1 static char help[] = "Time-Dependent Reactive Flow example in 2D with Darcy Flow"; 2 3 /* 4 5 This example solves the elementary chemical reaction: 6 7 SP_A + 2SP_B = SP_C 8 9 Subject to predetermined flow modeled as though it were in a porous media. 10 This flow is modeled as advection and diffusion of the three species as 11 12 v = porosity*saturation*grad(q) 13 14 and the time-dependent equation solved for each species as 15 advection + diffusion + reaction: 16 17 v dot grad SP_i + dSP_i / dt + dispersivity*div*grad(SP_i) + R(SP_i) = 0 18 19 The following options are available: 20 21 -length_x - The length of the domain in the direction of the flow 22 -length_y - The length of the domain in the direction orthogonal to the flow 23 24 -gradq_inflow - The inflow speed as if the saturation and porosity were 1. 25 -saturation - The saturation of the porous medium. 26 -porosity - The porosity of the medium. 27 -dispersivity - The dispersivity of the flow. 28 -rate_constant - The rate constant for the chemical reaction 29 -stoich - The stoichiometry matrix for the reaction 30 -sp_inflow - The species concentrations at the inflow 31 -sp_0 - The species concentrations at time 0 32 33 */ 34 35 #include <petscdm.h> 36 #include <petscdmda.h> 37 #include <petscsnes.h> 38 #include <petscts.h> 39 40 #define N_SPECIES 3 41 #define N_REACTIONS 1 42 #define DIM 2 43 44 #define stoich(i, j) ctx->stoichiometry[N_SPECIES * i + j] 45 46 typedef struct { 47 PetscScalar sp[N_SPECIES]; 48 } Field; 49 50 typedef struct { 51 Field x_inflow; 52 Field x_0; 53 PetscReal stoichiometry[N_SPECIES * N_REACTIONS]; 54 PetscReal porosity; 55 PetscReal dispersivity; 56 PetscReal saturation; 57 PetscReal rate_constant[N_REACTIONS]; 58 PetscReal gradq_inflow; 59 PetscReal length[DIM]; 60 } AppCtx; 61 62 extern PetscErrorCode FormInitialGuess(DM da, AppCtx *ctx, Vec X); 63 extern PetscErrorCode FormIFunctionLocal(DMDALocalInfo *, PetscReal, Field **, Field **, Field **, AppCtx *); 64 extern PetscErrorCode FormIFunction(TS, PetscReal, Vec, Vec, Vec, void *); 65 extern PetscErrorCode ReactingFlowPostCheck(SNESLineSearch, Vec, Vec, Vec, PetscBool *, PetscBool *, void *); 66 67 PetscErrorCode SetFromOptions(AppCtx *ctx) { 68 PetscInt i, j; 69 70 PetscFunctionBeginUser; 71 ctx->dispersivity = 0.5; 72 ctx->porosity = 0.25; 73 ctx->saturation = 1.0; 74 ctx->gradq_inflow = 1.0; 75 ctx->rate_constant[0] = 0.5; 76 77 ctx->length[0] = 100.0; 78 ctx->length[1] = 100.0; 79 80 ctx->x_0.sp[0] = 0.0; 81 ctx->x_0.sp[1] = 0.0; 82 ctx->x_0.sp[2] = 0.0; 83 84 ctx->x_inflow.sp[0] = 0.05; 85 ctx->x_inflow.sp[1] = 0.05; 86 ctx->x_inflow.sp[2] = 0.0; 87 88 for (i = 0; i < N_REACTIONS; i++) { 89 for (j = 0; j < N_SPECIES; j++) stoich(i, j) = 0.; 90 } 91 92 /* set up a pretty easy example */ 93 stoich(0, 0) = -1.; 94 stoich(0, 1) = -2.; 95 stoich(0, 2) = 1.; 96 97 PetscInt as = N_SPECIES; 98 PetscCall(PetscOptionsGetReal(NULL, NULL, "-length_x", &ctx->length[0], NULL)); 