1 static char help[] = "Time-Dependent Reactive Flow example in 2D with Darcy Flow"; 2 3 /*T 4 Concepts: Solving a multicomponent time-dependent reactive flow system 5 Concepts: DMDA with timestepping 6 Processors: n 7 T*/ 8 9 /* 10 11 This example solves the elementary chemical reaction: 12 13 SP_A + 2SP_B = SP_C 14 15 Subject to predetermined flow modeled as though it were in a porous media. 16 This flow is modeled as advection and diffusion of the three species as 17 18 v = porosity*saturation*grad(q) 19 20 and the time-dependent equation solved for each species as 21 advection + diffusion + reaction: 22 23 v dot grad SP_i + dSP_i / dt + dispersivity*div*grad(SP_i) + R(SP_i) = 0 24 25 The following options are available: 26 27 -length_x - The length of the domain in the direction of the flow 28 -length_y - The length of the domain in the direction orthogonal to the flow 29 30 -gradq_inflow - The inflow speed as if the saturation and porosity were 1. 31 -saturation - The saturation of the porous medium. 32 -porosity - The porosity of the medium. 33 -dispersivity - The dispersivity of the flow. 34 -rate_constant - The rate constant for the chemical reaction 35 -stoich - The stoichiometry matrix for the reaction 36 -sp_inflow - The species concentrations at the inflow 37 -sp_0 - The species concentrations at time 0 38 39 */ 40 41 #include <petscdm.h> 42 #include <petscdmda.h> 43 #include <petscsnes.h> 44 #include <petscts.h> 45 46 #define N_SPECIES 3 47 #define N_REACTIONS 1 48 #define DIM 2 49 50 #define stoich(i, j) ctx->stoichiometry[N_SPECIES*i + j] 51 52 typedef struct { 53 PetscScalar sp[N_SPECIES]; 54 } Field; 55 56 typedef struct { 57 58 Field x_inflow; 59 Field x_0; 60 PetscReal stoichiometry[N_SPECIES*N_REACTIONS]; 61 PetscReal porosity; 62 PetscReal dispersivity; 63 PetscReal saturation; 64 PetscReal rate_constant[N_REACTIONS]; 65 PetscReal gradq_inflow; 66 PetscReal length[DIM]; 67 } AppCtx; 68 69 extern PetscErrorCode FormInitialGuess(DM da,AppCtx *ctx,Vec X); 70 extern PetscErrorCode FormIFunctionLocal(DMDALocalInfo*,PetscReal,Field**,Field**,Field**,AppCtx*); 71 extern PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*); 72 extern PetscErrorCode ReactingFlowPostCheck(SNESLineSearch,Vec,Vec,Vec,PetscBool*,PetscBool*,void*); 73 74 PetscErrorCode SetFromOptions(AppCtx * ctx) 75 { 76 PetscErrorCode ierr; 77 PetscInt i,j; 78 79 PetscFunctionBeginUser; 80 ctx->dispersivity = 0.5; 81 ctx->porosity = 0.25; 82 ctx->saturation = 1.0; 83 ctx->gradq_inflow = 1.0; 84 ctx->rate_constant[0] = 0.5; 85 86 ctx->length[0] = 100.0; 87 ctx->length[1] = 100.0; 88 89 ctx->x_0.sp[0] = 0.0; 90 ctx->x_0.sp[1] = 0.0; 91 ctx->x_0.sp[2] = 0.0; 92 93 ctx->x_inflow.sp[0] = 0.05; 94 ctx->x_inflow.sp[1] = 0.05; 95 ctx->x_inflow.sp[2] = 0.0; 96 97 for (i = 0; i < N_REACTIONS; i++) { 98 for (j = 0; j < N_SPECIES; j++) stoich(i, j) = 0.; 99 } 100 101 /* set up a pretty easy example */ 102 stoich(0, 