1 // Copyright (c) 2017-2023, 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 differential filtering 10 11 #include <ceed.h> 12 13 #include "differential_filter_enums.h" 14 #include "newtonian_state.h" 15 #include "newtonian_types.h" 16 #include "utils.h" 17 18 enum DifferentialFilterDampingFunction { DIFF_FILTER_DAMP_NONE, DIFF_FILTER_DAMP_VAN_DRIEST, DIFF_FILTER_DAMP_MMS }; 19 20 typedef struct DifferentialFilterContext_ *DifferentialFilterContext; 21 struct DifferentialFilterContext_ { 22 bool grid_based_width; 23 CeedScalar width_scaling[3]; 24 CeedScalar kernel_scaling; 25 CeedScalar friction_length; 26 enum DifferentialFilterDampingFunction damping_function; 27 CeedScalar damping_constant; 28 struct NewtonianIdealGasContext_ gas; 29 }; 30 31 CEED_QFUNCTION_HELPER int DifferentialFilter_RHS(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, StateVariable state_var) { 32 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 33 const CeedScalar(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1]; 34 CeedScalar(*v0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 35 CeedScalar(*v1)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1]; 36 37 DifferentialFilterContext context = (DifferentialFilterContext)ctx; 38 NewtonianIdealGasContext gas = &context->gas; 39 40 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 41 const CeedScalar qi[5] = {q[0][i], q[1][i], q[2][i], q[3][i], q[4][i]}; 42 const CeedScalar wdetJ = q_data[0][i]; 43 const State s = StateFromQ(gas, qi, state_var); 44 45 v0[DIFF_FILTER_PRESSURE][i] = wdetJ * s.Y.pressure; 46 v0[DIFF_FILTER_VELOCITY_X][i] = wdetJ * s.Y.velocity[0]; 47 v0[DIFF_FILTER_VELOCITY_Y][i] = wdetJ * s.Y.velocity[1]; 48 v0[DIFF_FILTER_VELOCITY_Z][i] = wdetJ * s.Y.velocity[2]; 49 v0[DIFF_FILTER_TEMPERATURE][i] = wdetJ * s.Y.temperature; 50 v1[DIFF_FILTER_VELOCITY_SQUARED_XX][i] = wdetJ * s.Y.velocity[0] * s.Y.velocity[0]; 51 v1[DIFF_FILTER_VELOCITY_SQUARED_YY][i] = wdetJ * s.Y.velocity[1] * s.Y.velocity[1]; 52 v1[DIFF_FILTER_VELOCITY_SQUARED_ZZ][i] = wdetJ * s.Y.velocity[2] * s.Y.velocity[2]; 53 v1[DIFF_FILTER_VELOCITY_SQUARED_YZ][i] = wdetJ * s.Y.velocity[1] * s.Y.velocity[2]; 54 v1[DIFF_FILTER_VELOCITY_SQUARED_XZ][i] = wdetJ * s.Y.velocity[0] * s.Y.velocity[2]; 55 v1[DIFF_FILTER_VELOCITY_SQUARED_XY][i] = wdetJ * s.Y.velocity[0] * s.Y.velocity[1]; 56 } 57 return 0; 58 } 59 60 CEED_QFUNCTION(DifferentialFilter_RHS_Conserv)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 61 return DifferentialFilter_RHS(ctx, Q, in, out, STATEVAR_CONSERVATIVE); 62 } 63 64 CEED_QFUNCTION(DifferentialFilter_RHS_Prim)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 65 return DifferentialFilter_RHS(ctx, Q, in, out, STATEVAR_PRIMITIVE); 66 } 67 68 CEED_QFUNCTION_HELPER CeedScalar VanDriestWallDamping(const CeedScalar wall_dist_plus, const CeedScalar A_plus) { 69 return -expm1(-wall_dist_plus / A_plus); 70 } 71 72 CEED_QFUNCTION_HELPER int DifferentialFilter_LHS_N(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out, const CeedInt N) { 73 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 74 const CeedScalar(*Grad_q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1]; 75 const CeedScalar(*A_ij_delta)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[2]; 76 const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[3]; 77 const CeedScalar(*q_data) = in[4]; 