xref: /libCEED/examples/fluids/qfunctions/stg_shur14.h (revision 2b730f8b5a9c809740a0b3b302db43a719c636b1)
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     //*INDENT-OFF*
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     //*INDENT-ON*
74   } else {  // y outside bounds of prof_wd
75     ubar[0] = prof_ubar[1 * nprofs - 1];
76     ubar[1] = prof_ubar[2 * nprofs - 1];
77     ubar[2] = prof_ubar[3 * nprofs - 1];
78     cij[0]  = prof_cij[1 * nprofs - 1];
79     cij[1]  = prof_cij[2 * nprofs - 1];
80     cij[2]  = prof_cij[3 * nprofs - 1];
81     cij[3]  = prof_cij[4 * nprofs - 1];
82     cij[4]  = prof_cij[5 * nprofs - 1];
83     cij[5]  = prof_cij[6 * nprofs - 1];
84     *eps    = prof_eps[nprofs - 1];
85     *lt     = prof_lt[nprofs - 1];
86   }
87 }
88 
89 /*
90  * @brief Calculate spectrum coefficient, qn
91  *
92  * Calculates q_n at a given distance to the wall
93  *
94  * @param[in]  kappa  nth wavenumber
95  * @param[in]  dkappa Difference between wavenumbers
96  * @param[in]  keta   Dissipation wavenumber
97  * @param[in]  kcut   Mesh-induced cutoff wavenumber
98  * @param[in]  ke     Energy-containing wavenumber
99  * @param[in]  Ektot  Total turbulent kinetic energy of spectrum
100  * @returns    qn     Spectrum coefficient
101  */
102 CEED_QFUNCTION_HELPER CeedScalar Calc_qn(const CeedScalar kappa, const CeedScalar dkappa, const CeedScalar keta, const CeedScalar kcut,
103                                          const CeedScalar ke, const CeedScalar Ektot_inv) {
104   const CeedScalar feta_x_fcut = exp(-Square(12 * kappa / keta) - Cube(4 * Max(kappa - 0.9 * kcut, 0) / kcut));
105   return pow(kappa / ke, 4.) * pow(1 + 2.4 * Square(kappa / ke), -17. / 6) * feta_x_fcut * dkappa * Ektot_inv;
106 }
107 
108 // Calculate hmax, ke, keta, and kcut
109 CEED_QFUNCTION_HELPER void SpectrumConstants(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3],
110                                              const CeedScalar nu, CeedScalar *hmax, CeedScalar *ke, CeedScalar *keta, CeedScalar *kcut) {
111   *hmax = Max(Max(h[0], h[1]), h[2]);
112   *ke   = wall_dist == 0 ? 1e16 : 2 * M_PI / Min(2 * wall_dist, 3 * lt);
113   *keta = 2 * M_PI * pow(Cube(nu) / eps, -0.25);
114   *kcut = M_PI / Min(Max(Max(h[1], h[2]), 0.3 * (*hmax)) + 0.1 * wall_dist, *hmax);
115 }
116 
117 /*
118  * @brief Calculate spectrum coefficients for STG
119  *
120  * Calculates q_n at a given distance to the wall
121  *
122  * @param[in]  wall_dist Distance to the nearest wall
123  * @param[in]  eps       Turbulent dissipation w/rt wall_dist
124  * @param[in]  lt        Turbulent length scale w/rt wall_dist
125  * @param[in]  h         Element lengths in coordinate directions
126  * @param[in]  nu        Dynamic Viscosity;
127  * @param[in]  stg_ctx   STGShur14Context for the problem
128  * @param[out] qn        Spectrum coefficients, [nmodes]
129  */
130 CEED_QFUNCTION_HELPER void CalcSpectrum(const CeedScalar wall_dist, const CeedScalar eps, const CeedScalar lt, const CeedScalar h[3],
131                                         const CeedScalar nu, CeedScalar qn[], const STGShur14Context stg_ctx) {
132   const CeedInt     nmodes = stg_ctx->nmodes;
133   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
134   CeedScalar        hmax, ke, keta, kcut, Ektot = 0.0;
135 
136   SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
137 
138   for (CeedInt n = 0; n < nmodes; n++) {
139     const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
140     qn[n]                   = Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
141     Ektot += qn[n];
142   }
143 
144   if (Ektot == 0) return;
145   for (CeedInt n = 0; n < nmodes; n++) qn[n] /= Ektot;
146 }
147 
148 /******************************************************
149  * @brief Calculate u(x,t) for STG inflow condition
150  *
151  * @param[in]  X       Location to evaluate u(X,t)
152  * @param[in]  t       Time to evaluate u(X,t)
153  * @param[in]  ubar    Mean velocity at X
