xref: /libCEED/examples/fluids/qfunctions/stg_shur14.h (revision 47fa654bdb0443fad7121e250bf7da7adb8330de)
1 // Copyright (c) 2017-2022, 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. Then
13 /// STGShur14_CalcQF is run over quadrature points. Before the program exits,
14 /// TearDownSTG is run to free the memory of the allocated arrays.
15 
16 #ifndef stg_shur14_h
17 #define stg_shur14_h
18 
19 #include <ceed.h>
20 #include <math.h>
21 #include <stdlib.h>
22 
23 #include "stg_shur14_type.h"
24 #include "utils.h"
25 
26 #define STG_NMODES_MAX 1024
27 
28 /*
29  * @brief Interpolate quantities from input profile to given location
30  *
31  * Assumed that prof_wd[i+1] > prof_wd[i] and prof_wd[0] = 0
32  * If wall_dist > prof_wd[-1], then the interpolation takes the values at prof_wd[-1]
33  *
34  * @param[in]  wall_dist Distance to the nearest wall
35  * @param[out] ubar      Mean velocity at wall_dist
36  * @param[out] cij       Cholesky decomposition at wall_dist
37  * @param[out] eps       Turbulent dissipation at wall_dist
38  * @param[out] lt        Turbulent length scale at wall_dist
39  * @param[in]  stg_ctx   STGShur14Context for the problem
40  */
41 CEED_QFUNCTION_HELPER void InterpolateProfile(const CeedScalar wall_dist, CeedScalar ubar[3], CeedScalar cij[6], CeedScalar *eps, CeedScalar *lt,
42                                               const STGShur14Context stg_ctx) {
43   const CeedInt     nprofs    = stg_ctx->nprofs;
44   const CeedScalar *prof_wd   = &stg_ctx->data[stg_ctx->offsets.wall_dist];
45   const CeedScalar *prof_eps  = &stg_ctx->data[stg_ctx->offsets.eps];
46   const CeedScalar *prof_lt   = &stg_ctx->data[stg_ctx->offsets.lt];
47   const CeedScalar *prof_ubar = &stg_ctx->data[stg_ctx->offsets.ubar];
48   const CeedScalar *prof_cij  = &stg_ctx->data[stg_ctx->offsets.cij];
49   CeedInt           idx       = -1;
50 
51   for (CeedInt i = 0; i < nprofs; i++) {
52     if (wall_dist < prof_wd[i]) {
53       idx = i;
54       break;
55     }
56   }
57 
58   if (idx > 0) {  // y within the bounds of prof_wd
59     CeedScalar coeff = (wall_dist - prof_wd[idx - 1]) / (prof_wd[idx] - prof_wd[idx - 1]);
60 
61     ubar[0] = prof_ubar[0 * nprofs + idx - 1] + coeff * (prof_ubar[0 * nprofs + idx] - prof_ubar[0 * nprofs + idx - 1]);
62     ubar[1] = prof_ubar[1 * nprofs + idx - 1] + coeff * (prof_ubar[1 * nprofs + idx] - prof_ubar[1 * nprofs + idx - 1]);
63     ubar[2] = prof_ubar[2 * nprofs + idx - 1] + coeff * (prof_ubar[2 * nprofs + idx] - prof_ubar[2 * nprofs + idx - 1]);
64     cij[0]  = prof_cij[0 * nprofs + idx - 1] + coeff * (prof_cij[0 * nprofs + idx] - prof_cij[0 * nprofs + idx - 1]);
65     cij[1]  = prof_cij[1 * nprofs + idx - 1] + coeff * (prof_cij[1 * nprofs + idx] - prof_cij[1 * nprofs + idx - 1]);
66     cij[2]  = prof_cij[2 * nprofs + idx - 1] + coeff * (prof_cij[2 * nprofs + idx] - prof_cij[2 * nprofs + idx - 1]);
67     cij[3]  = prof_cij[3 * nprofs + idx - 1] + coeff * (prof_cij[3 * nprofs + idx] - prof_cij[3 * nprofs + idx - 1]);
68     cij[4]  = prof_cij[4 * nprofs + idx - 1] + coeff * (prof_cij[4 * nprofs + idx] - prof_cij[4 * nprofs + idx - 1]);
69     cij[5]  = prof_cij[5 * nprofs + idx - 1] + coeff * (prof_cij[5 * nprofs + idx] - prof_cij[5 * nprofs + idx - 1]);
70     *eps    = prof_eps[idx - 1] + coeff * (prof_eps[idx] - prof_eps[idx - 1]);
71     *lt     = prof_lt[idx - 1] + coeff * (prof_lt[idx] - prof_lt[idx - 1]);
72   } else {  // y outside bounds of prof_wd
73     ubar[0] = prof_ubar[1 * nprofs - 1];
74     ubar[1] = prof_ubar[2 * nprofs - 1];
75     ubar[2] = prof_ubar[3 * nprofs - 1];
76     cij[0]  = prof_cij[1 * nprofs - 1];
77     cij[1]  = prof_cij[2 * nprofs - 1];
78     cij[2]  = prof_cij[3 * nprofs - 1];
79     cij[3]  = prof_cij[4 * nprofs - 1];
80     cij[4]  = prof_cij[5 * nprofs - 1];
81     cij[5]  = prof_cij[6 * nprofs - 1];
82     *eps    = prof_eps[nprofs - 1];
83     *lt     = prof_lt[nprofs - 1];
84   }
85 }
86 
87 /*
88  * @brief Calculate spectrum coefficient, qn
89  *
