1 // Copyright (c) 2017-2026, 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 /// Element anisotropy tensor, as defined in 'Invariant data-driven subgrid stress modeling in the strain-rate eigenframe for large eddy simulation'
10 /// Prakash et al. 2022
11 #include <ceed/types.h>
12
13 #include "utils.h"
14 #include "utils_eigensolver_jacobi.h"
15
16 // @brief Get Anisotropy tensor from xi_{i,j}
17 // @details A_ij = \Delta_{ij} / ||\Delta_ij||, \Delta_ij = (xi_{i,j})^(-1/2)
AnisotropyTensor(const CeedScalar km_g_ij[6],CeedScalar A_ij[3][3],CeedScalar * delta,const CeedInt n_sweeps)18 CEED_QFUNCTION_HELPER void AnisotropyTensor(const CeedScalar km_g_ij[6], CeedScalar A_ij[3][3], CeedScalar *delta, const CeedInt n_sweeps) {
19 CeedScalar evals[3], evecs[3][3], evals_evecs[3][3] = {{0.}}, g_ij[3][3];
20 CeedInt work_vector[3];
21
22 // Invert square root of metric tensor to get \Delta_ij
23 KMUnpack(km_g_ij, g_ij);
24 Diagonalize3(g_ij, evals, evecs, work_vector, SORT_DECREASING_EVALS, true, n_sweeps);
25 for (int i = 0; i < 3; i++) evals[i] = 1 / sqrt(evals[i]);
26 MatDiag3(evecs, evals, CEED_NOTRANSPOSE, evals_evecs);
27 MatMat3(evecs, evals_evecs, CEED_TRANSPOSE, CEED_NOTRANSPOSE, A_ij); // A_ij = E^T D E
28
29 // Scale by delta to get anisotropy tensor
30 *delta = sqrt(Dot3(evals, evals));
31 ScaleN((CeedScalar *)A_ij, 1 / *delta, 9);
32 // NOTE Need 2 factor to get physical element size (rather than projected onto [-1,1]^dim)
33 // Should attempt to auto-determine this from the quadrature point coordinates in reference space
34 *delta *= 2;
35 }
36
37 // @brief RHS for L^2 projection of anisotropic tensor and it's Frobenius norm
AnisotropyTensorProjection(void * ctx,CeedInt Q,const CeedScalar * const * in,CeedScalar * const * out)38 CEED_QFUNCTION(AnisotropyTensorProjection)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
39 const CeedScalar(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
40 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
41
42 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
43 const CeedScalar wdetJ = q_data[0][i];
44 const CeedScalar dXdx[3][3] = {
45 {q_data[1][i], q_data[2][i], q_data[3][i]},
46 {q_data[4][i], q_data[5][i], q_data[6][i]},
47 {q_data[7][i], q_data[8][i], q_data[9][i]}
48 };
49
50 CeedScalar km_g_ij[6] = {0.}, A_ij[3][3] = {{0.}}, km_A_ij[6], delta;
51 KMMetricTensor(dXdx, km_g_ij);
52 AnisotropyTensor(km_g_ij, A_ij, &delta, 15);
53 KMPack(A_ij, km_A_ij);
54
55 for (CeedInt j = 0; j < 6; j++) v[j][i] = wdetJ * km_A_ij[j];
56 v[6][i] = wdetJ * delta;
57 }
58 return 0;
59 }
60
61 // @brief Get anisotropic tensor and it's Frobenius norm at quadrature points
AnisotropyTensorCollocate(void * ctx,CeedInt Q,const CeedScalar * const * in,CeedScalar * const * out)62 CEED_QFUNCTION(AnisotropyTensorCollocate)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
63 const CeedScalar(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
64 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];
65
66 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
67 const CeedScalar dXdx[3][3] = {
68 {q_data[1][i], q_data[2][i], q_data[3][i]},
69 {q_data[4][i], q_data[5][i], q_data[6][i]},
70 {q_data[7][i], q_data[8][i], q_data[9][i]}
71 };
72
73 CeedScalar km_g_ij[6] = {0.}, A_ij[3][3] = {{0.}}, km_A_ij[6], delta;
74 KMMetricTensor(dXdx, km_g_ij);
75 AnisotropyTensor(km_g_ij, A_ij, &delta, 15);
76 KMPack(A_ij, km_A_ij);
77
78 for (CeedInt j = 0; j < 6; j++) v[j][i] = km_A_ij[j];
79 v[6][i] = delta;
80 }
81 return 0;
82 }
83