154  * @param[in]  cij     Cholesky decomposition at X
155  * @param[in]  qn      Wavemode amplitudes at X, [nmodes]
156  * @param[out] u       Velocity at X and t
157  * @param[in]  stg_ctx STGShur14Context for the problem
158  */
159 CEED_QFUNCTION_HELPER void STGShur14_Calc(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
160                                           const CeedScalar qn[], CeedScalar u[3], const STGShur14Context stg_ctx) {
161   //*INDENT-OFF*
162   const CeedInt     nmodes = stg_ctx->nmodes;
163   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
164   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
165   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
166   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
167   //*INDENT-ON*
168   CeedScalar xdotd, vp[3] = {0.};
169   CeedScalar xhat[] = {0., X[1], X[2]};
170 
171   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
172     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
173     xdotd   = 0.;
174     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
175     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
176     vp[0] += sqrt(qn[n]) * sigma[0 * nmodes + n] * cos_kxdp;
177     vp[1] += sqrt(qn[n]) * sigma[1 * nmodes + n] * cos_kxdp;
178     vp[2] += sqrt(qn[n]) * sigma[2 * nmodes + n] * cos_kxdp;
179   }
180   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
181 
182   u[0] = ubar[0] + cij[0] * vp[0];
183   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
184   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
185 }
186 
187 /******************************************************
188  * @brief Calculate u(x,t) for STG inflow condition
189  *
190  * @param[in]  X         Location to evaluate u(X,t)
191  * @param[in]  t         Time to evaluate u(X,t)
192  * @param[in]  ubar      Mean velocity at X
193  * @param[in]  cij       Cholesky decomposition at X
194  * @param[in]  Ektot     Total spectrum energy at this location
195  * @param[in]  h         Element size in 3 directions
196  * @param[in]  wall_dist Distance to closest wall
197  * @param[in]  eps       Turbulent dissipation
198  * @param[in]  lt        Turbulent length scale
199  * @param[out] u         Velocity at X and t
200  * @param[in]  stg_ctx   STGShur14Context for the problem
201  */
202 CEED_QFUNCTION_HELPER void STGShur14_Calc_PrecompEktot(const CeedScalar X[3], const CeedScalar t, const CeedScalar ubar[3], const CeedScalar cij[6],
203                                                        const CeedScalar Ektot, const CeedScalar h[3], const CeedScalar wall_dist,
204                                                        const CeedScalar eps, const CeedScalar lt, const CeedScalar nu, CeedScalar u[3],
205                                                        const STGShur14Context stg_ctx) {
206   //*INDENT-OFF*
207   const CeedInt     nmodes = stg_ctx->nmodes;
208   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
209   const CeedScalar *phi    = &stg_ctx->data[stg_ctx->offsets.phi];
210   const CeedScalar *sigma  = &stg_ctx->data[stg_ctx->offsets.sigma];
211   const CeedScalar *d      = &stg_ctx->data[stg_ctx->offsets.d];
212   //*INDENT-ON*
213   CeedScalar hmax, ke, keta, kcut;
214   SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
215   CeedScalar xdotd, vp[3] = {0.};
216   CeedScalar xhat[] = {0., X[1], X[2]};
217 
218   CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
219     xhat[0] = (X[0] - stg_ctx->u0 * t) * Max(2 * kappa[0] / kappa[n], 0.1);
220     xdotd   = 0.;
221     for (CeedInt i = 0; i < 3; i++) xdotd += d[i * nmodes + n] * xhat[i];
222     const CeedScalar cos_kxdp = cos(kappa[n] * xdotd + phi[n]);
223     const CeedScalar dkappa   = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
224     const CeedScalar qn       = Calc_qn(kappa[n], dkappa, keta, kcut, ke, Ektot);
225     vp[0] += sqrt(qn) * sigma[0 * nmodes + n] * cos_kxdp;
226     vp[1] += sqrt(qn) * sigma[1 * nmodes + n] * cos_kxdp;