90  * Calculates q_n at a given distance to the wall
91  *
92  * @param[in]  kappa  nth wavenumber
93  * @param[in]  dkappa Difference between wavenumbers
94  * @param[in]  keta   Dissipation wavenumber
95  * @param[in]  kcut   Mesh-induced cutoff wavenumber
96  * @param[in]  ke     Energy-containing wavenumber
97  * @param[in]  Ektot  Total turbulent kinetic energy of spectrum
98  * @returns    qn     Spectrum coefficient
99  */
100 CEED_QFUNCTION_HELPER CeedScalar Calc_qn(const CeedScalar kappa, const CeedScalar dkappa, const CeedScalar keta, const CeedScalar kcut,
101                                          const CeedScalar ke, const CeedScalar Ektot_inv) {
102   const CeedScalar feta_x_fcut = exp(-Square(12 * kappa / keta) - Cube(4 * Max(kappa - 0.9 * kcut, 0) / kcut));
103   return pow(kappa / ke, 4.) * pow(1 + 2.4 * Square(kappa / ke), -17. / 6) * feta_x_fcut * dkappa * Ektot_inv;
104 }
105 
106 // Calculate hmax, ke, keta, and kcut
107 CEED_QFUNCTION_HELPER void SpectrumConstants(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3],
108                                              const CeedScalar nu, CeedScalar *hmax, CeedScalar *ke, CeedScalar *keta, CeedScalar *kcut) {
109   *hmax = Max(Max(h[0], h[1]), h[2]);
110   *ke   = wall_dist == 0 ? 1e16 : 2 * M_PI / Min(2 * wall_dist, 3 * lt);
111   *keta = 2 * M_PI * pow(Cube(nu) / eps, -0.25);
112   *kcut = M_PI / Min(Max(Max(h[1], h[2]), 0.3 * (*hmax)) + 0.1 * wall_dist, *hmax);
113 }
114 
115 /*
116  * @brief Calculate spectrum coefficients for STG
117  *
118  * Calculates q_n at a given distance to the wall
119  *
120  * @param[in]  wall_dist Distance to the nearest wall
121  * @param[in]  eps       Turbulent dissipation w/rt wall_dist
122  * @param[in]  lt        Turbulent length scale w/rt wall_dist
123  * @param[in]  h         Element lengths in coordinate directions
124  * @param[in]  nu        Dynamic Viscosity;
125  * @param[in]  stg_ctx   STGShur14Context for the problem
126  * @param[out] qn        Spectrum coefficients, [nmodes]
127  */
128 CEED_QFUNCTION_HELPER void CalcSpectrum(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3],
129                                         const CeedScalar nu, CeedScalar qn[], const STGShur14Context stg_ctx) {
130   const CeedInt     nmodes = stg_ctx->nmodes;
131   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
132   CeedScalar        hmax, ke, keta, kcut, Ektot = 0.0;
133 
134   SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
135 
136   for (CeedInt n = 0; n < nmodes; n++) {
137     const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
138     qn[n]                   = Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
139     Ektot += qn[n];
140   }
141 
142   if (Ektot == 0) return;
143   for (CeedInt n = 0; n < nmodes; n++) qn[n] /= Ektot;
144 }
145 
146 /******************************************************
147  * @brief Calculate u(x,t) for STG inflow condition
148  *
149  * @param[in]  X       Location to evaluate u(X,t)
150  * @param[in]  t       Time to evaluate u(X,t)
151  * @param[in]  ubar    Mean velocity at X
152  * @param[in]  cij     Cholesky decomposition at X
153  * @param[in]  qn      Wavemode amplitudes at X, [nmodes]
154  * @param[out] u       Velocity at X and t
155  * @param[in]  stg_ctx STGShur14Context for the problem
156  */
157 CEED_QFUNCTION_HELPER void STGShur14_Calc(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
158                                           const CeedScalar qn[], CeedScalar u[3], const STGShur14Context stg_ctx) {
159   const CeedInt     nmodes = stg_ctx->nmodes;
160   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
161   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
162   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
163   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
164   CeedScalar        xdotd, vp[3] = {0.};
165   CeedScalar        xhat[] = {0., X[1], X[2]};
166 
167   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
