xref: /libCEED/examples/fluids/qfunctions/newtonian.h (revision 242a7fda1390d71ae7a60a1ed0d03da31fa282cf)
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 /// Operator for Navier-Stokes example using PETSc
10 
11 #ifndef newtonian_h
12 #define newtonian_h
13 
14 #include <ceed.h>
15 #include <math.h>
16 #include <stdlib.h>
17 
18 #include "newtonian_state.h"
19 #include "newtonian_types.h"
20 #include "stabilization.h"
21 #include "utils.h"
22 
23 CEED_QFUNCTION_HELPER void InternalDampingLayer(const NewtonianIdealGasContext context, const State s, const CeedScalar x_i[3], CeedScalar damp_Y[5],
24                                                 CeedScalar damp_residual[5]) {
25   const CeedScalar sigma = LinearRampCoefficient(context->idl_amplitude, context->idl_length, context->idl_start, x_i[0]);
26   ScaleN(damp_Y, sigma, 5);
27   State damp_s = StateFromY_fwd(context, s, damp_Y);
28 
29   CeedScalar U[5];
30   UnpackState_U(damp_s.U, U);
31   for (int i = 0; i < 5; i++) damp_residual[i] += U[i];
32 }
33 
34 // *****************************************************************************
35 // This QFunction sets a "still" initial condition for generic Newtonian IG problems
36 // *****************************************************************************
37 CEED_QFUNCTION_HELPER int ICsNewtonianIG(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, StateVariable state_var) {
38   // Inputs
39 
40   // Outputs
41   CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
42 
43   // Context
44   const SetupContext context = (SetupContext)ctx;
45 
46   // Quadrature Point Loop
47   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
48     CeedScalar q[5] = {0.};
49     State      s    = StateFromPrimitive(&context->gas, context->reference);
50     StateToQ(&context->gas, s, q, state_var);
51     for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j];
52   }  // End of Quadrature Point Loop
53   return 0;
54 }
55 
56 CEED_QFUNCTION(ICsNewtonianIG_Prim)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
57   return ICsNewtonianIG(ctx, Q, in, out, STATEVAR_PRIMITIVE);
58 }
59 CEED_QFUNCTION(ICsNewtonianIG_Conserv)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
60   return ICsNewtonianIG(ctx, Q, in, out, STATEVAR_CONSERVATIVE);
61 }
62 
63 // *****************************************************************************
64 // This QFunction implements the following formulation of Navier-Stokes with explicit time stepping method
65 //
66 // This is 3D compressible Navier-Stokes in conservation form with state variables of density, momentum density, and total energy density.
67 //
68 // State Variables: q = ( rho, U1, U2, U3, E )
69 //   rho - Mass Density
70 //   Ui  - Momentum Density,      Ui = rho ui
71 //   E   - Total Energy Density,  E  = rho (cv T + (u u)/2 + g z)
72 //
73 // Navier-Stokes Equations:
74 //   drho/dt + div( U )                               = 0
75 //   dU/dt   + div( rho (u x u) + P I3 ) + rho g khat = div( Fu )
76 //   dE/dt   + div( (E + P) u )                       = div( Fe )
77 //
78 // Viscous Stress:
79 //   Fu = mu (grad( u ) + grad( u )^T + lambda div ( u ) I3)
80 //
81 // Thermal Stress:
82 //   Fe = u Fu + k grad( T )
83 // Equation of State
84 //   P = (gamma - 1) (E - rho (u u) / 2 - rho g z)
85 //
86 // Stabilization:
87 //   Tau = diag(TauC, TauM, TauM, TauM, TauE)
88 //     f1 = rho  sqrt(ui uj gij)
89 //     gij = dXi/dX * dXi/dX
90 //     TauC = Cc f1 / (8 gii)
91 //     TauM = min( 1 , 1 / f1 )
92 //     TauE = TauM / (Ce cv)
93 //
94 //  SU   = Galerkin + grad(v) . ( Ai^T * Tau * (Aj q,j) )
95 //
96 // Constants:
97 //   lambda = - 2 / 3,  From Stokes hypothesis