227     vp[2] += sqrt(qn) * sigma[2 * nmodes + n] * cos_kxdp;
228   }
229   for (CeedInt i = 0; i < 3; i++) vp[i] *= 2 * sqrt(1.5);
230 
231   u[0] = ubar[0] + cij[0] * vp[0];
232   u[1] = ubar[1] + cij[3] * vp[0] + cij[1] * vp[1];
233   u[2] = ubar[2] + cij[4] * vp[0] + cij[5] * vp[1] + cij[2] * vp[2];
234 }
235 
236 // Create preprocessed input for the stg calculation
237 //
238 // stg_data[0] = 1 / Ektot (inverse of total spectrum energy)
239 CEED_QFUNCTION(Preprocess_STGShur14)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
240   //*INDENT-OFF*
241   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];
242 
243   CeedScalar(*stg_data) = (CeedScalar(*))out[0];
244 
245   //*INDENT-ON*
246   CeedScalar             ubar[3], cij[6], eps, lt;
247   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
248   const CeedScalar       dx      = stg_ctx->dx;
249   const CeedScalar       mu      = stg_ctx->newtonian_ctx.mu;
250   const CeedScalar       theta0  = stg_ctx->theta0;
251   const CeedScalar       P0      = stg_ctx->P0;
252   const CeedScalar       cv      = stg_ctx->newtonian_ctx.cv;
253   const CeedScalar       cp      = stg_ctx->newtonian_ctx.cp;
254   const CeedScalar       Rd      = cp - cv;
255   const CeedScalar       rho     = P0 / (Rd * theta0);
256   const CeedScalar       nu      = mu / rho;
257 
258   const CeedInt     nmodes = stg_ctx->nmodes;
259   const CeedScalar *kappa  = &stg_ctx->data[stg_ctx->offsets.kappa];
260   CeedScalar        hmax, ke, keta, kcut;
261 
262   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
263     const CeedScalar wall_dist  = x[1][i];
264     const CeedScalar dXdx[2][3] = {
265         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
266         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
267     };
268 
269     CeedScalar h[3];
270     h[0] = dx;
271     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(dXdx[0][j] * dXdx[0][j] + dXdx[1][j] * dXdx[1][j]);
272 
273     InterpolateProfile(wall_dist, ubar, cij, &eps, &lt, stg_ctx);
274     SpectrumConstants(wall_dist, eps, lt, h, nu, &hmax, &ke, &keta, &kcut);
275 
276     // Calculate total TKE per spectrum
277     CeedScalar Ek_tot = 0;
278     CeedPragmaSIMD for (CeedInt n = 0; n < nmodes; n++) {
279       const CeedScalar dkappa = n == 0 ? kappa[0] : kappa[n] - kappa[n - 1];
280       Ek_tot += Calc_qn(kappa[n], dkappa, keta, kcut, ke, 1.0);
281     }
282     // avoid underflowed and poorly defined spectrum coefficients
283     stg_data[i] = Ek_tot != 0 ? 1 / Ek_tot : 0;
284   }
285   return 0;
286 }
287 
288 // Extrude the STGInflow profile through out the domain for an initial condition
289 CEED_QFUNCTION(ICsSTG)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
290   // Inputs
291   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];
292   // Outputs
293   CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
294 
295   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
296   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
297   const CeedScalar       dx     = stg_ctx->dx;
298   const CeedScalar       time   = stg_ctx->time;
299   const CeedScalar       theta0 = stg_ctx->theta0;
300   const CeedScalar       P0     = stg_ctx->P0;
301   const CeedScalar       mu     = stg_ctx->newtonian_ctx.mu;
302   const CeedScalar       cv     = stg_ctx->newtonian_ctx.cv;
303   const CeedScalar       cp     = stg_ctx->newtonian_ctx.cp;
304   const CeedScalar       Rd     = cp - cv;
305   const CeedScalar       rho    = P0 / (Rd * theta0);
306 
307   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
308     const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]};
309     // *INDENT-OFF*
310     const CeedScalar dXdx[3][3] = {
311         {q_data[1][i], q_data[2][i], q_data[3][i]},
312         {q_data[4][i], q_data[5][i], q_data[6][i]},
313         {q_data[7][i], q_data[8][i], q_data[9][i]}
314     };
315     // *INDENT-ON*
316 
317     CeedScalar h[3];
