xref: /libCEED/examples/fluids/qfunctions/stg_shur14.h (revision e7f679fc6de93686a880ec2b7b7a43611d8847a6)
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.
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 
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 "newtonian_state.h"
24 #include "stg_shur14_type.h"
25 #include "utils.h"
26 
27 #define STG_NMODES_MAX 1024
28 
29 /*
30  * @brief Interpolate quantities from input profile to given location
31  *
32  * Assumed that prof_wd[i+1] > prof_wd[i] and prof_wd[0] = 0
33  * If wall_dist > prof_wd[-1], then the interpolation takes the values at prof_wd[-1]
34  *
35  * @param[in]  wall_dist Distance to the nearest wall
36  * @param[out] ubar      Mean velocity at wall_dist
37  * @param[out] cij       Cholesky decomposition at wall_dist
38  * @param[out] eps       Turbulent dissipation at wall_dist
39  * @param[out] lt        Turbulent length scale at wall_dist
40  * @param[in]  stg_ctx   STGShur14Context for the problem
41  */
42 CEED_QFUNCTION_HELPER void InterpolateProfile(const CeedScalar wall_dist, CeedScalar ubar[3], CeedScalar cij[6], CeedScalar *eps, CeedScalar *lt,
43                                               const STGShur14Context stg_ctx) {
44   const CeedInt     nprofs    = stg_ctx->nprofs;
45   const CeedScalar *prof_wd   = &stg_ctx->data[stg_ctx->offsets.wall_dist];
46   const CeedScalar *prof_eps  = &stg_ctx->data[stg_ctx->offsets.eps];
47   const CeedScalar *prof_lt   = &stg_ctx->data[stg_ctx->offsets.lt];
48   const CeedScalar *prof_ubar = &stg_ctx->data[stg_ctx->offsets.ubar];
49   const CeedScalar *prof_cij  = &stg_ctx->data[stg_ctx->offsets.cij];
50   CeedInt           idx       = -1;
51 
52   for (CeedInt i = 0; i < nprofs; i++) {
53     if (wall_dist < prof_wd[i]) {
54       idx = i;
55       break;
56     }
57   }
58 
59   if (idx > 0) {  // y within the bounds of prof_wd
60     CeedScalar coeff = (wall_dist - prof_wd[idx - 1]) / (prof_wd[idx] - prof_wd[idx - 1]);
61 
62     ubar[0] = prof_ubar[0 * nprofs + idx - 1] + coeff * (prof_ubar[0 * nprofs + idx] - prof_ubar[0 * nprofs + idx - 1]);
63     ubar[1] = prof_ubar[1 * nprofs + idx - 1] + coeff * (prof_ubar[1 * nprofs + idx] - prof_ubar[1 * nprofs + idx - 1]);
64     ubar[2] = prof_ubar[2 * nprofs + idx - 1] + coeff * (prof_ubar[2 * nprofs + idx] - prof_ubar[2 * nprofs + idx - 1]);
65     cij[0]  = prof_cij[0 * nprofs + idx - 1] + coeff * (prof_cij[0 * nprofs + idx] - prof_cij[0 * nprofs + idx - 1]);
66     cij[1]  = prof_cij[1 * nprofs + idx - 1] + coeff * (prof_cij[1 * nprofs + idx] - prof_cij[1 * nprofs + idx - 1]);
67     cij[2]  = prof_cij[2 * nprofs + idx - 1] + coeff * (prof_cij[2 * nprofs + idx] - prof_cij[2 * nprofs + idx - 1]);
68     cij[3]  = prof_cij[3 * nprofs + idx - 1] + coeff * (prof_cij[3 * nprofs + idx] - prof_cij[3 * nprofs + idx - 1]);
69     cij[4]  = prof_cij[4 * nprofs + idx - 1] + coeff * (prof_cij[4 * nprofs + idx] - prof_cij[4 * nprofs + idx - 1]);
70     cij[5]  = prof_cij[5 * nprofs + idx - 1] + coeff * (prof_cij[5 * nprofs + idx] - prof_cij[5 * nprofs + idx - 1]);
71     *eps    = prof_eps[idx - 1] + coeff * (prof_eps[idx] - prof_eps[idx - 1]);
72     *lt     = prof_lt[idx - 1] + coeff * (prof_lt[idx] - prof_lt[idx - 1]);
73   } else {  // y outside bounds of prof_wd
74     ubar[0] = prof_ubar[1 * nprofs - 1];
75     ubar[1] = prof_ubar[2 * nprofs - 1];
76     ubar[2] = prof_ubar[3 * nprofs - 1];
77     cij[0]  = prof_cij[1 * nprofs - 1];
78     cij[1]  = prof_cij[2 * nprofs - 1];
79     cij[2]  = prof_cij[3 * nprofs - 1];
80     cij[3]  = prof_cij[4 * nprofs - 1];
81     cij[4]  = prof_cij[5 * nprofs - 1];
82     cij[5]  = prof_cij[6 * nprofs - 1];
83     *eps    = prof_eps[nprofs - 1];
84     *lt     = prof_lt[nprofs - 1];
85   }
86 }
87 
88 /*
89  * @brief Calculate spectrum coefficient, qn
90  *
91  * Calculates q_n at a given distance to the wall