168     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
169     xdotd   = 0.;
170     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
171     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
172     vp[0] += sqrt(qn[n]) * sigma[0 * nmodes + n] * cos_kxdp;
173     vp[1] += sqrt(qn[n]) * sigma[1 * nmodes + n] * cos_kxdp;
174     vp[2] += sqrt(qn[n]) * sigma[2 * nmodes + n] * cos_kxdp;
175   }
176   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
177 
178   u[0] = ubar[0] + cij[0] * vp[0];
179   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
180   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
181 }
182 
183 /******************************************************
184  * @brief Calculate u(x,t) for STG inflow condition
185  *
186  * @param[in]  X         Location to evaluate u(X,t)
187  * @param[in]  t         Time to evaluate u(X,t)
188  * @param[in]  ubar      Mean velocity at X
189  * @param[in]  cij       Cholesky decomposition at X
190  * @param[in]  Ektot     Total spectrum energy at this location
191  * @param[in]  h         Element size in 3 directions
192  * @param[in]  wall_dist Distance to closest wall
193  * @param[in]  eps       Turbulent dissipation
194  * @param[in]  lt        Turbulent length scale
195  * @param[out] u         Velocity at X and t
196  * @param[in]  stg_ctx   STGShur14Context for the problem
197  */
198 CEED_QFUNCTION_HELPER void STGShur14_Calc_PrecompEktot(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
199                                                        const CeedScalar Ektot, const CeedScalar h[3], const CeedScalar wall_dist,
200                                                        const CeedScalar eps, const CeedScalar lt, const CeedScalar nu, CeedScalar u[3],
201                                                        const STGShur14Context stg_ctx) {
202   const CeedInt     nmodes = stg_ctx->nmodes;
203   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
204   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
205   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
206   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
207   CeedScalar        hmax, ke, keta, kcut;
208   SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
209   CeedScalar xdotd, vp[3] = {0.};
210   CeedScalar xhat[] = {0., X[1], X[2]};
211 
212   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
213     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
214     xdotd   = 0.;
215     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
216     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
217     const CeedScalar dkappa   = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
218     const CeedScalar qn       = Calc_qn(kappa[n], dkappa, keta, kcut, ke, Ektot);
219     vp[0] += sqrt(qn) * sigma[0 * nmodes + n] * cos_kxdp;
220     vp[1] += sqrt(qn) * sigma[1 * nmodes + n] * cos_kxdp;
221     vp[2] += sqrt(qn) * sigma[2 * nmodes + n] * cos_kxdp;
222   }
223   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
224 
225   u[0] = ubar[0] + cij[0] * vp[0];
226   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
227   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
228 }
229 
230 // Create preprocessed input for the stg calculation
231 //
232 // stg_data[0] = 1 / Ektot (inverse of total spectrum energy)
233 CEED_QFUNCTION(Preprocess_STGShur14)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
234   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1];
235 
236   CeedScalar(*stg_data) = (CeedScalar(*))out[0];
237 
238   CeedScalar             ubar[3], cij[6], eps, lt;
239   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
240   const CeedScalar       dx      = stg_ctx->dx;
241   const CeedScalar       mu      = stg_ctx->newtonian_ctx.mu;
242   const CeedScalar       theta0  = stg_ctx->theta0;
243   const CeedScalar       P0      = stg_ctx->P0;
244   const CeedScalar       cv      = stg_ctx->newtonian_ctx.cv;
245   const CeedScalar       cp      = stg_ctx->newtonian_ctx.cp;
