xref: /libCEED/examples/fluids/qfunctions/stg_shur14.h (revision ea61e9ac44808524e4667c1525a05976f536c19c)
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  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(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[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     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, nu, 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];
348   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2];
349   const CeedScalar(*X)[CEED_Q_VLA]          = (const CeedScalar(*)[CEED_Q_VLA])in[3];
350 
351   CeedScalar(*v)[CEED_Q_VLA]            = (CeedScalar(*)[CEED_Q_VLA])out[0];
352   CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1];
353 
354   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
355   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
356   const bool             is_implicit = stg_ctx->is_implicit;
357   const bool             mean_only   = stg_ctx->mean_only;
358   const bool             prescribe_T = stg_ctx->prescribe_T;
359   const CeedScalar       dx          = stg_ctx->dx;
360   const CeedScalar       mu          = stg_ctx->newtonian_ctx.mu;
361   const CeedScalar       time        = stg_ctx->time;
362   const CeedScalar       theta0      = stg_ctx->theta0;
363   const CeedScalar       P0          = stg_ctx->P0;
364   const CeedScalar       cv          = stg_ctx->newtonian_ctx.cv;
365   const CeedScalar       Rd          = GasConstant(&stg_ctx->newtonian_ctx);
366   const CeedScalar       gamma       = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
367 
368   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
369     const CeedScalar rho        = prescribe_T ? q[0][i] : P0 / (Rd * theta0);
370     const CeedScalar x[]        = {X[0][i], X[1][i], X[2][i]};
371     const CeedScalar dXdx[2][3] = {
372         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
373         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
374     };
375 
376     CeedScalar h[3];
377     h[0] = dx;
378     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
379 
380     InterpolateProfile(X[1][i], ubar, cij, &eps, &lt, stg_ctx);
381     if (!mean_only) {
382       CalcSpectrum(X[1][i], eps, lt, h, mu / rho, qn, stg_ctx);
383       STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
384     } else {
385       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
386     }
387 
388     const CeedScalar E_kinetic = .5 * rho * Dot3(u, u);
389     CeedScalar       E_internal, P;
390     if (prescribe_T) {
391       // Temperature is being set weakly (theta0) and for constant cv this sets E_internal
392       E_internal = rho * cv * theta0;
393       // Find pressure using
394       P = rho * Rd * theta0;  // interior rho with exterior T
395     } else {
396       E_internal = q[4][i] - E_kinetic;  // uses prescribed rho and u, E from solution
397       P          = E_internal * (gamma - 1.);
398     }
399 
400     const CeedScalar wdetJb = (is_implicit ? -1. : 1.) * q_data_sur[0][i];
401     // ---- Normal vect
402     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
403 
404     const CeedScalar E = E_internal + E_kinetic;
405 
406     // Velocity normal to the boundary
407     const CeedScalar u_normal = Dot3(norm, u);
408 
409     // The Physics
410     // Zero v so all future terms can safely sum into it
411     for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.;
412 
413     // The Physics
414     // -- Density
415     v[0][i] -= wdetJb * rho * u_normal;
416 
417     // -- Momentum
418     for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P);
419 
420     // -- Total Energy Density
421     v[4][i] -= wdetJb * u_normal * (E + P);
422 
423     jac_data_sur[0][i] = rho;
424     jac_data_sur[1][i] = u[0];
425     jac_data_sur[2][i] = u[1];
426     jac_data_sur[3][i] = u[2];
427     jac_data_sur[4][i] = E;
428     for (int j = 0; j < 6; j++) jac_data_sur[5 + j][i] = 0.;
429   }
430   return 0;
431 }
432 
433 CEED_QFUNCTION(STGShur14_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
434   // Inputs
435   const CeedScalar(*dq)[CEED_Q_VLA]           = (const CeedScalar(*)[CEED_Q_VLA])in[0];
436   const CeedScalar(*q_data_sur)[CEED_Q_VLA]   = (const CeedScalar(*)[CEED_Q_VLA])in[2];
437   const CeedScalar(*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4];
438   // Outputs
439   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
440 
441   const STGShur14Context stg_ctx  = (STGShur14Context)ctx;
442   const bool             implicit = stg_ctx->is_implicit;
443   const CeedScalar       cv       = stg_ctx->newtonian_ctx.cv;
444   const CeedScalar       Rd       = GasConstant(&stg_ctx->newtonian_ctx);
445   const CeedScalar       gamma    = HeatCapacityRatio(&stg_ctx->newtonian_ctx);