98 //   mu              ,  Dynamic viscosity
99 //   k               ,  Thermal conductivity
100 //   cv              ,  Specific heat, constant volume
101 //   cp              ,  Specific heat, constant pressure
102 //   g               ,  Gravity
103 //   gamma  = cp / cv,  Specific heat ratio
104 //
105 // We require the product of the inverse of the Jacobian (dXdx_j,k) and its transpose (dXdx_k,j) to properly compute integrals of the form: int( gradv
106 // gradu )
107 // *****************************************************************************
108 CEED_QFUNCTION(RHSFunction_Newtonian)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
109   // Inputs
110   const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
111   const CeedScalar(*Grad_q)        = in[1];
112   const CeedScalar(*q_data)        = in[2];
113 
114   // Outputs
115   CeedScalar(*v)[CEED_Q_VLA]         = (CeedScalar(*)[CEED_Q_VLA])out[0];
116   CeedScalar(*Grad_v)[5][CEED_Q_VLA] = (CeedScalar(*)[5][CEED_Q_VLA])out[1];
117 
118   // Context
119   NewtonianIdealGasContext context = (NewtonianIdealGasContext)ctx;
120   const CeedScalar        *g       = context->g;
121   const CeedScalar         dt      = context->dt;
122 
123   // Quadrature Point Loop
124   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
125     CeedScalar U[5], wdetJ, dXdx[3][3];
126     for (int j = 0; j < 5; j++) U[j] = q[j][i];
127     StoredValuesUnpack(Q, i, 0, 1, q_data, &wdetJ);
128     StoredValuesUnpack(Q, i, 1, 9, q_data, (CeedScalar *)dXdx);
129     State            s      = StateFromU(context, U);
130 
131     State grad_s[3];
132     StatePhysicalGradientFromReference(Q, i, context, s, STATEVAR_CONSERVATIVE, Grad_q, dXdx, grad_s);
133 
134     CeedScalar strain_rate[6], kmstress[6], stress[3][3], Fe[3];
135     KMStrainRate_State(grad_s, strain_rate);
136     NewtonianStress(context, strain_rate, kmstress);
137     KMUnpack(kmstress, stress);
138     ViscousEnergyFlux(context, s.Y, grad_s, stress, Fe);
139 
140     StateConservative F_inviscid[3];
141     FluxInviscid(context, s, F_inviscid);
142 
143     // Total flux
144     CeedScalar Flux[5][3];
145     FluxTotal(F_inviscid, stress, Fe, Flux);
146 
147     for (CeedInt j = 0; j < 5; j++) {
148       for (CeedInt k = 0; k < 3; k++) Grad_v[k][j][i] = wdetJ * (dXdx[k][0] * Flux[j][0] + dXdx[k][1] * Flux[j][1] + dXdx[k][2] * Flux[j][2]);
149     }
150 
151     const CeedScalar body_force[5] = {0, s.U.density * g[0], s.U.density * g[1], s.U.density * g[2], Dot3(s.U.momentum, g)};
152     for (int j = 0; j < 5; j++) v[j][i] = wdetJ * body_force[j];
153 
154     // -- Stabilization method: none (Galerkin), SU, or SUPG
155     CeedScalar Tau_d[3], stab[5][3], U_dot[5] = {0};
156     Tau_diagPrim(context, s, dXdx, dt, Tau_d);
157     Stabilization(context, s, Tau_d, grad_s, U_dot, body_force, stab);
158 
159     for (CeedInt j = 0; j < 5; j++) {
160       for (CeedInt k = 0; k < 3; k++) Grad_v[k][j][i] -= wdetJ * (stab[j][0] * dXdx[k][0] + stab[j][1] * dXdx[k][1] + stab[j][2] * dXdx[k][2]);
161     }
162   }  // End Quadrature Point Loop
163 
164   // Return
165   return 0;
166 }
167 
168 // *****************************************************************************
169 // This QFunction implements the Navier-Stokes equations (mentioned above) with implicit time stepping method
170 //
171 //  SU   = Galerkin + grad(v) . ( Ai^T * Tau * (Aj q,j) )
172 //  SUPG = Galerkin + grad(v) . ( Ai^T * Tau * (q_dot + Aj q,j - body force) )
173 //                                       (diffusive terms will be added later)
174 // *****************************************************************************
