateElementLengths(dXdx, stg_ctx->h_scale_factor, h_node_sep);
492     InterpolateProfile(coords[1][i], ubar, cij, &eps, &lt, stg_ctx);
493     if (!mean_only) {
494       if (1) {
495         StgShur14Calc_PrecompEktot(x, time, ubar, cij, inv_Ektotal[i], h_node_sep, x[1], eps, lt, nu, u, stg_ctx);
496       } else {  // Original way
497         CeedScalar qn[STG_NMODES_MAX];
498         CalcSpectrum(coords[1][i], eps, lt, h_node_sep, nu, qn, stg_ctx);
499         StgShur14Calc(x, time, ubar, cij, qn, u, stg_ctx);
500       }
501     } else {
502       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
503     }
504 
505     CeedScalar Y[5] = {P0, u[0], u[1], u[2], theta0}, q[5];
506     State      s    = StateFromY(gas, Y);
507     StateToQ(gas, s, q, gas->state_var);
508     switch (gas->state_var) {
509       case STATEVAR_CONSERVATIVE:
510         q[4] = 0.;  // Don't set energy
511         break;
512       case STATEVAR_PRIMITIVE:
513         q[0] = 0;  // Don't set pressure
514         break;
515       case STATEVAR_ENTROPY:
516         q[0] = 0;  // Don't set V_density
517         break;
518     }
519     for (CeedInt j = 0; j < 5; j++) {
520       bcval[j][i] = scale[i] * q[j];
521     }
522   }
523   return 0;
524 }
525