92  *
93  * @param[in]  kappa     nth wavenumber
94  * @param[in]  dkappa    Difference between wavenumbers
95  * @param[in]  keta      Dissipation wavenumber
96  * @param[in]  kcut      Mesh-induced cutoff wavenumber
97  * @param[in]  ke        Energy-containing wavenumber
98  * @param[in]  Ektot_inv Inverse of total turbulent kinetic energy of spectrum
99  * @returns    qn        Spectrum coefficient
100  */
101 CEED_QFUNCTION_HELPER CeedScalar Calc_qn(const CeedScalar kappa, const CeedScalar dkappa, const CeedScalar keta, const CeedScalar kcut,
102                                          const CeedScalar ke, const CeedScalar Ektot_inv) {
103   const CeedScalar feta_x_fcut = exp(-Square(12 * kappa / keta) - Cube(4 * Max(kappa - 0.9 * kcut, 0) / kcut));
104   return pow(kappa / ke, 4.) * pow(1 + 2.4 * Square(kappa / ke), -17. / 6) * feta_x_fcut * dkappa * Ektot_inv;
105 }
106 
107 // Calculate hmax, ke, keta, and kcut
108 CEED_QFUNCTION_HELPER void SpectrumConstants(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3],
109                                              const CeedScalar nu, CeedScalar *hmax, CeedScalar *ke, CeedScalar *keta, CeedScalar *kcut) {
110   *hmax = Max(Max(h[0], h[1]), h[2]);
111   *ke   = wall_dist == 0 ? 1e16 : 2 * M_PI / Min(2 * wall_dist, 3 * lt);
112   *keta = 2 * M_PI * pow(Cube(nu) / eps, -0.25);
113   *kcut = M_PI / Min(Max(Max(h[1], h[2]), 0.3 * (*hmax)) + 0.1 * wall_dist, *hmax);
114 }
115 
116 /*
117  * @brief Calculate spectrum coefficients for STG
118  *
119  * Calculates q_n at a given distance to the wall
120  *
121  * @param[in]  wall_dist Distance to the nearest wall
122  * @param[in]  eps       Turbulent dissipation w/rt wall_dist
123  * @param[in]  lt        Turbulent length scale w/rt wall_dist
124  * @param[in]  h         Element lengths in coordinate directions
125  * @param[in]  nu        Dynamic Viscosity;
126  * @param[in]  stg_ctx   STGShur14Context for the problem
127  * @param[out] qn        Spectrum coefficients, [nmodes]
128  */
129 CEED_QFUNCTION_HELPER void CalcSpectrum(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3],
130                                         const CeedScalar nu, CeedScalar qn[], const STGShur14Context stg_ctx) {
131   const CeedInt     nmodes = stg_ctx->nmodes;
132   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
133   CeedScalar        hmax, ke, keta, kcut, Ektot = 0.0;
134 
135   SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
136 
137   for (CeedInt n = 0; n < nmodes; n++) {
138     const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
139     qn[n]                   = Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
140     Ektot += qn[n];
141   }
142 
143   if (Ektot == 0) return;
144   for (CeedInt n = 0; n < nmodes; n++) qn[n] /= Ektot;
145 }
146 
147 /******************************************************
148  * @brief Calculate u(x,t) for STG inflow condition
149  *
150  * @param[in]  X       Location to evaluate u(X,t)
151  * @param[in]  t       Time to evaluate u(X,t)
152  * @param[in]  ubar    Mean velocity at X
153  * @param[in]  cij     Cholesky decomposition at X
154  * @param[in]  qn      Wavemode amplitudes at X, [nmodes]
155  * @param[out] u       Velocity at X and t
156  * @param[in]  stg_ctx STGShur14Context for the problem
157  */
158 CEED_QFUNCTION_HELPER void STGShur14_Calc(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
159                                           const CeedScalar qn[], CeedScalar u[3], const STGShur14Context stg_ctx) {
160   const CeedInt     nmodes = stg_ctx->nmodes;
161   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
162   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
163   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
164   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