78 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 79 CeedScalar(*Grad_v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[1]; 80 81 DifferentialFilterContext context = (DifferentialFilterContext)ctx; 82 83 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 84 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 85 const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]}; 86 CeedScalar wdetJ, dXdx[3][3]; 87 QdataUnpack_3D(Q, i, q_data, &wdetJ, dXdx); 88 89 CeedScalar Delta_ij[3][3] = {{0.}}; 90 if (context->grid_based_width) { 91 CeedScalar km_A_ij[6] = {A_ij_delta[0][i], A_ij_delta[1][i], A_ij_delta[2][i], A_ij_delta[3][i], A_ij_delta[4][i], A_ij_delta[5][i]}; 92 const CeedScalar delta = A_ij_delta[6][i]; 93 ScaleN(km_A_ij, delta, 6); // Dimensionalize the normalized anisotropy tensor 94 KMUnpack(km_A_ij, Delta_ij); 95 } else { 96 Delta_ij[0][0] = Delta_ij[1][1] = Delta_ij[2][2] = 1; 97 } 98 99 CeedScalar scaling_matrix[3][3] = {{0}}; 100 if (context->damping_function == DIFF_FILTER_DAMP_VAN_DRIEST) { 101 const CeedScalar damping_coeff = VanDriestWallDamping(x_i[1] / context->friction_length, context->damping_constant); 102 scaling_matrix[0][0] = Max(1, damping_coeff * context->width_scaling[0]); 103 scaling_matrix[1][1] = damping_coeff * context->width_scaling[1]; 104 scaling_matrix[2][2] = Max(1, damping_coeff * context->width_scaling[2]); 105 } else if (context->damping_function == DIFF_FILTER_DAMP_NONE) { 106 scaling_matrix[0][0] = context->width_scaling[0]; 107 scaling_matrix[1][1] = context->width_scaling[1]; 108 scaling_matrix[2][2] = context->width_scaling[2]; 109 } else if (context->damping_function == DIFF_FILTER_DAMP_MMS) { 110 const CeedScalar damping_coeff = tanh(60 * x_i[1]); 111 scaling_matrix[0][0] = 1; 112 scaling_matrix[1][1] = damping_coeff; 113 scaling_matrix[2][2] = 1; 114 } 115 116 CeedScalar scaled_Delta_ij[3][3] = {{0.}}; 117 MatMat3(scaling_matrix, Delta_ij, CEED_NOTRANSPOSE, CEED_NOTRANSPOSE, scaled_Delta_ij); 118 CopyMat3(scaled_Delta_ij, Delta_ij); 119 120 CeedScalar alpha_ij[3][3] = {{0.}}; 121 MatMat3(Delta_ij, Delta_ij, CEED_NOTRANSPOSE, CEED_NOTRANSPOSE, alpha_ij); 122 ScaleN((CeedScalar *)alpha_ij, context->kernel_scaling, 9); 123 124 v[j][i] = wdetJ * q[j][i]; 125 CeedScalar dq[3], dq_dXdx[3] = {0.}, dq_dXdx_a[3] = {0.}; 126 for (int k = 0; k < 3; k++) { 127 dq[k] = Grad_q[0 * N + j][i] * dXdx[0][k] + Grad_q[1 * N + j][i] * dXdx[1][k] + Grad_q[2 * N + j][i] * dXdx[2][k]; 128 } 129 MatVec3(dXdx, dq, CEED_NOTRANSPOSE, dq_dXdx); 130 MatVec3(alpha_ij, dq_dXdx, CEED_NOTRANSPOSE, dq_dXdx_a); 131 for (int k = 0; k < 3; k++) { 132 Grad_v[k * N + j][i] = wdetJ * dq_dXdx_a[k]; 133 } 134 } 135 } 136 return 0; 137 } 138 139 CEED_QFUNCTION(DifferentialFilter_LHS_1)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 140 return DifferentialFilter_LHS_N(ctx, Q, in, out, 1); 141 } 142 143 CEED_QFUNCTION(DifferentialFilter_LHS_5)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 144 return DifferentialFilter_LHS_N(ctx, Q, in, out, 5); 145 } 146 147 CEED_QFUNCTION(DifferentialFilter_LHS_6)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 148 return DifferentialFilter_LHS_N(ctx, Q, in, out, 6); 149 } 150 151 CEED_QFUNCTION(DifferentialFilter_LHS_11)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 152 return DifferentialFilter_LHS_N(ctx, Q, in, out, 