xref: /honee/qfunctions/stg_shur14.h (revision d251f31f871a8e7ede595d3d842ce4d71f68b88c)
1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 /// @file
9 /// Implementation of the Synthetic Turbulence Generation (STG) algorithm
10 /// presented in Shur et al. 2014
11 //
12 /// SetupSTG_Rand reads in the input files and fills in STGShur14Context.
13 /// Then STGShur14_CalcQF is run over quadrature points.
14 /// Before the program exits, TearDownSTG is run to free the memory of the allocated arrays.
15 #include <ceed.h>
16 #include <math.h>
17 #include <stdlib.h>
18 
19 #include "newtonian_state.h"
20 #include "setupgeo_helpers.h"
21 #include "stg_shur14_type.h"
22 #include "utils.h"
23 
24 #define STG_NMODES_MAX 1024
25 
26 /*
27  * @brief Interpolate quantities from input profile to given location
28  *
29  * Assumed that prof_wd[i+1] > prof_wd[i] and prof_wd[0] = 0
30  * If wall_dist > prof_wd[-1], then the interpolation takes the values at prof_wd[-1]
31  *
32  * @param[in]  wall_dist Distance to the nearest wall
33  * @param[out] ubar      Mean velocity at wall_dist
34  * @param[out] cij       Cholesky decomposition at wall_dist
35  * @param[out] eps       Turbulent dissipation at wall_dist
36  * @param[out] lt        Turbulent length scale at wall_dist
37  * @param[in]  stg_ctx   STGShur14Context for the problem
38  */
39 CEED_QFUNCTION_HELPER void InterpolateProfile(const CeedScalar wall_dist, CeedScalar ubar[3], CeedScalar cij[6], CeedScalar *eps, CeedScalar *lt,
40                                               const StgShur14Context stg_ctx) {
41   const CeedInt     nprofs    = stg_ctx->nprofs;
42   const CeedScalar *prof_wd   = &stg_ctx->data[stg_ctx->offsets.wall_dist];
43   const CeedScalar *prof_eps  = &stg_ctx->data[stg_ctx->offsets.eps];
44   const CeedScalar *prof_lt   = &stg_ctx->data[stg_ctx->offsets.lt];
45   const CeedScalar *prof_ubar = &stg_ctx->data[stg_ctx->offsets.ubar];
46   const CeedScalar *prof_cij  = &stg_ctx->data[stg_ctx->offsets.cij];
47   CeedInt           idx       = -1;
48 
49   for (CeedInt i = 0; i < nprofs; i++) {
50     if (wall_dist < prof_wd[i]) {
51       idx = i;
52       break;
53     }
54   }
55 
56   if (idx > 0) {  // y within the bounds of prof_wd
57     CeedScalar coeff = (wall_dist - prof_wd[idx - 1]) / (prof_wd[idx] - prof_wd[idx - 1]);
58 
59     ubar[0] = prof_ubar[0 * nprofs + idx - 1] + coeff * (prof_ubar[0 * nprofs + idx] - prof_ubar[0 * nprofs + idx - 1]);
60     ubar[1] = prof_ubar[1 * nprofs + idx - 1] + coeff * (prof_ubar[1 * nprofs + idx] - prof_ubar[1 * nprofs + idx - 1]);
61     ubar[2] = prof_ubar[2 * nprofs + idx - 1] + coeff * (prof_ubar[2 * nprofs + idx] - prof_ubar[2 * nprofs + idx - 1]);
62     cij[0]  = prof_cij[0 * nprofs + idx - 1] + coeff * (prof_cij[0 * nprofs + idx] - prof_cij[0 * nprofs + idx - 1]);
63     cij[1]  = prof_cij[1 * nprofs + idx - 1] + coeff * (prof_cij[1 * nprofs + idx] - prof_cij[1 * nprofs + idx - 1]);
64     cij[2]  = prof_cij[2 * nprofs + idx - 1] + coeff * (prof_cij[2 * nprofs + idx] - prof_cij[2 * nprofs + idx - 1]);
65     cij[3]  = prof_cij[3 * nprofs + idx - 1] + coeff * (prof_cij[3 * nprofs + idx] - prof_cij[3 * nprofs + idx - 1]);
66     cij[4]  = prof_cij[4 * nprofs + idx - 1] + coeff * (prof_cij[4 * nprofs + idx] - prof_cij[4 * nprofs + idx - 1]);
67     cij[5]  = prof_cij[5 * nprofs + idx - 1] + coeff * (prof_cij[5 * nprofs + idx] - prof_cij[5 * nprofs + idx - 1]);
68     *eps    = prof_eps[idx - 1] + coeff * (prof_eps[idx] - prof_eps[idx - 1]);
69     *lt     = prof_lt[idx - 1] + coeff * (prof_lt[idx] - prof_lt[idx - 1]);