318     h[0] = dx;
319     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]) + Square(dXdx[2][j]));
320 
321     InterpolateProfile(x_i[1], ubar, cij, &eps, &lt, stg_ctx);
322     if (stg_ctx->use_fluctuating_IC) {
323       CalcSpectrum(x_i[1], eps, lt, h, mu / rho, qn, stg_ctx);
324       STGShur14_Calc(x_i, time, ubar, cij, qn, u, stg_ctx);
325     } else {
326       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
327     }
328 
329     switch (stg_ctx->newtonian_ctx.state_var) {
330       case STATEVAR_CONSERVATIVE:
331         q0[0][i] = rho;
332         q0[1][i] = u[0] * rho;
333         q0[2][i] = u[1] * rho;
334         q0[3][i] = u[2] * rho;
335         q0[4][i] = rho * (0.5 * Dot3(u, u) + cv * theta0);
336         break;
337 
338       case STATEVAR_PRIMITIVE:
339         q0[0][i] = P0;
340         q0[1][i] = u[0];
341         q0[2][i] = u[1];
342         q0[3][i] = u[2];
343         q0[4][i] = theta0;
344         break;
345     }
346   }  // End of Quadrature Point Loop
347   return 0;
348 }
349 
350 /********************************************************************
351  * @brief QFunction to calculate the inflow boundary condition
352  *
353  * This will loop through quadrature points, calculate the wavemode amplitudes
354  * at each location, then calculate the actual velocity.
355  */
356 CEED_QFUNCTION(STGShur14_Inflow)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
357   //*INDENT-OFF*
358   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],
359         (*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3];
360 
361   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0], (*jac_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1];
362 
363   //*INDENT-ON*
364 
365   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
366   CeedScalar             qn[STG_NMODES_MAX], u[3], ubar[3], cij[6], eps, lt;
367   const bool             is_implicit = stg_ctx->is_implicit;
368   const bool             mean_only   = stg_ctx->mean_only;
369   const bool             prescribe_T = stg_ctx->prescribe_T;
370   const CeedScalar       dx          = stg_ctx->dx;
371   const CeedScalar       mu          = stg_ctx->newtonian_ctx.mu;
372   const CeedScalar       time        = stg_ctx->time;
373   const CeedScalar       theta0      = stg_ctx->theta0;
374   const CeedScalar       P0          = stg_ctx->P0;
375   const CeedScalar       cv          = stg_ctx->newtonian_ctx.cv;
376   const CeedScalar       cp          = stg_ctx->newtonian_ctx.cp;
377   const CeedScalar       Rd          = cp - cv;
378   const CeedScalar       gamma       = cp / cv;
379 
380   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
381     const CeedScalar rho        = prescribe_T ? q[0][i] : P0 / (Rd * theta0);
382     const CeedScalar x[]        = {X[0][i], X[1][i], X[2][i]};
383     const CeedScalar dXdx[2][3] = {
384         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
385         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
386     };
387 
388     CeedScalar h[3];
389     h[0] = dx;
390     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
391 
392     InterpolateProfile(X[1][i], ubar, cij, &eps, &lt, stg_ctx);
393     if (!mean_only) {
394       CalcSpectrum(X[1][i], eps, lt, h, mu / rho, qn, stg_ctx);
395       STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
396     } else {
397       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
398     }
399 
400     const CeedScalar E_kinetic = .5 * rho * Dot3(u, u);
401     CeedScalar       E_internal, P;
402     if (prescribe_T) {
403       // Temperature is being set weakly (theta0) and for constant cv this sets E_internal
404       E_internal = rho * cv * theta0;
405       // Find pressure using
406       P = rho * Rd * theta0;  // interior rho with exterior T
407     } else {
408       E_internal = q[4][i] - E_kinetic;  // uses prescribed rho and u, E from solution
409       P          = E_internal * (gamma - 1.);