446 
447   const CeedScalar theta0      = stg_ctx->theta0;
448   const bool       prescribe_T = stg_ctx->prescribe_T;
449 
450   CeedPragmaSIMD
451       // Quadrature Point Loop
452       for (CeedInt i = 0; i < Q; i++) {
453     // Setup
454     // -- Interp-to-Interp q_data
455     // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
456     // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
457     // We can effect this by swapping the sign on this weight
458     const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];
459 
460     // Calculate inflow values
461     CeedScalar velocity[3];
462     for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i];
463 
464     // enabling user to choose between weak T and weak rho inflow
465     CeedScalar drho, dE, dP;
466     if (prescribe_T) {
467       // rho should be from the current solution
468       drho                   = dq[0][i];
469       CeedScalar dE_internal = drho * cv * theta0;
470       CeedScalar dE_kinetic  = .5 * drho * Dot3(velocity, velocity);
471       dE                     = dE_internal + dE_kinetic;
472       dP                     = drho * Rd * theta0;  // interior rho with exterior T
473     } else {                                        // rho specified, E_internal from solution
474       drho = 0;
475       dE   = dq[4][i];
476       dP   = dE * (gamma - 1.);
477     }
478     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
479 
480     const CeedScalar u_normal = Dot3(norm, velocity);
481 
482     v[0][i] = -wdetJb * drho * u_normal;
483     for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP);
484     v[4][i] = -wdetJb * u_normal * (dE + dP);
485   }  // End Quadrature Point Loop
486   return 0;
487 }
488 
489 /********************************************************************
490  * @brief QFunction to calculate the strongly enforce inflow BC
491  *
492  * This QF is for the strong application of STG via libCEED (rather than
493  * through the native PETSc `DMAddBoundary` -> `bcFunc` method.
494  */
495 CEED_QFUNCTION(STGShur14_Inflow_StrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
496   const CeedScalar(*q_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
497   const CeedScalar(*coords)[CEED_Q_VLA]     = (const CeedScalar(*)[CEED_Q_VLA])in[1];
498   const CeedScalar(*scale)                  = (const CeedScalar(*))in[2];
499   const CeedScalar(*stg_data)[CEED_Q_VLA]   = (const CeedScalar(*)[CEED_Q_VLA])in[3];
500 
501   CeedScalar(*bcval)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
502 
503   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
504   CeedScalar             u[3], ubar[3], cij[6], eps, lt;
505   const bool             mean_only = stg_ctx->mean_only;
506   const CeedScalar       dx        = stg_ctx->dx;
507   const CeedScalar       time      = stg_ctx->time;
508   const CeedScalar       theta0    = stg_ctx->theta0;
509   const CeedScalar       P0        = stg_ctx->P0;
510   const CeedScalar       rho       = P0 / (GasConstant(&stg_ctx->newtonian_ctx) * theta0);
511   const CeedScalar       nu        = stg_ctx->newtonian_ctx.mu / rho;
512 
513   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
514     const CeedScalar x[]        = {coords[0][i], coords[1][i], coords[2][i]};
515     const CeedScalar dXdx[2][3] = {
516         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
517         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
518     };
519 
520     CeedScalar h[3];
521     h[0] = dx;
522     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
523 
524     InterpolateProfile(coords[1][i], ubar, cij, &eps, &lt, stg_ctx);
525     if (!mean_only) {
526       if (1) {
527         STGShur14_Calc_PrecompEktot(x, time, ubar, cij, stg_data[0][i], h, x[1], eps, lt, nu, u, stg_ctx);
528       } else {  // Original way
529         CeedScalar qn[STG_NMODES_MAX];
530         CalcSpectrum(coords[1][i], eps, lt, h, nu, qn, stg_ctx);
531         STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
532       }
533     } else {
534       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
535     }
536 
537     switch (stg_ctx->newtonian_ctx.state_var) {
538       case STATEVAR_CONSERVATIVE:
539         bcval[0][i] = scale[i] * rho;
540         bcval[1][i] = scale[i] * rho * u[0];
541         bcval[2][i] = scale[i] * rho * u[1];
542         bcval[3][i] = scale[i] * rho * u[2];
543         bcval[4][i] = 0.;
544         break;
545 
546       case STATEVAR_PRIMITIVE:
547         bcval[0][i] = 0;
548         bcval[1][i] = scale[i] * u[0];
549         bcval[2][i] = scale[i] * u[1];
550         bcval[3][i] = scale[i] * u[2];
551         bcval[4][i] = scale[i] * theta0;
552         break;
553     }
554   }
555   return 0;
556 }
557 
558 #endif  // stg_shur14_h
559