70   } else {  // y outside bounds of prof_wd
71     ubar[0] = prof_ubar[1 * nprofs - 1];
72     ubar[1] = prof_ubar[2 * nprofs - 1];
73     ubar[2] = prof_ubar[3 * nprofs - 1];
74     cij[0]  = prof_cij[1 * nprofs - 1];
75     cij[1]  = prof_cij[2 * nprofs - 1];
76     cij[2]  = prof_cij[3 * nprofs - 1];
77     cij[3]  = prof_cij[4 * nprofs - 1];
78     cij[4]  = prof_cij[5 * nprofs - 1];
79     cij[5]  = prof_cij[6 * nprofs - 1];
80     *eps    = prof_eps[nprofs - 1];
81     *lt     = prof_lt[nprofs - 1];
82   }
83 }
84 
85 /*
86  * @brief Calculate spectrum coefficient, qn
87  *
88  * Calculates q_n at a given distance to the wall
89  *
90  * @param[in]  kappa     nth wavenumber
91  * @param[in]  dkappa    Difference between wavenumbers
92  * @param[in]  keta      Dissipation wavenumber
93  * @param[in]  kcut      Mesh-induced cutoff wavenumber
94  * @param[in]  ke        Energy-containing wavenumber
95  * @param[in]  Ektot_inv Inverse of total turbulent kinetic energy of spectrum
96  * @returns    qn        Spectrum coefficient
97  */
98 CEED_QFUNCTION_HELPER CeedScalar Calc_qn(const CeedScalar kappa, const CeedScalar dkappa, const CeedScalar keta, const CeedScalar kcut,
99                                          const CeedScalar ke, const CeedScalar Ektot_inv) {
100   const CeedScalar feta_x_fcut = exp(-Square(12 * kappa / keta) - Cube(4 * Max(kappa - 0.9 * kcut, 0) / kcut));
101   return pow(kappa / ke, 4.) * pow(1 + 2.4 * Square(kappa / ke), -17. / 6) * feta_x_fcut * dkappa * Ektot_inv;
102 }
103 
104 // Calculate hmax, ke, keta, and kcut
105 CEED_QFUNCTION_HELPER void SpectrumConstants(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar hNodSep[3],
106                                              const CeedScalar nu, CeedScalar *hmax, CeedScalar *ke, CeedScalar *keta, CeedScalar *kcut) {
107   *hmax = Max(Max(hNodSep[0], hNodSep[1]), hNodSep[2]);
108   *ke   = wall_dist == 0 ? 1e16 : 2 * M_PI / Min(2 * wall_dist, 3 * lt);
109   *keta = 2 * M_PI * pow(Cube(nu) / eps, -0.25);
110   *kcut = M_PI / Min(Max(Max(hNodSep[1], hNodSep[2]), 0.3 * (*hmax)) + 0.1 * wall_dist, *hmax);
111 }
112 
113 /*
114  * @brief Calculate spectrum coefficients for STG
115  *
116  * Calculates q_n at a given distance to the wall
117  *
118  * @param[in]  wall_dist  Distance to the nearest wall
119  * @param[in]  eps        Turbulent dissipation w/rt wall_dist
120  * @param[in]  lt         Turbulent length scale w/rt wall_dist
121  * @param[in]  h_node_sep Element lengths in coordinate directions
122  * @param[in]  nu         Dynamic Viscosity;
123  * @param[in]  stg_ctx    STGShur14Context for the problem
124  * @param[out] qn         Spectrum coefficients, [nmodes]
125  */
126 CEED_QFUNCTION_HELPER void CalcSpectrum(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h_node_sep[3],
127                                         const CeedScalar nu, CeedScalar qn[], const StgShur14Context stg_ctx) {
128   const CeedInt     nmodes = stg_ctx->nmodes;
129   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
130   CeedScalar        hmax, ke, keta, kcut, Ektot = 0.0;
131 
132   SpectrumConstants(wall_dist, eps, lt, h_node_sep, nu, &hmax, &ke, &keta, &kcut);
133 
134   for (CeedInt n = 0; n < nmodes; n++) {
135     const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
136     qn[n]                   = Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
137     Ektot += qn[n];
138   }
139 
140   if (Ektot == 0) return;
141   for (CeedInt n = 0; n < nmodes; n++) qn[n] /= Ektot;
142 }
143 
144 /******************************************************