410     }
411 
412     const CeedScalar wdetJb = (is_implicit ? -1. : 1.) * q_data_sur[0][i];
413     // ---- Normal vect
414     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
415 
416     const CeedScalar E = E_internal + E_kinetic;
417 
418     // Velocity normal to the boundary
419     const CeedScalar u_normal = Dot3(norm, u);
420 
421     // The Physics
422     // Zero v so all future terms can safely sum into it
423     for (CeedInt j = 0; j < 5; j++) v[j][i] = 0.;
424 
425     // The Physics
426     // -- Density
427     v[0][i] -= wdetJb * rho * u_normal;
428 
429     // -- Momentum
430     for (CeedInt j = 0; j < 3; j++) v[j + 1][i] -= wdetJb * (rho * u_normal * u[j] + norm[j] * P);
431 
432     // -- Total Energy Density
433     v[4][i] -= wdetJb * u_normal * (E + P);
434 
435     jac_data_sur[0][i] = rho;
436     jac_data_sur[1][i] = u[0];
437     jac_data_sur[2][i] = u[1];
438     jac_data_sur[3][i] = u[2];
439     jac_data_sur[4][i] = E;
440     for (int j = 0; j < 6; j++) jac_data_sur[5 + j][i] = 0.;
441   }
442   return 0;
443 }
444 
445 CEED_QFUNCTION(STGShur14_Inflow_Jacobian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
446   // *INDENT-OFF*
447   // Inputs
448   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],
449         (*jac_data_sur)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[4];
450   // Outputs
451   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
452   // *INDENT-ON*
453   const STGShur14Context stg_ctx  = (STGShur14Context)ctx;
454   const bool             implicit = stg_ctx->is_implicit;
455   const CeedScalar       cv       = stg_ctx->newtonian_ctx.cv;
456   const CeedScalar       cp       = stg_ctx->newtonian_ctx.cp;
457   const CeedScalar       Rd       = cp - cv;
458   const CeedScalar       gamma    = cp / cv;
459 
460   const CeedScalar theta0      = stg_ctx->theta0;
461   const bool       prescribe_T = stg_ctx->prescribe_T;
462 
463   CeedPragmaSIMD
464       // Quadrature Point Loop
465       for (CeedInt i = 0; i < Q; i++) {
466     // Setup
467     // -- Interp-to-Interp q_data
468     // For explicit mode, the surface integral is on the RHS of ODE q_dot = f(q).
469     // For implicit mode, it gets pulled to the LHS of implicit ODE/DAE g(q_dot, q).
470     // We can effect this by swapping the sign on this weight
471     const CeedScalar wdetJb = (implicit ? -1. : 1.) * q_data_sur[0][i];
472 
473     // Calculate inflow values
474     CeedScalar velocity[3];
475     for (CeedInt j = 0; j < 3; j++) velocity[j] = jac_data_sur[5 + j][i];
476 
477     // enabling user to choose between weak T and weak rho inflow
478     CeedScalar drho, dE, dP;
479     if (prescribe_T) {
480       // rho should be from the current solution
481       drho                   = dq[0][i];
482       CeedScalar dE_internal = drho * cv * theta0;
483       CeedScalar dE_kinetic  = .5 * drho * Dot3(velocity, velocity);
484       dE                     = dE_internal + dE_kinetic;
485       dP                     = drho * Rd * theta0;  // interior rho with exterior T
486     } else {                                        // rho specified, E_internal from solution
487       drho = 0;
488       dE   = dq[4][i];
489       dP   = dE * (gamma - 1.);
490     }
491     const CeedScalar norm[3] = {q_data_sur[1][i], q_data_sur[2][i], q_data_sur[3][i]};
492 
493     const CeedScalar u_normal = Dot3(norm, velocity);
494 
495     v[0][i] = -wdetJb * drho * u_normal;
496     for (int j = 0; j < 3; j++) v[j + 1][i] = -wdetJb * (drho * u_normal * velocity[j] + norm[j] * dP);
497     v[4][i] = -wdetJb * u_normal * (dE + dP);
498   }  // End Quadrature Point Loop
499   return 0;
500 }
501 
502 /********************************************************************
503  * @brief QFunction to calculate the strongly enforce inflow BC
504  *
505  * This QF is for the strong application of STG via libCEED (rather than
506  * through the native PETSc `DMAddBoundary` -> `bcFunc` method.