175 CEED_QFUNCTION_HELPER int IFunction_Newtonian(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, StateVariable state_var) {
176   // Inputs
177   const CeedScalar(*q)[CEED_Q_VLA]     = (const CeedScalar(*)[CEED_Q_VLA])in[0];
178   const CeedScalar(*Grad_q)            = in[1];
179   const CeedScalar(*q_dot)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2];
180   const CeedScalar(*q_data)            = in[3];
181   const CeedScalar(*x)[CEED_Q_VLA]     = (const CeedScalar(*)[CEED_Q_VLA])in[4];
182 
183   // Outputs
184   CeedScalar(*v)[CEED_Q_VLA]         = (CeedScalar(*)[CEED_Q_VLA])out[0];
185   CeedScalar(*Grad_v)[5][CEED_Q_VLA] = (CeedScalar(*)[5][CEED_Q_VLA])out[1];
186   CeedScalar(*jac_data)              = out[2];
187 
188   // Context
189   NewtonianIdealGasContext context = (NewtonianIdealGasContext)ctx;
190   const CeedScalar        *g       = context->g;
191   const CeedScalar         dt      = context->dt;
192   const CeedScalar         P0      = context->P0;
193 
194   // Quadrature Point Loop
195   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
196     const CeedScalar qi[5]  = {q[0][i], q[1][i], q[2][i], q[3][i], q[4][i]};
197     const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]};
198     const State      s      = StateFromQ(context, qi, state_var);
199 
200     CeedScalar wdetJ, dXdx[3][3];
201     QdataUnpack_3D(Q, i, q_data, &wdetJ, dXdx);
202     State grad_s[3];
203     StatePhysicalGradientFromReference(Q, i, context, s, state_var, Grad_q, dXdx, grad_s);
204 
205     CeedScalar strain_rate[6], kmstress[6], stress[3][3], Fe[3];
206     KMStrainRate_State(grad_s, strain_rate);
207     NewtonianStress(context, strain_rate, kmstress);
208     KMUnpack(kmstress, stress);
209     ViscousEnergyFlux(context, s.Y, grad_s, stress, Fe);
210 
211     StateConservative F_inviscid[3];
212     FluxInviscid(context, s, F_inviscid);
213 
214     // Total flux
215     CeedScalar Flux[5][3];
216     FluxTotal(F_inviscid, stress, Fe, Flux);
217 
218     for (CeedInt j = 0; j < 5; j++) {
219       for (CeedInt k = 0; k < 3; k++) {
220         Grad_v[k][j][i] = -wdetJ * (dXdx[k][0] * Flux[j][0] + dXdx[k][1] * Flux[j][1] + dXdx[k][2] * Flux[j][2]);
221       }
222     }
223 
224     const CeedScalar body_force[5] = {0, s.U.density * g[0], s.U.density * g[1], s.U.density * g[2], Dot3(s.U.momentum, g)};
225 
226     // -- Stabilization method: none (Galerkin), SU, or SUPG
227     CeedScalar Tau_d[3], stab[5][3], U_dot[5] = {0}, qi_dot[5];
228     for (int j = 0; j < 5; j++) qi_dot[j] = q_dot[j][i];
229     State s_dot = StateFromQ_fwd(context, s, qi_dot, state_var);
230     UnpackState_U(s_dot.U, U_dot);
231 
232     for (CeedInt j = 0; j < 5; j++) v[j][i] = wdetJ * (U_dot[j] - body_force[j]);
233     if (context->idl_enable) {
234       CeedScalar damp_state[5] = {s.Y.pressure - P0, 0, 0, 0, 0}, idl_residual[5] = {0.};
235       InternalDampingLayer(context, s, x_i, damp_state, idl_residual);
236       for (int j = 0; j < 5; j++) v[j][i] += wdetJ * idl_residual[j];
237     }
238 
239     Tau_diagPrim(context, s, dXdx, dt, Tau_d);
240     Stabilization(context, s, Tau_d, grad_s, U_dot, body_force, stab);
241 
242     for (CeedInt j = 0; j < 5; j++) {
243       for (CeedInt k = 0; k < 3; k++) {
244         Grad_v[k][j][i] += wdetJ * (stab[j][0] * dXdx[k][0] + stab[j][1] * dXdx[k][1] + stab[j][2] * dXdx[k][2]);
245       }
246     }
247     StoredValuesPack(Q, i, 0, 5, qi, jac_data);
248     StoredValuesPack(Q, i, 5, 6, kmstress, jac_data);
249     StoredValuesPack(Q, i, 11, 3, Tau_d, jac_data);
250 
251   }  // End Quadrature Point Loop
252 
253   // Return