99 PetscCall(PetscOptionsGetReal(NULL, NULL, "-length_y", &ctx->length[1], NULL)); 100 PetscCall(PetscOptionsGetReal(NULL, NULL, "-porosity", &ctx->porosity, NULL)); 101 PetscCall(PetscOptionsGetReal(NULL, NULL, "-saturation", &ctx->saturation, NULL)); 102 PetscCall(PetscOptionsGetReal(NULL, NULL, "-dispersivity", &ctx->dispersivity, NULL)); 103 PetscCall(PetscOptionsGetReal(NULL, NULL, "-gradq_inflow", &ctx->gradq_inflow, NULL)); 104 PetscCall(PetscOptionsGetReal(NULL, NULL, "-rate_constant", &ctx->rate_constant[0], NULL)); 105 PetscCall(PetscOptionsGetRealArray(NULL, NULL, "-sp_inflow", ctx->x_inflow.sp, &as, NULL)); 106 PetscCall(PetscOptionsGetRealArray(NULL, NULL, "-sp_0", ctx->x_0.sp, &as, NULL)); 107 as = N_SPECIES; 108 PetscCall(PetscOptionsGetRealArray(NULL, NULL, "-stoich", ctx->stoichiometry, &as, NULL)); 109 PetscFunctionReturn(0); 110 } 111 112 int main(int argc, char **argv) { 113 TS ts; 114 SNES snes; 115 SNESLineSearch linesearch; 116 Vec x; 117 AppCtx ctx; 118 DM da; 119 120 PetscFunctionBeginUser; 121 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 122 PetscCall(SetFromOptions(&ctx)); 123 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 124 PetscCall(TSSetType(ts, TSCN)); 125 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 126 PetscCall(TSSetIFunction(ts, NULL, FormIFunction, &ctx)); 127 PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, -4, -4, PETSC_DECIDE, PETSC_DECIDE, N_SPECIES, 1, NULL, NULL, &da)); 128 PetscCall(DMSetFromOptions(da)); 129 PetscCall(DMSetUp(da)); 130 PetscCall(DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0)); 131 PetscCall(DMDASetFieldName(da, 0, "species A")); 132 PetscCall(DMDASetFieldName(da, 1, "species B")); 133 PetscCall(DMDASetFieldName(da, 2, "species C")); 134 PetscCall(DMSetApplicationContext(da, &ctx)); 135 PetscCall(DMCreateGlobalVector(da, &x)); 136 PetscCall(FormInitialGuess(da, &ctx, x)); 137 138 PetscCall(TSSetDM(ts, da)); 139 PetscCall(TSSetMaxTime(ts, 1000.0)); 140 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 141 PetscCall(TSSetTimeStep(ts, 1.0)); 142 PetscCall(TSSetSolution(ts, x)); 143 PetscCall(TSSetFromOptions(ts)); 144 145 PetscCall(TSGetSNES(ts, &snes)); 146 PetscCall(SNESGetLineSearch(snes, &linesearch)); 147 PetscCall(SNESLineSearchSetPostCheck(linesearch, ReactingFlowPostCheck, (void *)&ctx)); 148 PetscCall(SNESSetFromOptions(snes)); 149 PetscCall(TSSolve(ts, x)); 150 151 PetscCall(VecDestroy(&x)); 152 PetscCall(TSDestroy(&ts)); 153 PetscCall(DMDestroy(&da)); 154 PetscCall(PetscFinalize()); 155 PetscFunctionReturn(0); 156 } 157 158 /* ------------------------------------------------------------------- */ 159 160 PetscErrorCode FormInitialGuess(DM da, AppCtx *ctx, Vec X) { 161 PetscInt i, j, l, Mx, My, xs, ys, xm, ym; 162 Field **x; 163 164 PetscFunctionBeginUser; 165 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, &My, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE)); 166 