507  */
508 CEED_QFUNCTION(STGShur14_Inflow_StrongQF)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
509   //*INDENT-OFF*
510   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],
511         (*scale) = (const CeedScalar(*))in[2], (*stg_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3];
512 
513   CeedScalar(*bcval)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
514   //*INDENT-ON*
515 
516   const STGShur14Context stg_ctx = (STGShur14Context)ctx;
517   CeedScalar             u[3], ubar[3], cij[6], eps, lt;
518   const bool             mean_only = stg_ctx->mean_only;
519   const CeedScalar       dx        = stg_ctx->dx;
520   const CeedScalar       mu        = stg_ctx->newtonian_ctx.mu;
521   const CeedScalar       time      = stg_ctx->time;
522   const CeedScalar       theta0    = stg_ctx->theta0;
523   const CeedScalar       P0        = stg_ctx->P0;
524   const CeedScalar       cv        = stg_ctx->newtonian_ctx.cv;
525   const CeedScalar       cp        = stg_ctx->newtonian_ctx.cp;
526   const CeedScalar       Rd        = cp - cv;
527   const CeedScalar       rho       = P0 / (Rd * theta0);
528 
529   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
530     const CeedScalar x[]        = {coords[0][i], coords[1][i], coords[2][i]};
531     const CeedScalar dXdx[2][3] = {
532         {q_data_sur[4][i], q_data_sur[5][i], q_data_sur[6][i]},
533         {q_data_sur[7][i], q_data_sur[8][i], q_data_sur[9][i]}
534     };
535 
536     CeedScalar h[3];
537     h[0] = dx;
538     for (CeedInt j = 1; j < 3; j++) h[j] = 2 / sqrt(Square(dXdx[0][j]) + Square(dXdx[1][j]));
539 
540     InterpolateProfile(coords[1][i], ubar, cij, &eps, &lt, stg_ctx);
541     if (!mean_only) {
542       if (1) {
543         STGShur14_Calc_PrecompEktot(x, time, ubar, cij, stg_data[0][i], h, x[1], eps, lt, mu / rho, u, stg_ctx);
544       } else {  // Original way
545         CeedScalar qn[STG_NMODES_MAX];
546         CalcSpectrum(coords[1][i], eps, lt, h, mu / rho, qn, stg_ctx);
547         STGShur14_Calc(x, time, ubar, cij, qn, u, stg_ctx);
548       }
549     } else {
550       for (CeedInt j = 0; j < 3; j++) u[j] = ubar[j];
551     }
552 
553     switch (stg_ctx->newtonian_ctx.state_var) {
554       case STATEVAR_CONSERVATIVE:
555         bcval[0][i] = scale[i] * rho;
556         bcval[1][i] = scale[i] * rho * u[0];
557         bcval[2][i] = scale[i] * rho * u[1];
558         bcval[3][i] = scale[i] * rho * u[2];
559         bcval[4][i] = 0.;
560         break;
561 
562       case STATEVAR_PRIMITIVE:
563         bcval[0][i] = 0;
564         bcval[1][i] = scale[i] * u[0];
565         bcval[2][i] = scale[i] * u[1];
566         bcval[3][i] = scale[i] * u[2];
567         bcval[4][i] = scale[i] * theta0;
568         break;
569     }
570   }
571   return 0;
572 }
573 
574 #endif  // stg_shur14_h
575