145  * @brief Calculate u(x,t) for STG inflow condition
146  *
147  * @param[in]  X       Location to evaluate u(X,t)
148  * @param[in]  t       Time to evaluate u(X,t)
149  * @param[in]  ubar    Mean velocity at X
150  * @param[in]  cij     Cholesky decomposition at X
151  * @param[in]  qn      Wavemode amplitudes at X, [nmodes]
152  * @param[out] u       Velocity at X and t
153  * @param[in]  stg_ctx STGShur14Context for the problem
154  */
155 CEED_QFUNCTION_HELPER void StgShur14Calc(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
156                                          const CeedScalar qn[], CeedScalar u[3], const StgShur14Context stg_ctx) {
157   const CeedInt     nmodes = stg_ctx->nmodes;
158   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
159   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
160   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
161   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
162   CeedScalar        xdotd, vp[3] = {0.};
163   CeedScalar        xhat[] = {0., X[1], X[2]};
164 
165   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
166     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
167     xdotd   = 0.;
168     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
169     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
170     vp[0] += sqrt(qn[n]) * sigma[0 * nmodes + n] * cos_kxdp;
171     vp[1] += sqrt(qn[n]) * sigma[1 * nmodes + n] * cos_kxdp;
172     vp[2] += sqrt(qn[n]) * sigma[2 * nmodes + n] * cos_kxdp;
173   }
174   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
175 
176   u[0] = ubar[0] + cij[0] * vp[0];
177   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
178   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
179 }
180 
181 /******************************************************
182  * @brief Calculate u(x,t) for STG inflow condition
183  *
184  * @param[in]  X          Location to evaluate u(X,t)
185  * @param[in]  t          Time to evaluate u(X,t)
186  * @param[in]  ubar       Mean velocity at X
187  * @param[in]  cij        Cholesky decomposition at X
188  * @param[in]  Ektot      Total spectrum energy at this location
189  * @param[in]  h_node_sep Element size in 3 directions
190  * @param[in]  wall_dist  Distance to closest wall
191  * @param[in]  eps        Turbulent dissipation
192  * @param[in]  lt         Turbulent length scale
193  * @param[out] u          Velocity at X and t
194  * @param[in]  stg_ctx    STGShur14Context for the problem
195  */
196 CEED_QFUNCTION_HELPER void StgShur14Calc_PrecompEktot(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
197                                                       const CeedScalar Ektot, const CeedScalar h_node_sep[3], const CeedScalar wall_dist,
198                                                       const CeedScalar eps, const CeedScalar lt, const CeedScalar nu, CeedScalar u[3],
199                                                       const StgShur14Context stg_ctx) {
200   const CeedInt     nmodes = stg_ctx->nmodes;
201   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
202   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
203   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
204   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
205   CeedScalar        hmax, ke, keta, kcut;
206   SpectrumConstants(wall_dist, eps, lt, h_node_sep, nu, &hmax, &ke, &keta, &kcut);
207   CeedScalar xdotd, vp[3] = {0.};
208   CeedScalar xhat[] = {0., X[1], X[2]};
209 
210   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
211     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