165   CeedScalar        xdotd, vp[3] = {0.};
166   CeedScalar        xhat[] = {0., X[1], X[2]};
167 
168   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
169     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
170     xdotd   = 0.;
171     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
172     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
173     vp[0] += sqrt(qn[n]) * sigma[0 * nmodes + n] * cos_kxdp;
174     vp[1] += sqrt(qn[n]) * sigma[1 * nmodes + n] * cos_kxdp;
175     vp[2] += sqrt(qn[n]) * sigma[2 * nmodes + n] * cos_kxdp;
176   }
177   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
178 
179   u[0] = ubar[0] + cij[0] * vp[0];
180   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
181   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
182 }
183 
184 /******************************************************
185  * @brief Calculate u(x,t) for STG inflow condition
186  *
187  * @param[in]  X         Location to evaluate u(X,t)
188  * @param[in]  t         Time to evaluate u(X,t)
189  * @param[in]  ubar      Mean velocity at X
190  * @param[in]  cij       Cholesky decomposition at X
191  * @param[in]  Ektot     Total spectrum energy at this location
192  * @param[in]  h         Element size in 3 directions
193  * @param[in]  wall_dist Distance to closest wall
194  * @param[in]  eps       Turbulent dissipation
195  * @param[in]  lt        Turbulent length scale
196  * @param[out] u         Velocity at X and t
197  * @param[in]  stg_ctx   STGShur14Context for the problem
198  */
199 CEED_QFUNCTION_HELPER void STGShur14_Calc_PrecompEktot(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
200                                                        const CeedScalar Ektot, const CeedScalar h[3], const CeedScalar wall_dist,
201                                                        const CeedScalar eps, const CeedScalar lt, const CeedScalar nu, CeedScalar u[3],
202                                                        const STGShur14Context stg_ctx) {
203   const CeedInt     nmodes = stg_ctx->nmodes;
204   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
205   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
206   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
207   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
208   CeedScalar        hmax, ke, keta, kcut;
209   SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
210   CeedScalar xdotd, vp[3] = {0.};
211   CeedScalar xhat[] = {0., X[1], X[2]};
212 
213   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
214     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
215     xdotd   = 0.;
216     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
217     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
218     const CeedScalar dkappa   = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
219     const CeedScalar qn       = Calc_qn(kappa[n], dkappa, keta, kcut, ke, Ektot);
220     vp[0] += sqrt(qn) * sigma[0 * nmodes + n] * cos_kxdp;
221     vp[1] += sqrt(qn) * sigma[1 * nmodes + n] * cos_kxdp;
222     vp[2] += sqrt(qn) * sigma[2 * nmodes + n] * cos_kxdp;
223   }
224   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
225 
226   u[0] = ubar[0] + cij[0] * vp[0];
227   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
228   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
229 }
230 
231 // Create preprocessed input for the stg calculation
232 //
233 // stg_data[0] = 1 / Ektot (inverse of total spectrum energy)
234 CEED_QFUNCTION(Preprocess_STGShur14)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
235   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
236   const CeedScalar(*x)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[1];
237 
238   CeedScalar(*stg_data) = (CeedScalar(*))out[0];
239 
240   CeedScalar             ubar[3], cij[6], eps, lt;