11); 153 } 154 155 CEED_QFUNCTION_HELPER CeedScalar MMS_Solution(const CeedScalar x_i[3], const CeedScalar omega) { 156 return sin(6 * omega * x_i[0]) + sin(6 * omega * x_i[1]); 157 } 158 159 CEED_QFUNCTION(DifferentialFilter_MMS_RHS)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 160 const CeedScalar(*q)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 161 const CeedScalar(*q_data)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[1]; 162 CeedScalar(*v)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 163 164 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 165 const CeedScalar wdetJ = q_data[0][i]; 166 v[0][i] = wdetJ * q[0][i]; 167 } 168 return 0; 169 } 170 171 // @brief Generate initial condition such that the solution of the differential filtering is given by MMS_Solution() above 172 // 173 // This requires a *very* specific grid, as the anisotropic filtering is grid dependent. 174 // It's for a 75x75x1 grid on a [0,0.5]x3 domain. 175 // The grid is evenly distributed in x, but distributed based on the analytical mesh distribution \Delta_y = .001 + .01*tanh(6*y). 176 // The MMS test can optionally include a wall damping function (must also be enabled for the differential filtering itself). 177 // It can be run via: 178 // ./navierstokes -options_file tests-output/blasius_test.yaml -diff_filter_monitor -diff_filter_view cgns:filtered_solution.cgns -ts_max_steps 0 179 // -diff_filter_mms -diff_filter_kernel_scaling 1 -diff_filter_wall_damping_function mms -dm_plex_box_upper 0.5,0.5,0.5 -dm_plex_box_faces 75,75,1 180 // -mesh_transform platemesh -platemesh_y_node_locs_path tests-output/diff_filter_mms_y_spacing.dat -platemesh_top_angle 0 181 // -diff_filter_grid_based_width 182 CEED_QFUNCTION(DifferentialFilter_MMS_IC)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 183 const CeedScalar(*x)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 184 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 185 186 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 187 const CeedScalar x_i[3] = {x[0][i], x[1][i], x[2][i]}; 188 189 const CeedScalar aniso_scale_factor = 1; // Must match the one passed in by -diff_filter_aniso_scale 190 const CeedScalar omega = 2 * M_PI; 191 const CeedScalar omega6 = 6 * omega; 192 const CeedScalar phi_bar = MMS_Solution(x_i, omega); 193 const CeedScalar dx = 0.5 / 75; 194 const CeedScalar dy_analytic = .001 + .01 * tanh(6 * x_i[1]); 195 const CeedScalar dy = dy_analytic; 196 const CeedScalar d_dy_dy = 0.06 * Square(1 / cosh(6 * x_i[1])); // Change of \Delta_y w.r.t. y 197 CeedScalar alpha[2] = {Square(dx) * aniso_scale_factor, Square(dy) * aniso_scale_factor}; 198 bool damping = true; 199 CeedScalar dalpha1dy; 200 if (damping) { 201 CeedScalar damping_coeff = tanh(60 * x_i[1]); 202 CeedScalar d_damping_coeff = 60 / Square(cosh(60 * x_i[1])); 203 dalpha1dy = aniso_scale_factor * 2 * (damping_coeff * dy) * (dy * d_damping_coeff + damping_coeff * d_dy_dy); 204 alpha[1] *= Square(damping_coeff); 205 } else { 206 dalpha1dy = aniso_scale_factor * 2 * dy * d_dy_dy; 207 } 208 209 CeedScalar phi = phi_bar + alpha[0] * Square(omega6) * sin(6 * omega * x_i[0]) + alpha[1] * Square(omega6) * sin(omega6 * x_i[1]); 210 phi -= dalpha1dy * omega6 * cos(omega6 * x_i[1]); 211 212 for (CeedInt j = 0; j < 5; j++) q0[j][i] = phi; 213 } 214 return 0; 215 } 216