254   return 0;
255 }
256 
257 CEED_QFUNCTION(IFunction_Newtonian_Conserv)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
258   return IFunction_Newtonian(ctx, Q, in, out, STATEVAR_CONSERVATIVE);
259 }
260 
261 CEED_QFUNCTION(IFunction_Newtonian_Prim)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
262   return IFunction_Newtonian(ctx, Q, in, out, STATEVAR_PRIMITIVE);
263 }
264 
265 // *****************************************************************************
266 // This QFunction implements the jacobian of the Navier-Stokes equations for implicit time stepping method.
267 // *****************************************************************************
268 CEED_QFUNCTION_HELPER int IJacobian_Newtonian(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, StateVariable state_var) {
269   // Inputs
270   const CeedScalar(*dq)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
271   const CeedScalar(*Grad_dq)        = in[1];
272   const CeedScalar(*q_data)         = in[2];
273   const CeedScalar(*x)[CEED_Q_VLA]  = (const CeedScalar(*)[CEED_Q_VLA])in[3];
274   const CeedScalar(*jac_data)       = in[4];
275 
276   // Outputs
277   CeedScalar(*v)[CEED_Q_VLA]         = (CeedScalar(*)[CEED_Q_VLA])out[0];
278   CeedScalar(*Grad_v)[5][CEED_Q_VLA] = (CeedScalar(*)[5][CEED_Q_VLA])out[1];
279 
280   // Context
281   NewtonianIdealGasContext context = (NewtonianIdealGasContext)ctx;
282   const CeedScalar        *g       = context->g;
283 
284   // Quadrature Point Loop
285   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
286     CeedScalar wdetJ, dXdx[3][3];
287     QdataUnpack_3D(Q, i, q_data, &wdetJ, dXdx);
288 
289     CeedScalar qi[5], kmstress[6], Tau_d[3];
290     StoredValuesUnpack(Q, i, 0, 5, jac_data, qi);
291     StoredValuesUnpack(Q, i, 5, 6, jac_data, kmstress);
292     StoredValuesUnpack(Q, i, 11, 3, jac_data, Tau_d);
293     const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]};
294     State            s      = StateFromQ(context, qi, state_var);
295 
296     CeedScalar dqi[5];
297     for (int j = 0; j < 5; j++) dqi[j] = dq[j][i];
298     State ds = StateFromQ_fwd(context, s, dqi, state_var);
299 
300     State grad_ds[3];
301     StatePhysicalGradientFromReference(Q, i, context, s, state_var, Grad_dq, dXdx, grad_ds);
302 
303     CeedScalar dstrain_rate[6], dkmstress[6], stress[3][3], dstress[3][3], dFe[3];
304     KMStrainRate_State(grad_ds, dstrain_rate);
305     NewtonianStress(context, dstrain_rate, dkmstress);
306     KMUnpack(dkmstress, dstress);
307     KMUnpack(kmstress, stress);
308     ViscousEnergyFlux_fwd(context, s.Y, ds.Y, grad_ds, stress, dstress, dFe);
309 
310     StateConservative dF_inviscid[3];
311     FluxInviscid_fwd(context, s, ds, dF_inviscid);
312 
313     // Total flux
314     CeedScalar dFlux[5][3];
315     FluxTotal(dF_inviscid, dstress, dFe, dFlux);
316 
317     for (int j = 0; j < 5; j++) {
318       for (int k = 0; k < 3; k++) Grad_v[k][j][i] = -wdetJ * (dXdx[k][0] * dFlux[j][0] + dXdx[k][1] * dFlux[j][1] + dXdx[k][2] * dFlux[j][2]);
319     }
320 
321     const CeedScalar dbody_force[5] = {0, ds.U.density * g[0], ds.U.density * g[1], ds.U.density * g[2], Dot3(ds.U.momentum, g)};
322     CeedScalar       dU[5]          = {0.};
323     UnpackState_U(ds.U, dU);
324     for (int j = 0; j < 5; j++) v[j][i] = wdetJ * (context->ijacobian_time_shift * dU[j] - dbody_force[j]);
325 
326     if (context->idl_enable) {
327       CeedScalar damp_state[5] = {ds.Y.pressure, 0, 0, 0, 0}, idl_residual[5] = {0.};
328       // This is a Picard-type linearization of the damping and could be replaced by an InternalDampingLayer_fwd that uses s and ds.