241   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
242   const CeedScalar       dx      = stg_ctx->dx;
243   const CeedScalar       mu      = stg_ctx->newtonian_ctx.mu;
244   const CeedScalar       theta0  = stg_ctx->theta0;
245   const CeedScalar       P0      = stg_ctx->P0;
246   const CeedScalar       Rd      = GasConstant(&stg_ctx->newtonian_ctx);
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];
284   const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[1];
285 
286   // Outputs
287   CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
288 
289   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
290   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
291   const CeedScalar       dx     = stg_ctx->dx;
292   const CeedScalar       time   = stg_ctx->time;
293   const CeedScalar       theta0 = stg_ctx->theta0;
294   const CeedScalar       P0     = stg_ctx->P0;
295   const CeedScalar       cv     = stg_ctx->newtonian_ctx.cv;
296   const CeedScalar       rho    = P0 / (GasConstant(&stg_ctx->newtonian_ctx) * theta0);
297   const CeedScalar       nu     = stg_ctx->newtonian_ctx.mu / rho;
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     CeedScalar       dXdx[3][3];
302     {
303       const CeedScalar J11  = J[0][0][i];
304       const CeedScalar J21  = J[0][1][i];
305       const CeedScalar J31  = J[0][2][i];
306       const CeedScalar J12  = J[1][0][i];
307       const CeedScalar J22  = J[1][1][i];
308       const CeedScalar J32  = J[1][2][i];
309       const CeedScalar J13  = J[2][0][i];
310       const CeedScalar J23  = J[2][1][i];
311       const CeedScalar J33  = J[2][2][i];
312       const CeedScalar A11  = J22 * J33 - J23 * J32;
313       const CeedScalar A12  = J13 * J32 - J12 * J33;
314       const CeedScalar A13  = J12 * J23 - J13 * J22;
315       const CeedScalar A21  = J23 * J31 - J21 * J33;
316       const CeedScalar A22  = J11 * J33 - J13 * J31;
317       const CeedScalar A23  = J13 * J21 - J11 * J23;
318       const CeedScalar A31  = J21 * J32 - J22 * J31;
319       const CeedScalar A32  = J12 * J31 - J11 * J32;
320       const CeedScalar A33  = J11 * J22 - J12 * J21;
321       const CeedScalar detJ = J11 * A11 + J21 * A12 + J31 * A13;
322 
323       dXdx[0][0] = A11 / detJ;
324       dXdx[0][1] = A12 / detJ;
325       dXdx[0][2] = A13 / detJ;
326       dXdx[1][0] = A21 / detJ;
327       dXdx[1][1] = A22 / detJ;
328       dXdx[1][2] = A23 / detJ;
329       dXdx[2][0] = A31 / detJ;
330       dXdx[2][1] = A32 / detJ;
331       dXdx[2][2] = A33 / detJ;
332     }
333 
334     CeedScalar h[3];
335     h[0] = dx;
336     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j]));
337 
338     InterpolateProfile(x_i[1], ubar, cij, &eps, &lt, stg_ctx);
339     if (stg_ctx->use_fluctuating_IC) {
340       CalcSpectrum(x_i[1], eps, lt, h, nu, qn, stg_ctx);
341       STGShur14_Calc(x_i, time, ubar, cij, qn, u, stg_ctx);
342     } else {
343       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
344     }
345 
346     switch (stg_ctx->newtonian_ctx.state_var) {
347       case STATEVAR_CONSERVATIVE:
348         q0[0][i] = rho;
349         q0[1][i] = u[0] * rho;
350         q0[2][i] = u[1] * rho;
351         q0[3][i] = u[2] * rho;
352         q0[4][i] = rho * (0.5 * Dot3(u, u) + cv * theta0);
353         break;
354 
355       case STATEVAR_PRIMITIVE:
356         q0[0][i] = P0;
357         q0[1][i] = u[0];
358         q0[2][i] = u[1];
359         q0[3][i] = u[2];
360         q0[4][i] = theta0;
361         break;
362     }
363   }  // End of Quadrature Point Loop
364   return 0;
365 }
366 
367 /********************************************************************
368  * @brief QFunction to calculate the inflow boundary condition
369  *
370  * This will loop through quadrature points, calculate the wavemode amplitudes
371  * at each location, then calculate the actual velocity.