246   const CeedScalar       Rd      = cp - cv;
247   const CeedScalar       rho     = P0 / (Rd * theta0);
248   const CeedScalar       nu      = mu / rho;
249 
250   const CeedInt     nmodes = stg_ctx->nmodes;
251   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
252   CeedScalar        hmax, ke, keta, kcut;
253 
254   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
255     const CeedScalar wall_dist  = x[1][i];
256     const CeedScalar dXdx[2][3] = {
257         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
258         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
259     };
260 
261     CeedScalar h[3];
262     h[0] = dx;
263     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(dXdx[0][j] * dXdx[0][j] + dXdx[1][j] * dXdx[1][j]);
264 
265     InterpolateProfile(wall_dist, ubar, cij, &eps, &lt, stg_ctx);
266     SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
267 
268     // Calculate total TKE per spectrum
269     CeedScalar Ek_tot = 0;
270     CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
271       const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
272       Ek_tot += Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
273     }
274     // avoid underflowed and poorly defined spectrum coefficients
275     stg_data[i] = Ek_tot != 0 ? 1 / Ek_tot : 0;
276   }
277   return 0;
278 }
279 
280 // Extrude the STGInflow profile through out the domain for an initial condition
281 CEED_QFUNCTION(ICsSTG)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
282   // Inputs
283   const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1];
284   // Outputs
285   CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
286 
287   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
288   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
289   const CeedScalar       dx     = stg_ctx->dx;
290   const CeedScalar       time   = stg_ctx->time;
291   const CeedScalar       theta0 = stg_ctx->theta0;
292   const CeedScalar       P0     = stg_ctx->P0;
293   const CeedScalar       mu     = stg_ctx->newtonian_ctx.mu;
294   const CeedScalar       cv     = stg_ctx->newtonian_ctx.cv;
295   const CeedScalar       cp     = stg_ctx->newtonian_ctx.cp;
296   const CeedScalar       Rd     = cp - cv;
297   const CeedScalar       rho    = P0 / (Rd * theta0);
298 
299   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
300     const CeedScalar x_i[3]     = {x[0][i], x[1][i], x[2][i]};
301     const CeedScalar dXdx[3][3] = {
302         {q_data[1][i], q_data[2][i], q_data[3][i]},
303         {q_data[4][i], q_data[5][i], q_data[6][i]},
304         {q_data[7][i], q_data[8][i], q_data[9][i]}
305     };
306 
307     CeedScalar h[3];
308     h[0] = dx;
309     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j]));
310 
311     InterpolateProfile(x_i[1], ubar, cij, &eps, &lt, stg_ctx);
312     if (stg_ctx->use_fluctuating_IC) {
313       CalcSpectrum(x_i[1], eps, lt, h, mu / rho, qn, stg_ctx);
314       STGShur14_Calc(x_i, time, ubar, cij, qn, u, stg_ctx);
315     } else {
316       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
317     }
318 
319     switch (stg_ctx->newtonian_ctx.state_var) {
320       case STATEVAR_CONSERVATIVE:
321         q0[0][i] = rho;
322         q0[1][i] = u[0] * rho;
323         q0[2][i] = u[1] * rho;
324         q0[3][i] = u[2] * rho;
325         q0[4][i] = rho * (0.5 * Dot3(u, u) + cv * theta0);
326         break;
327 
328       case STATEVAR_PRIMITIVE:
329         q0[0][i] = P0;
330         q0[1][i] = u[0];
331         q0[2][i] = u[1];
332         q0[3][i] = u[2];
333         q0[4][i] = theta0;
334         break;
335     }
336   }  // End of Quadrature Point Loop
337   return 0;
338 }
339 
340 /********************************************************************
341  * @brief QFunction to calculate the inflow boundary condition
342  *
343  * This will loop through quadrature points, calculate the wavemode amplitudes
344  * at each location, then calculate the actual velocity.