212     xdotd   = 0.;
213     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
214     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
215     const CeedScalar dkappa   = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
216     const CeedScalar qn       = Calc_qn(kappa[n], dkappa, keta, kcut, ke, Ektot);
217     vp[0] += sqrt(qn) * sigma[0 * nmodes + n] * cos_kxdp;
218     vp[1] += sqrt(qn) * sigma[1 * nmodes + n] * cos_kxdp;
219     vp[2] += sqrt(qn) * sigma[2 * nmodes + n] * cos_kxdp;
220   }
221   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
222 
223   u[0] = ubar[0] + cij[0] * vp[0];
224   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
225   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
226 }
227 
228 /**
229    @brief Calculate the element length scales based on dXdx
230 
231    WARNING: This assumes the reference domain is [-1,1], which is not true for tetrahedral elements
232 
233    @param[in]  dXdx    Inverse mapping Jacobian, d\xi/dx
234    @param[in]  scale   Scale factor for the element lengths
235    @param[out] lengths The element lengths in each cartesian direction
236 **/
237 CEED_QFUNCTION_HELPER void CalculateElementLengths(CeedScalar dXdx[3][3], CeedScalar scale, CeedScalar lengths[3]) {
238   for (CeedInt j = 0; j < 3; j++) lengths[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j]));
239   ScaleN(lengths, scale, 3);
240 }
241 
242 // Create preprocessed input for the stg calculation
243 //
244 // stg_data[0] = 1 / Ektot (inverse of total spectrum energy)
245 CEED_QFUNCTION(StgShur14Preprocess)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
246   const CeedScalar *dXdx_q         = in[0];
247   const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1];
248 
249   CeedScalar(*stg_data) = (CeedScalar(*))out[0];
250 
251   CeedScalar             ubar[3], cij[6], eps, lt;
252   const StgShur14Context stg_ctx = (StgShur14Context)ctx;
253   const CeedScalar       mu      = stg_ctx->newtonian_ctx.mu;
254   const CeedScalar       theta0  = stg_ctx->theta0;
255   const CeedScalar       P0      = stg_ctx->P0;
256   const CeedScalar       Rd      = GasConstant(&stg_ctx->newtonian_ctx);
257   const CeedScalar       rho     = P0 / (Rd * theta0);
258   const CeedScalar       nu      = mu / rho;
259 
260   const CeedInt     nmodes = stg_ctx->nmodes;
261   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
262   CeedScalar        hmax, ke, keta, kcut;
263 
264   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
265     const CeedScalar wall_dist = x[1][i];
266     CeedScalar       dXdx[3][3], h_node_sep[3];
267     StoredValuesUnpack(Q, i, 0, 9, dXdx_q, (CeedScalar *)dXdx);
268 
269     CalculateElementLengths(dXdx, stg_ctx->h_scale_factor, h_node_sep);
270     InterpolateProfile(wall_dist, ubar, cij, &eps, &lt, stg_ctx);
271     SpectrumConstants(wall_dist, eps, lt, h_node_sep, nu, &hmax, &ke, &keta, &kcut);
272 
273     // Calculate total TKE per spectrum
274     CeedScalar Ek_tot = 0;
275     CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
276       const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
277       Ek_tot += Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
278     }
279     // avoid underflowed and poorly defined spectrum coefficients
280     stg_data[i] = Ek_tot != 0 ? 1 / Ek_tot : 0;
281   }
282   return 0;
283 }
284 
285 // Extrude the STGInflow profile through out the domain for an initial condition
286 CEED_QFUNCTION(ICsStg)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