372  */
373 CEED_QFUNCTION(STGShur14_Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
374   const CeedScalar(*q)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[0];
375   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2];
376   const CeedScalar(*X)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[3];
377 
378   CeedScalar(*v)[CEED_Q_VLA]            = (CeedScalar(*)[CEED_Q_VLA])out[0];
379   CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1];
380 
381   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
382   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
383   const bool             is_implicit = stg_ctx->is_implicit;
384   const bool             mean_only   = stg_ctx->mean_only;
385   const bool             prescribe_T = stg_ctx->prescribe_T;
386   const CeedScalar       dx          = stg_ctx->dx;
387   const CeedScalar       mu          = stg_ctx->newtonian_ctx.mu;
388   const CeedScalar       time        = stg_ctx->time;
389   const CeedScalar       theta0      = stg_ctx->theta0;
390   const CeedScalar       P0          = stg_ctx->P0;
391   const CeedScalar       cv          = stg_ctx->newtonian_ctx.cv;
392   const CeedScalar       Rd          = GasConstant(&stg_ctx->newtonian_ctx);
393   const CeedScalar       gamma       = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
394 
395   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
396     const CeedScalar rho        = prescribe_T ? q[0][i] : P0 / (Rd * theta0);
397     const CeedScalar x[]        = {X[0][i], X[1][i], X[2][i]};
398     const CeedScalar dXdx[2][3] = {
399         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
400         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
401     };
402 
403     CeedScalar h[3];
404     h[0] = dx;
405     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
406 
407     InterpolateProfile(X[1][i], ubar, cij, &eps, &lt, stg_ctx);
408     if (!mean_only) {
409       CalcSpectrum(X[1][i], eps, lt, h, mu / rho, qn, stg_ctx);
410       STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
411     } else {
412       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
413     }
414 
415     const CeedScalar E_kinetic = .5 * rho * Dot3(u, u);
416     CeedScalar       E_internal, P;
417     if (prescribe_T) {
418       // Temperature is being set weakly (theta0) and for constant cv this sets E_internal
419       E_internal = rho * cv * theta0;
420       // Find pressure using
421       P = rho * Rd * theta0;  // interior rho with exterior T
422     } else {
423       E_internal = q[4][i] - E_kinetic;  // uses prescribed rho and u, E from solution
424       P          = E_internal * (gamma - 1.);
425     }
426 
427     const CeedScalar wdetJb = (is_implicit ? -1. : 1.) * q_data_sur[0][i];
428     // ---- Normal vect
429     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
430 
431     const CeedScalar E = E_internal + E_kinetic;
432 
433     // Velocity normal to the boundary
434     const CeedScalar u_normal = Dot3(norm, u);
435 
436     // The Physics
437     // Zero v so all future terms can safely sum into it
438     for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.;
439 
440     // The Physics
441     // -- Density
442     v[0][i] -= wdetJb * rho * u_normal;
443 
444     // -- Momentum
445     for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P);
446 
447     // -- Total Energy Density
448     v[4][i] -= wdetJb * u_normal * (E + P);
449 
450     jac_data_sur[0][i] = rho;
451     jac_data_sur[1][i] = u[0];
452     jac_data_sur[2][i] = u[1];
453     jac_data_sur[3][i] = u[2];
454     jac_data_sur[4][i] = E;
455     for (int j = 0; j < 6; j++) jac_data_sur[5 + j][i] = 0.;
456   }
457   return 0;
458 }
459 
460 CEED_QFUNCTION(STGShur14_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
461   // Inputs
462   const CeedScalar(*dq)[CEED_Q_VLA]           = (const CeedScalar(*)[CEED_Q_VLA])in[0];
463   const CeedScalar(*q_data_sur)[CEED_Q_VLA]   = (const CeedScalar(*)[CEED_Q_VLA])in[2];
464   const CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4];
465   // Outputs
466   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
467 
468   const STGShur14Context stg_ctx  = (STGShur14Context)ctx;
469   const bool             implicit = stg_ctx->is_implicit;
470   const CeedScalar       cv       = stg_ctx->newtonian_ctx.cv;
471   const CeedScalar       Rd       = GasConstant(&stg_ctx->newtonian_ctx);
472   const CeedScalar       gamma    = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
473 
474   const CeedScalar theta0      = stg_ctx->theta0;
475   const bool       prescribe_T = stg_ctx->prescribe_T;
