1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors. 2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause 3 4 /// @file 5 /// Element anisotropy tensor, as defined in 'Invariant data-driven subgrid stress modeling in the strain-rate eigenframe for large eddy simulation' 6 /// Prakash et al. 2022 7 #include <ceed.h> 8 9 #include "utils.h" 10 #include "utils_eigensolver_jacobi.h" 11 12 // @brief Get Anisotropy tensor from xi_{i,j} 13 // @details A_ij = \Delta_{ij} / ||\Delta_ij||, \Delta_ij = (xi_{i,j})^(-1/2) 14 CEED_QFUNCTION_HELPER void AnisotropyTensor(const CeedScalar km_g_ij[6], CeedScalar A_ij[3][3], CeedScalar *delta, const CeedInt n_sweeps) { 15 CeedScalar evals[3], evecs[3][3], evals_evecs[3][3] = {{0.}}, g_ij[3][3]; 16 CeedInt work_vector[3]; 17 18 // Invert square root of metric tensor to get \Delta_ij 19 KMUnpack(km_g_ij, g_ij); 20 Diagonalize3(g_ij, evals, evecs, work_vector, SORT_DECREASING_EVALS, true, n_sweeps); 21 for (int i = 0; i < 3; i++) evals[i] = 1 / sqrt(evals[i]); 22 MatDiag3(evecs, evals, CEED_NOTRANSPOSE, evals_evecs); 23 MatMat3(evecs, evals_evecs, CEED_TRANSPOSE, CEED_NOTRANSPOSE, A_ij); // A_ij = E^T D E 24 25 // Scale by delta to get anisotropy tensor 26 *delta = Norm3(evals); 27 ScaleN((CeedScalar *)A_ij, 1 / *delta, 9); 28 // NOTE Need 2 factor to get physical element size (rather than projected onto [-1,1]^dim) 29 // Should attempt to auto-determine this from the quadrature point coordinates in reference space 30 *delta *= 2; 31 } 32 33 // @brief RHS for L^2 projection of anisotropic tensor and it's Frobenius norm 34 CEED_QFUNCTION(AnisotropyTensorProjection)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 35 const CeedScalar(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 36 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 37 38 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 39 const CeedScalar wdetJ = q_data[0][i]; 40 const CeedScalar dXdx[3][3] = { 41 {q_data[1][i], q_data[2][i], q_data[3][i]}, 42 {q_data[4][i], q_data[5][i], q_data[6][i]}, 43 {q_data[7][i], q_data[8][i], q_data[9][i]} 44 }; 45 46 CeedScalar km_g_ij[6] = {0.}, A_ij[3][3] = {{0.}}, km_A_ij[6], delta; 47 KMMetricTensor(dXdx, km_g_ij); 48 AnisotropyTensor(km_g_ij, A_ij, &delta, 15); 49 KMPack(A_ij, km_A_ij); 50 51 for (CeedInt j = 0; j < 6; j++) v[j][i] = wdetJ * km_A_ij[j]; 52 v[6][i] = wdetJ * delta; 53 } 54 return 0; 55 } 56 57 // @brief Get anisotropic tensor and it's Frobenius norm at quadrature points 58 CEED_QFUNCTION(AnisotropyTensorCollocate)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 59 const CeedScalar(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 60 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 61 62 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 63 const CeedScalar dXdx[3][3] = { 64 {q_data[1][i], q_data[2][i], q_data[3][i]}, 65 {q_data[4][i], q_data[5][i], q_data[6][i]}, 66 {q_data[7][i], q_data[8][i], q_data[9][i]} 67 }; 68 69 CeedScalar km_g_ij[6] = {0.}, A_ij[3][3] = {{0.}}, km_A_ij[6], delta; 70 KMMetricTensor(dXdx, km_g_ij); 71 AnisotropyTensor(km_g_ij, A_ij, &delta, 15); 72 KMPack(A_ij, km_A_ij); 73 74 for (CeedInt j = 0; j < 6; j++) v[j][i] = km_A_ij[j]; 75 v[6][i] = delta; 76 } 77 return 0; 78 } 79