PetscCall(DMDAVecGetArray(da, X, &x)); 167 PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL)); 168 169 for (j = ys; j < ys + ym; j++) { 170 for (i = xs; i < xs + xm; i++) { 171 for (l = 0; l < N_SPECIES; l++) { 172 if (i == 0) { 173 if (l == 0) x[j][i].sp[l] = (ctx->x_inflow.sp[l] * ((PetscScalar)j) / (My - 1)); 174 else if (l == 1) x[j][i].sp[l] = (ctx->x_inflow.sp[l] * (1. - ((PetscScalar)j) / (My - 1))); 175 else x[j][i].sp[l] = ctx->x_0.sp[l]; 176 } 177 } 178 } 179 } 180 PetscCall(DMDAVecRestoreArray(da, X, &x)); 181 PetscFunctionReturn(0); 182 } 183 184 PetscErrorCode FormIFunctionLocal(DMDALocalInfo *info, PetscScalar ptime, Field **x, Field **xt, Field **f, AppCtx *ctx) { 185 PetscInt i, j, l, m; 186 PetscReal hx, hy, dhx, dhy, hxdhy, hydhx, scale; 187 PetscScalar u, uxx, uyy; 188 PetscScalar vx, vy, sxp, syp, sxm, sym, avx, vxp, vxm, avy, vyp, vym, f_advect; 189 PetscScalar rate; 190 191 PetscFunctionBeginUser; 192 hx = ctx->length[0] / ((PetscReal)(info->mx - 1)); 193 hy = ctx->length[1] / ((PetscReal)(info->my - 1)); 194 195 dhx = 1. / hx; 196 dhy = 1. / hy; 197 hxdhy = hx / hy; 198 hydhx = hy / hx; 199 scale = hx * hy; 200 201 for (j = info->ys; j < info->ys + info->ym; j++) { 202 for (i = info->xs; i < info->xs + info->xm; i++) { 203 vx = ctx->gradq_inflow * ctx->porosity * ctx->saturation; 204 vy = 0.0 * dhy; 205 avx = PetscAbsScalar(vx); 206 vxp = .5 * (vx + avx); 207 vxm = .5 * (vx - avx); 208 avy = PetscAbsScalar(vy); 209 vyp = .5 * (vy + avy); 210 vym = .5 * (vy - avy); 211 /* chemical reactions */ 212 for (l = 0; l < N_SPECIES; l++) { 213 /* determine the velocites as the gradients of the pressure */ 214 if (i == 0) { 215 sxp = (x[j][i + 1].sp[l] - x[j][i].sp[l]) * dhx; 216 sxm = sxp; 217 } else if (i == info->mx - 1) { 218 sxp = (x[j][i].sp[l] - x[j][i - 1].sp[l]) * dhx; 219 sxm = sxp; 220 } else { 221 sxm = (x[j][i + 1].sp[l] - x[j][i].sp[l]) * dhx; 222 sxp = (x[j][i].sp[l] - x[j][i - 1].sp[l]) * dhx; 223 } 224 if (j == 0) { 225 syp = (x[j + 1][i].sp[l] - x[j][i].sp[l]) * dhy; 226 sym = syp; 227 } else if (j == info->my - 1) { 228 syp = (x[j][i].sp[l] - x[j - 1][i].sp[l]) * dhy; 229 sym = syp; 230 } else { 231 sym = (x[j + 1][i].sp[l] - x[j][i].sp[l]) * dhy; 232 syp = (x[j][i].sp[l] - x[j - 1][i].sp[l]) * dhy; 233 } /* 4 flops per species*point */ 234 235 if (i == 0) { 236 if (l == 0) f[j][i].sp[l] = (x[j][i].sp[l] - ctx->x_inflow.sp[l] * ((PetscScalar)j) / (info->my - 1)); 237 else if (l == 1) f[j][i].sp[l] = (x[j][i].sp[l] - ctx->x_inflow.sp[l] * (1. - ((PetscScalar)j) / (info->my - 1))); 238 else f[j][i].sp[l] = x[j][i].sp[l]; 239 240 } else { 241 f[j][i].sp[l] = xt[j][i].sp[l] * scale; 242 u = x[j][i].sp[l]; 243 if (j == 0) uyy = u - x[j + 1][i].sp[l]; 244 else if (j == info->my - 1) uyy = u - x[j - 1][i].sp[l]; 245 else uyy = (2.0 * u - x[j - 1][i].sp[l] - x[j + 1][i].sp[l]) * hxdhy; 246 247 if (i != info->mx - 1) uxx = (2.0 * u - x[j][i - 1].sp[l] - x[j][i + 