476 
477   CeedPragmaSIMD
478       // Quadrature Point Loop
479       for (CeedInt i = 0; i < Q; i++) {
480     // Setup
481     // -- Interp-to-Interp q_data
482     // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
483     // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
484     // We can effect this by swapping the sign on this weight
485     const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];
486 
487     // Calculate inflow values
488     CeedScalar velocity[3];
489     for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i];
490 
491     // enabling user to choose between weak T and weak rho inflow
492     CeedScalar drho, dE, dP;
493     if (prescribe_T) {
494       // rho should be from the current solution
495       drho                   = dq[0][i];
496       CeedScalar dE_internal = drho * cv * theta0;
497       CeedScalar dE_kinetic  = .5 * drho * Dot3(velocity, velocity);
498       dE                     = dE_internal + dE_kinetic;
499       dP                     = drho * Rd * theta0;  // interior rho with exterior T
500     } else {                                        // rho specified, E_internal from solution
501       drho = 0;
502       dE   = dq[4][i];
503       dP   = dE * (gamma - 1.);
504     }
505     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
506 
507     const CeedScalar u_normal = Dot3(norm, velocity);
508 
509     v[0][i] = -wdetJb * drho * u_normal;
510     for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP);
511     v[4][i] = -wdetJb * u_normal * (dE + dP);
512   }  // End Quadrature Point Loop
513   return 0;
514 }
515 
516 /********************************************************************
517  * @brief QFunction to calculate the strongly enforce inflow BC
518  *
519  * This QF is for the strong application of STG via libCEED (rather than
520  * through the native PETSc `DMAddBoundary` -> `bcFunc` method.
521  */
522 CEED_QFUNCTION(STGShur14_Inflow_StrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
523   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
524   const CeedScalar(*coords)[CEED_Q_VLA]     = (const CeedScalar(*)[CEED_Q_VLA])in[1];
525   const CeedScalar(*scale)                  = (const CeedScalar(*))in[2];
526   const CeedScalar(*inv_Ektotal)            = (const CeedScalar(*))in[3];
527 
528   CeedScalar(*bcval)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
529 
530   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
531   CeedScalar             u[3], ubar[3], cij[6], eps, lt;
532   const bool             mean_only = stg_ctx->mean_only;
533   const CeedScalar       dx        = stg_ctx->dx;
534   const CeedScalar       time      = stg_ctx->time;
535   const CeedScalar       theta0    = stg_ctx->theta0;
536   const CeedScalar       P0        = stg_ctx->P0;
537   const CeedScalar       rho       = P0 / (GasConstant(&stg_ctx->newtonian_ctx) * theta0);
538   const CeedScalar       nu        = stg_ctx->newtonian_ctx.mu / rho;
539 
540   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
541     const CeedScalar x[]        = {coords[0][i], coords[1][i], coords[2][i]};
542     const CeedScalar dXdx[2][3] = {
543         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
544         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
545     };
546 
547     CeedScalar h[3];
548     h[0] = dx;
549     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
550 
551     InterpolateProfile(coords[1][i], ubar, cij, &eps, &lt, stg_ctx);
552     if (!mean_only) {
553       if (1) {
554         STGShur14_Calc_PrecompEktot(x, time, ubar, cij, inv_Ektotal[i], h, x[1], eps, lt, nu, u, stg_ctx);
555       } else {  // Original way
556         CeedScalar qn[STG_NMODES_MAX];
557         CalcSpectrum(coords[1][i], eps, lt, h, nu, qn, stg_ctx);
558         STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
559       }
560     } else {
561       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
562     }
563 
564     switch (stg_ctx->newtonian_ctx.state_var) {
565       case STATEVAR_CONSERVATIVE:
566         bcval[0][i] = scale[i] * rho;
567         bcval[1][i] = scale[i] * rho * u[0];
568         bcval[2][i] = scale[i] * rho * u[1];
569         bcval[3][i] = scale[i] * rho * u[2];
570         bcval[4][i] = 0.;
571         break;
572 
573       case STATEVAR_PRIMITIVE:
574         bcval[0][i] = 0;
575         bcval[1][i] = scale[i] * u[0];
576         bcval[2][i] = scale[i] * u[1];
577         bcval[3][i] = scale[i] * u[2];
578         bcval[4][i] = scale[i] * theta0;
579         break;
580     }
581   }
582   return 0;
583 }
584 
585 #endif  // stg_shur14_h
586