345  */
346 CEED_QFUNCTION(STGShur14_Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
347   const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2],
348         (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3];
349 
350   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0], (*jac_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1];
351 
352   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
353   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
354   const bool             is_implicit = stg_ctx->is_implicit;
355   const bool             mean_only   = stg_ctx->mean_only;
356   const bool             prescribe_T = stg_ctx->prescribe_T;
357   const CeedScalar       dx          = stg_ctx->dx;
358   const CeedScalar       mu          = stg_ctx->newtonian_ctx.mu;
359   const CeedScalar       time        = stg_ctx->time;
360   const CeedScalar       theta0      = stg_ctx->theta0;
361   const CeedScalar       P0          = stg_ctx->P0;
362   const CeedScalar       cv          = stg_ctx->newtonian_ctx.cv;
363   const CeedScalar       cp          = stg_ctx->newtonian_ctx.cp;
364   const CeedScalar       Rd          = cp - cv;
365   const CeedScalar       gamma       = cp / cv;
366 
367   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
368     const CeedScalar rho        = prescribe_T ? q[0][i] : P0 / (Rd * theta0);
369     const CeedScalar x[]        = {X[0][i], X[1][i], X[2][i]};
370     const CeedScalar dXdx[2][3] = {
371         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
372         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
373     };
374 
375     CeedScalar h[3];
376     h[0] = dx;
377     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
378 
379     InterpolateProfile(X[1][i], ubar, cij, &eps, &lt, stg_ctx);
380     if (!mean_only) {
381       CalcSpectrum(X[1][i], eps, lt, h, mu / rho, qn, stg_ctx);
382       STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
383     } else {
384       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
385     }
386 
387     const CeedScalar E_kinetic = .5 * rho * Dot3(u, u);
388     CeedScalar       E_internal, P;
389     if (prescribe_T) {
390       // Temperature is being set weakly (theta0) and for constant cv this sets E_internal
391       E_internal = rho * cv * theta0;
392       // Find pressure using
393       P = rho * Rd * theta0;  // interior rho with exterior T
394     } else {
395       E_internal = q[4][i] - E_kinetic;  // uses prescribed rho and u, E from solution
396       P          = E_internal * (gamma - 1.);
397     }
398 
399     const CeedScalar wdetJb = (is_implicit ? -1. : 1.) * q_data_sur[0][i];
400     // ---- Normal vect
401     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
402 
403     const CeedScalar E = E_internal + E_kinetic;
404 
405     // Velocity normal to the boundary
406     const CeedScalar u_normal = Dot3(norm, u);
407 
408     // The Physics
409     // Zero v so all future terms can safely sum into it
410     for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.;
411 
412     // The Physics
413     // -- Density
414     v[0][i] -= wdetJb * rho * u_normal;
415 
416     // -- Momentum
417     for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P);
418 
419     // -- Total Energy Density
420     v[4][i] -= wdetJb * u_normal * (E + P);
421 
422     jac_data_sur[0][i] = rho;
423     jac_data_sur[1][i] = u[0];
424     jac_data_sur[2][i] = u[1];
425     jac_data_sur[3][i] = u[2];
426     jac_data_sur[4][i] = E;
427     for (int j = 0; j < 6; j++) jac_data_sur[5 + j][i] = 0.;
428   }
429   return 0;
430 }
431 
432 CEED_QFUNCTION(STGShur14_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
433   // Inputs
434   const CeedScalar(*dq)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2],
435         (*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4];
436   // Outputs
437   CeedScalar(*v)[CEED_Q_VLA]      = (CeedScalar(*)[CEED_Q_VLA])out[0];
438   const STGShur14Context stg_ctx  = (STGShur14Context)ctx;
439   const bool             implicit = stg_ctx->is_implicit;
440   const CeedScalar       cv       = stg_ctx->newtonian_ctx.cv;
441   const CeedScalar       cp       = stg_ctx->newtonian_ctx.cp;
442   const CeedScalar       Rd       = cp - cv;
443   const CeedScalar       gamma    = cp / cv;
444 
445   const CeedScalar theta0      = stg_ctx->theta0;
446   const bool       prescribe_T = stg_ctx->prescribe_T;
447 
448   CeedPragmaSIMD
449       // Quadrature Point Loop
450       for (CeedInt i = 0; i < Q; i++) {
451     // Setup
452     // -- Interp-to-Interp q_data