329       InternalDampingLayer(context, s, x_i, damp_state, idl_residual);
330       for (int j = 0; j < 5; j++) v[j][i] += wdetJ * idl_residual[j];
331     }
332 
333     // -- Stabilization method: none (Galerkin), SU, or SUPG
334     CeedScalar dstab[5][3], U_dot[5] = {0};
335     for (CeedInt j = 0; j < 5; j++) U_dot[j] = context->ijacobian_time_shift * dU[j];
336     Stabilization(context, s, Tau_d, grad_ds, U_dot, dbody_force, dstab);
337 
338     for (int j = 0; j < 5; j++) {
339       for (int k = 0; k < 3; k++) Grad_v[k][j][i] += wdetJ * (dstab[j][0] * dXdx[k][0] + dstab[j][1] * dXdx[k][1] + dstab[j][2] * dXdx[k][2]);
340     }
341   }  // End Quadrature Point Loop
342   return 0;
343 }
344 
345 CEED_QFUNCTION(IJacobian_Newtonian_Conserv)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
346   return IJacobian_Newtonian(ctx, Q, in, out, STATEVAR_CONSERVATIVE);
347 }
348 
349 CEED_QFUNCTION(IJacobian_Newtonian_Prim)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
350   return IJacobian_Newtonian(ctx, Q, in, out, STATEVAR_PRIMITIVE);
351 }
352 
353 // *****************************************************************************
354 // Compute boundary integral (ie. for strongly set inflows)
355 // *****************************************************************************
356 CEED_QFUNCTION_HELPER int BoundaryIntegral(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, StateVariable state_var) {
357   const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
358   const CeedScalar(*Grad_q)        = in[1];
359   const CeedScalar(*q_data_sur)    = in[2];
360 
361   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
362   CeedScalar(*jac_data_sur)  = out[1];
363 
364   const NewtonianIdealGasContext context     = (NewtonianIdealGasContext)ctx;
365   const bool                     is_implicit = context->is_implicit;
366 
367   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
368     const CeedScalar qi[5] = {q[0][i], q[1][i], q[2][i], q[3][i], q[4][i]};
369     State            s     = StateFromQ(context, qi, state_var);
370 
371     CeedScalar wdetJb, dXdx[2][3], norm[3];
372     QdataBoundaryUnpack_3D(Q, i, q_data_sur, &wdetJb, dXdx, norm);
373     wdetJb *= is_implicit ? -1. : 1.;
374 
375     State grad_s[3];
376     StatePhysicalGradientFromReference_Boundary(Q, i, context, s, state_var, Grad_q, dXdx, grad_s);
377 
378     CeedScalar strain_rate[6], kmstress[6], stress[3][3], Fe[3];
379     KMStrainRate_State(grad_s, strain_rate);
380     NewtonianStress(context, strain_rate, kmstress);
381     KMUnpack(kmstress, stress);
382     ViscousEnergyFlux(context, s.Y, grad_s, stress, Fe);
383 
384     StateConservative F_inviscid[3];
385     FluxInviscid(context, s, F_inviscid);
386 
387     CeedScalar Flux[5];
388     FluxTotal_Boundary(F_inviscid, stress, Fe, norm, Flux);
389 
390     for (CeedInt j = 0; j < 5; j++) v[j][i] = -wdetJb * Flux[j];
391 
392     StoredValuesPack(Q, i, 0, 5, qi, jac_data_sur);
393     StoredValuesPack(Q, i, 5, 6, kmstress, jac_data_sur);
394   }
395   return 0;
396 }
397 