287   const CeedScalar(*x)[CEED_Q_VLA]    = (const CeedScalar(*)[CEED_Q_VLA])in[0];
288   const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[1];
289   CeedScalar(*q0)[CEED_Q_VLA]         = (CeedScalar(*)[CEED_Q_VLA])out[0];
290 
291   const StgShur14Context         stg_ctx = (StgShur14Context)ctx;
292   const NewtonianIdealGasContext gas     = &stg_ctx->newtonian_ctx;
293   CeedScalar                     qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
294   const CeedScalar               dx     = stg_ctx->dx;
295   const CeedScalar               time   = stg_ctx->time;
296   const CeedScalar               theta0 = stg_ctx->theta0;
297   const CeedScalar               P0     = stg_ctx->P0;
298   const CeedScalar               rho    = P0 / (GasConstant(gas) * theta0);
299   const CeedScalar               nu     = gas->mu / rho;
300 
301   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
302     const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]};
303     CeedScalar       dXdx[3][3];
304     InvertMappingJacobian_3D(Q, i, J, dXdx, NULL);
305     CeedScalar h_node_sep[3];
306     h_node_sep[0] = dx;
307     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]));
308     ScaleN(h_node_sep, stg_ctx->h_scale_factor, 3);
309 
310     InterpolateProfile(x_i[1], ubar, cij, &eps, &lt, stg_ctx);
311     if (stg_ctx->use_fluctuating_IC) {
312       CalcSpectrum(x_i[1], eps, lt, h_node_sep, nu, qn, stg_ctx);
313       StgShur14Calc(x_i, time, ubar, cij, qn, u, stg_ctx);
314     } else {
315       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
316     }
317 
318     CeedScalar Y[5] = {P0, u[0], u[1], u[2], theta0}, q[5];
319     State      s    = StateFromY(gas, Y);
320     StateToQ(gas, s, q, gas->state_var);
321     for (CeedInt j = 0; j < 5; j++) {
322       q0[j][i] = q[j];
323     }
324   }
325   return 0;
326 }
327 
328 /********************************************************************
329  * @brief QFunction to calculate the inflow boundary condition
330  *
331  * This will loop through quadrature points, calculate the wavemode amplitudes
332  * at each location, then calculate the actual velocity.
333  */
334 CEED_QFUNCTION(StgShur14Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
335   const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
336   const CeedScalar(*q_data_sur)    = in[2];
337   const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3];
338 
339   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
340   CeedScalar(*jac_data_sur)  = out[1];
341 
342   const StgShur14Context stg_ctx = (StgShur14Context)ctx;
343   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
344   const bool             is_implicit = stg_ctx->is_implicit;
345   const bool             mean_only   = stg_ctx->mean_only;
346   const bool             prescribe_T = stg_ctx->prescribe_T;
347   const CeedScalar       dx          = stg_ctx->dx;
348   const CeedScalar       mu          = stg_ctx->newtonian_ctx.mu;
349   const CeedScalar       time        = stg_ctx->time;
350   const CeedScalar       theta0      = stg_ctx->theta0;
351   const CeedScalar       P0          = stg_ctx->P0;
352   const CeedScalar       cv          = stg_ctx->newtonian_ctx.cv;
353   const CeedScalar       Rd          = GasConstant(&stg_ctx->newtonian_ctx);
354   const CeedScalar       gamma       = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
355 
356   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
357     const CeedScalar rho = prescribe_T ? q[0][i] : P0 / (Rd * theta0);
358     const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]};