453     // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
454     // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
455     // We can effect this by swapping the sign on this weight
456     const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];
457 
458     // Calculate inflow values
459     CeedScalar velocity[3];
460     for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i];
461 
462     // enabling user to choose between weak T and weak rho inflow
463     CeedScalar drho, dE, dP;
464     if (prescribe_T) {
465       // rho should be from the current solution
466       drho                   = dq[0][i];
467       CeedScalar dE_internal = drho * cv * theta0;
468       CeedScalar dE_kinetic  = .5 * drho * Dot3(velocity, velocity);
469       dE                     = dE_internal + dE_kinetic;
470       dP                     = drho * Rd * theta0;  // interior rho with exterior T
471     } else {                                        // rho specified, E_internal from solution
472       drho = 0;
473       dE   = dq[4][i];
474       dP   = dE * (gamma - 1.);
475     }
476     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
477 
478     const CeedScalar u_normal = Dot3(norm, velocity);
479 
480     v[0][i] = -wdetJb * drho * u_normal;
481     for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP);
482     v[4][i] = -wdetJb * u_normal * (dE + dP);
483   }  // End Quadrature Point Loop
484   return 0;
485 }
486 
487 /********************************************************************
488  * @brief QFunction to calculate the strongly enforce inflow BC
489  *
490  * This QF is for the strong application of STG via libCEED (rather than
491  * through the native PETSc `DMAddBoundary` -> `bcFunc` method.
492  */
493 CEED_QFUNCTION(STGShur14_Inflow_StrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
494   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0], (*coords)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1],
495         (*scale) = (const CeedScalar(*))in[2], (*stg_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3];
496 
497   CeedScalar(*bcval)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
498 
499   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
500   CeedScalar             u[3], ubar[3], cij[6], eps, lt;
501   const bool             mean_only = stg_ctx->mean_only;
502   const CeedScalar       dx        = stg_ctx->dx;
503   const CeedScalar       mu        = stg_ctx->newtonian_ctx.mu;
504   const CeedScalar       time      = stg_ctx->time;
505   const CeedScalar       theta0    = stg_ctx->theta0;
506   const CeedScalar       P0        = stg_ctx->P0;
507   const CeedScalar       cv        = stg_ctx->newtonian_ctx.cv;
508   const CeedScalar       cp        = stg_ctx->newtonian_ctx.cp;
509   const CeedScalar       Rd        = cp - cv;
510   const CeedScalar       rho       = P0 / (Rd * theta0);
511 
512   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
513     const CeedScalar x[]        = {coords[0][i], coords[1][i], coords[2][i]};
514     const CeedScalar dXdx[2][3] = {
515         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
516         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
517     };
518 
519     CeedScalar h[3];
520     h[0] = dx;
521     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
522 
523     InterpolateProfile(coords[1][i], ubar, cij, &eps, &lt, stg_ctx);
524     if (!mean_only) {
525       if (1) {
526         STGShur14_Calc_PrecompEktot(x, time, ubar, cij, stg_data[0][i], h, x[1], eps, lt, mu / rho, u, stg_ctx);
527       } else {  // Original way
528         CeedScalar qn[STG_NMODES_MAX];
529         CalcSpectrum(coords[1][i], eps, lt, h, mu / rho, qn, stg_ctx);
530         STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
531       }
532     } else {
533       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
534     }
535 
536     switch (stg_ctx->newtonian_ctx.state_var) {
537       case STATEVAR_CONSERVATIVE:
538         bcval[0][i] = scale[i] * rho;
539         bcval[1][i] = scale[i] * rho * u[0];
540         bcval[2][i] = scale[i] * rho * u[1];
541         bcval[3][i] = scale[i] * rho * u[2];
542         bcval[4][i] = 0.;
543         break;
544 
545       case STATEVAR_PRIMITIVE:
546         bcval[0][i] = 0;
547         bcval[1][i] = scale[i] * u[0];
548         bcval[2][i] = scale[i] * u[1];
549         bcval[3][i] = scale[i] * u[2];
550         bcval[4][i] = scale[i] * theta0;
551         break;
552     }
553   }
554   return 0;
555 }
556 
557 #endif  // stg_shur14_h
558