398 CEED_QFUNCTION(BoundaryIntegral_Conserv)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
399   return BoundaryIntegral(ctx, Q, in, out, STATEVAR_CONSERVATIVE);
400 }
401 
402 CEED_QFUNCTION(BoundaryIntegral_Prim)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
403   return BoundaryIntegral(ctx, Q, in, out, STATEVAR_PRIMITIVE);
404 }
405 
406 // *****************************************************************************
407 // Jacobian for "set nothing" boundary integral
408 // *****************************************************************************
409 CEED_QFUNCTION_HELPER int BoundaryIntegral_Jacobian(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out,
410                                                     StateVariable state_var) {
411   // Inputs
412   const CeedScalar(*dq)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
413   const CeedScalar(*Grad_dq)        = in[1];
414   const CeedScalar(*q_data_sur)     = in[2];
415   const CeedScalar(*jac_data_sur)   = in[4];
416 
417   // Outputs
418   CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
419 
420   const NewtonianIdealGasContext context     = (NewtonianIdealGasContext)ctx;
421   const bool                     is_implicit = context->is_implicit;
422 
423   // Quadrature Point Loop
424   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
425     CeedScalar wdetJb, dXdx[2][3], norm[3];
426     QdataBoundaryUnpack_3D(Q, i, q_data_sur, &wdetJb, dXdx, norm);
427     wdetJb *= is_implicit ? -1. : 1.;
428 
429     CeedScalar qi[5], kmstress[6], dqi[5];
430     StoredValuesUnpack(Q, i, 0, 5, jac_data_sur, qi);
431     StoredValuesUnpack(Q, i, 5, 6, jac_data_sur, kmstress);
432     for (int j = 0; j < 5; j++) dqi[j] = dq[j][i];
433 
434     State s  = StateFromQ(context, qi, state_var);
435     State ds = StateFromQ_fwd(context, s, dqi, state_var);
436 
437     State grad_ds[3];
438     StatePhysicalGradientFromReference_Boundary(Q, i, context, s, state_var, Grad_dq, dXdx, grad_ds);
439 
440     CeedScalar dstrain_rate[6], dkmstress[6], stress[3][3], dstress[3][3], dFe[3];
441     KMStrainRate_State(grad_ds, dstrain_rate);
442     NewtonianStress(context, dstrain_rate, dkmstress);
443     KMUnpack(dkmstress, dstress);
444     KMUnpack(kmstress, stress);
445     ViscousEnergyFlux_fwd(context, s.Y, ds.Y, grad_ds, stress, dstress, dFe);
446 
447     StateConservative dF_inviscid[3];
448     FluxInviscid_fwd(context, s, ds, dF_inviscid);
449 
450     CeedScalar dFlux[5];
451     FluxTotal_Boundary(dF_inviscid, dstress, dFe, norm, dFlux);
452 
453     for (int j = 0; j < 5; j++) v[j][i] = -wdetJb * dFlux[j];
454   }  // End Quadrature Point Loop
455   return 0;
456 }
457 
458 CEED_QFUNCTION(BoundaryIntegral_Jacobian_Conserv)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
459   return BoundaryIntegral_Jacobian(ctx, Q, in, out, STATEVAR_CONSERVATIVE);
460 }
461 
462 CEED_QFUNCTION(BoundaryIntegral_Jacobian_Prim)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
463   return BoundaryIntegral_Jacobian(ctx, Q, in, out, STATEVAR_PRIMITIVE);
464 }
465 
466 #endif  // newtonian_h
467