359     CeedScalar       wdetJb, dXdx[2][3], norm[3];
360     QdataBoundaryUnpack_3D(Q, i, q_data_sur, &wdetJb, dXdx, norm);
361     wdetJb *= is_implicit ? -1. : 1.;
362 
363     CeedScalar h_node_sep[3];
364     h_node_sep[0] = dx;
365     for (CeedInt j = 1; j < 3; j++) h_node_sep[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
366     ScaleN(h_node_sep, stg_ctx->h_scale_factor, 3);
367 
368     InterpolateProfile(X[1][i], ubar, cij, &eps, &lt, stg_ctx);
369     if (!mean_only) {
370       CalcSpectrum(X[1][i], eps, lt, h_node_sep, mu / rho, qn, stg_ctx);
371       StgShur14Calc(x, time, ubar, cij, qn, u, stg_ctx);
372     } else {
373       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
374     }
375 
376     const CeedScalar E_kinetic = .5 * rho * Dot3(u, u);
377     CeedScalar       E_internal, P;
378     if (prescribe_T) {
379       // Temperature is being set weakly (theta0) and for constant cv this sets E_internal
380       E_internal = rho * cv * theta0;
381       // Find pressure using
382       P = rho * Rd * theta0;  // interior rho with exterior T
383     } else {
384       E_internal = q[4][i] - E_kinetic;  // uses prescribed rho and u, E from solution
385       P          = E_internal * (gamma - 1.);
386     }
387 
388     const CeedScalar E = E_internal + E_kinetic;
389 
390     // Velocity normal to the boundary
391     const CeedScalar u_normal = Dot3(norm, u);
392 
393     // The Physics
394     // Zero v so all future terms can safely sum into it
395     for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.;
396 
397     // The Physics
398     // -- Density
399     v[0][i] -= wdetJb * rho * u_normal;
400 
401     // -- Momentum
402     for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P);
403 
404     // -- Total Energy Density
405     v[4][i] -= wdetJb * u_normal * (E + P);
406 
407     const CeedScalar U[] = {rho, u[0], u[1], u[2], E}, kmstress[6] = {0.};
408     StoredValuesPack(Q, i, 0, 5, U, jac_data_sur);
409     StoredValuesPack(Q, i, 5, 6, kmstress, jac_data_sur);
410   }
411   return 0;
412 }
413 
414 CEED_QFUNCTION(StgShur14Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
415   const CeedScalar(*dq)[CEED_Q_VLA]           = (const CeedScalar(*)[CEED_Q_VLA])in[0];
416   const CeedScalar(*q_data_sur)[CEED_Q_VLA]   = (const CeedScalar(*)[CEED_Q_VLA])in[2];
417   const CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4];
418   CeedScalar(*v)[CEED_Q_VLA]                  = (CeedScalar(*)[CEED_Q_VLA])out[0];
419 
420   const StgShur14Context stg_ctx  = (StgShur14Context)ctx;
421   const bool             implicit = stg_ctx->is_implicit;
422   const CeedScalar       cv       = stg_ctx->newtonian_ctx.cv;
423   const CeedScalar       Rd       = GasConstant(&stg_ctx->newtonian_ctx);
424   const CeedScalar       gamma    = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
425 
426   const CeedScalar theta0      = stg_ctx->theta0;
427   const bool       prescribe_T = stg_ctx->prescribe_T;
428 
429   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
430     // Setup
431     // -- Interp-to-Interp q_data
432     // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
433     // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
434     // We can effect this by swapping the sign on this weight
435     const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];
436 
437     // Calculate inflow values
438     CeedScalar velocity[3];
439     for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i];
440     // TODO This is almost certainly a bug. Velocity isn't stored here, only 0s.