1].sp[l]) * hydhx; 248 else uxx = u - x[j][i - 1].sp[l]; 249 /* 10 flops per species*point */ 250 251 f_advect = 0.; 252 f_advect += scale * (vxp * sxp + vxm * sxm); 253 f_advect += scale * (vyp * syp + vym * sym); 254 f[j][i].sp[l] += f_advect + ctx->dispersivity * (uxx + uyy); 255 /* 14 flops per species*point */ 256 } 257 } 258 /* reaction */ 259 if (i != 0) { 260 for (m = 0; m < N_REACTIONS; m++) { 261 rate = ctx->rate_constant[m]; 262 for (l = 0; l < N_SPECIES; l++) { 263 if (stoich(m, l) < 0) { 264 /* assume an elementary reaction */ 265 rate *= PetscPowScalar(x[j][i].sp[l], PetscAbsScalar(stoich(m, l))); 266 /* ~10 flops per reaction per species per point */ 267 } 268 } 269 for (l = 0; l < N_SPECIES; l++) { 270 f[j][i].sp[l] += -scale * stoich(m, l) * rate; /* Reaction term */ 271 /* 3 flops per reaction per species per point */ 272 } 273 } 274 } 275 } 276 } 277 PetscCall(PetscLogFlops((N_SPECIES * (28.0 + 13.0 * N_REACTIONS)) * info->ym * info->xm)); 278 PetscFunctionReturn(0); 279 } 280 281 PetscErrorCode ReactingFlowPostCheck(SNESLineSearch linesearch, Vec X, Vec Y, Vec W, PetscBool *changed_y, PetscBool *changed_w, void *vctx) { 282 PetscInt i, j, l, Mx, My, xs, ys, xm, ym; 283 Field **x; 284 SNES snes; 285 DM da; 286 PetscScalar min; 287 288 PetscFunctionBeginUser; 289 *changed_w = PETSC_FALSE; 290 PetscCall(VecMin(X, NULL, &min)); 291 if (min >= 0.) PetscFunctionReturn(0); 292 293 *changed_w = PETSC_TRUE; 294 PetscCall(SNESLineSearchGetSNES(linesearch, &snes)); 295 PetscCall(SNESGetDM(snes, &da)); 296 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, &My, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE)); 297 PetscCall(DMDAVecGetArray(da, W, &x)); 298 PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL)); 299 for (j = ys; j < ys + ym; j++) { 300 for (i = xs; i < xs + xm; i++) { 301 for (l = 0; l < N_SPECIES; l++) { 302 if (x[j][i].sp[l] < 0.) x[j][i].sp[l] = 0.; 303 } 304 } 305 } 306 PetscCall(DMDAVecRestoreArray(da, W, &x)); 307 PetscFunctionReturn(0); 308 } 309 310 PetscErrorCode FormIFunction(TS ts, PetscReal ptime, Vec X, Vec Xdot, Vec F, void *user) { 311 DMDALocalInfo info; 312 Field **u, **udot, **fu; 313 Vec localX; 314 DM da; 315 316 PetscFunctionBeginUser; 317 PetscCall(TSGetDM(ts, (DM *)&da)); 318 PetscCall(DMGetLocalVector(da, &localX)); 319 PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX)); 320 PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX)); 321 PetscCall(DMDAGetLocalInfo(da, &info)); 322 PetscCall(DMDAVecGetArrayRead(da, localX, &u)); 323 PetscCall(DMDAVecGetArrayRead(da, Xdot, &udot)); 324 PetscCall(DMDAVecGetArray(da, F, &fu)); 325 PetscCall(FormIFunctionLocal(&info, ptime, u, udot, fu, (AppCtx *)user)); 326 PetscCall(DMDAVecRestoreArrayRead(da, localX, &u)); 327 PetscCall(DMDAVecRestoreArrayRead(da, Xdot, &udot)); 328 PetscCall(DMDAVecRestoreArray(da, F, &fu)); 329 PetscCall(DMRestoreLocalVector(da, &localX)); 330 PetscFunctionReturn(0); 331 } 332