441 
442     // enabling user to choose between weak T and weak rho inflow
443     CeedScalar drho, dE, dP;
444     if (prescribe_T) {
445       // rho should be from the current solution
446       drho                   = dq[0][i];
447       CeedScalar dE_internal = drho * cv * theta0;
448       CeedScalar dE_kinetic  = .5 * drho * Dot3(velocity, velocity);
449       dE                     = dE_internal + dE_kinetic;
450       dP                     = drho * Rd * theta0;  // interior rho with exterior T
451     } else {                                        // rho specified, E_internal from solution
452       drho = 0;
453       dE   = dq[4][i];
454       dP   = dE * (gamma - 1.);
455     }
456     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
457 
458     const CeedScalar u_normal = Dot3(norm, velocity);
459 
460     v[0][i] = -wdetJb * drho * u_normal;
461     for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP);
462     v[4][i] = -wdetJb * u_normal * (dE + dP);
463   }
464   return 0;
465 }
466 
467 /********************************************************************
468  * @brief QFunction to calculate the strongly enforce inflow BC
469  *
470  * This QF is for the strong application of STG via libCEED (rather than
471  * through the native PETSc `DMAddBoundary` -> `bcFunc` method.
472  */
473 CEED_QFUNCTION(StgShur14InflowStrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
474   const CeedScalar *dXdx_q              = in[0];
475   const CeedScalar(*coords)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1];
476   const CeedScalar(*scale)              = (const CeedScalar(*))in[2];
477   const CeedScalar(*inv_Ektotal)        = (const CeedScalar(*))in[3];
478   CeedScalar(*bcval)[CEED_Q_VLA]        = (CeedScalar(*)[CEED_Q_VLA])out[0];
479 
480   const StgShur14Context         stg_ctx = (StgShur14Context)ctx;
481   const NewtonianIdealGasContext gas     = &stg_ctx->newtonian_ctx;
482   CeedScalar                     u[3], ubar[3], cij[6], eps, lt;
483   const bool                     mean_only = stg_ctx->mean_only;
484   const CeedScalar               time      = stg_ctx->time;
485   const CeedScalar               theta0    = stg_ctx->theta0;
486   const CeedScalar               P0        = stg_ctx->P0;
487   const CeedScalar               rho       = P0 / (GasConstant(gas) * theta0);
488   const CeedScalar               nu        = gas->mu / rho;
489 
490   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
491     const CeedScalar x[] = {coords[0][i], coords[1][i], coords[2][i]};
492     CeedScalar       dXdx[3][3], h_node_sep[3];
493     StoredValuesUnpack(Q, i, 0, 9, dXdx_q, (CeedScalar *)dXdx);
494 
495     CalculateElementLengths(dXdx, stg_ctx->h_scale_factor, h_node_sep);
496     InterpolateProfile(coords[1][i], ubar, cij, &eps, &lt, stg_ctx);
497     if (!mean_only) {
498       if (1) {
499         StgShur14Calc_PrecompEktot(x, time, ubar, cij, inv_Ektotal[i], h_node_sep, x[1], eps, lt, nu, u, stg_ctx);
500       } else {  // Original way
501         CeedScalar qn[STG_NMODES_MAX];
502         CalcSpectrum(coords[1][i], eps, lt, h_node_sep, nu, qn, stg_ctx);
503         StgShur14Calc(x, time, ubar, cij, qn, u, stg_ctx);
504       }
505     } else {
506       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
507     }
508 
509     CeedScalar Y[5] = {P0, u[0], u[1], u[2], theta0}, q[5];
510     State      s    = StateFromY(gas, Y);
511     StateToQ(gas, s, q, gas->state_var);
512     switch (gas->state_var) {
513       case STATEVAR_CONSERVATIVE:
514         q[4] = 0.;  // Don't set energy
515         break;
516       case STATEVAR_PRIMITIVE:
517         q[0] = 0;  // Don't set pressure
518         break;
519       case STATEVAR_ENTROPY:
520         q[0] = 0;  // Don't set V_density
521         break;
522     }
523     for (CeedInt j = 0; j < 5; j++) {
524       bcval[j][i] = scale[i] * q[j];
525     }
526   }
527   return 0;
528 }
529