0) = -1.; 103 stoich(0, 1) = -2.; 104 stoich(0, 2) = 1.; 105 106 PetscInt as = N_SPECIES; 107 ierr = PetscOptionsGetReal(NULL,NULL,"-length_x",&ctx->length[0],NULL);CHKERRQ(ierr); 108 ierr = PetscOptionsGetReal(NULL,NULL,"-length_y",&ctx->length[1],NULL);CHKERRQ(ierr); 109 ierr = PetscOptionsGetReal(NULL,NULL,"-porosity",&ctx->porosity,NULL);CHKERRQ(ierr); 110 ierr = PetscOptionsGetReal(NULL,NULL,"-saturation",&ctx->saturation,NULL);CHKERRQ(ierr); 111 ierr = PetscOptionsGetReal(NULL,NULL,"-dispersivity",&ctx->dispersivity,NULL);CHKERRQ(ierr); 112 ierr = PetscOptionsGetReal(NULL,NULL,"-gradq_inflow",&ctx->gradq_inflow,NULL);CHKERRQ(ierr); 113 ierr = PetscOptionsGetReal(NULL,NULL,"-rate_constant",&ctx->rate_constant[0],NULL);CHKERRQ(ierr); 114 ierr = PetscOptionsGetRealArray(NULL,NULL,"-sp_inflow",ctx->x_inflow.sp,&as,NULL);CHKERRQ(ierr); 115 ierr = PetscOptionsGetRealArray(NULL,NULL,"-sp_0",ctx->x_0.sp,&as,NULL);CHKERRQ(ierr); 116 as = N_SPECIES; 117 ierr = PetscOptionsGetRealArray(NULL,NULL,"-stoich",ctx->stoichiometry,&as,NULL);CHKERRQ(ierr); 118 PetscFunctionReturn(0); 119 } 120 121 int main(int argc,char **argv) 122 { 123 TS ts; 124 SNES snes; 125 SNESLineSearch linesearch; 126 Vec x; 127 AppCtx ctx; 128 PetscErrorCode ierr; 129 DM da; 130 131 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 132 ierr = SetFromOptions(&ctx);CHKERRQ(ierr); 133 ierr = TSCreate(PETSC_COMM_WORLD, &ts);CHKERRQ(ierr); 134 ierr = TSSetType(ts,TSCN);CHKERRQ(ierr); 135 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 136 ierr = TSSetIFunction(ts, NULL, FormIFunction, &ctx);CHKERRQ(ierr); 137 ierr = 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);CHKERRQ(ierr); 138 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 139 ierr = DMSetUp(da);CHKERRQ(ierr); 140 ierr = DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);CHKERRQ(ierr); 141 ierr = DMDASetFieldName(da,0,"species A");CHKERRQ(ierr); 142 ierr = DMDASetFieldName(da,1,"species B");CHKERRQ(ierr); 143 ierr = DMDASetFieldName(da,2,"species C");CHKERRQ(ierr); 144 ierr = DMSetApplicationContext(da,&ctx);CHKERRQ(ierr); 145 ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr); 146 ierr = FormInitialGuess(da, &ctx, x);CHKERRQ(ierr); 147 148 ierr = TSSetDM(ts, da);CHKERRQ(ierr); 149 ierr = TSSetMaxTime(ts,1000.0);CHKERRQ(ierr); 150 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 151 ierr = TSSetTimeStep(ts,1.0);CHKERRQ(ierr); 152 ierr = TSSetSolution(ts,x);CHKERRQ(ierr); 153 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 154 155 ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr); 156 ierr = SNESGetLineSearch(snes,&linesearch);CHKERRQ(ierr); 157 ierr = SNESLineSearchSetPostCheck(linesearch, ReactingFlowPostCheck, (void*)&ctx);CHKERRQ(ierr); 158 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); 159 ierr = TSSolve(ts,x);CHKERRQ(ierr); 160 161 ierr = VecDestroy(&x);CHKERRQ(ierr); 162 ierr = TSDestroy(&ts);CHKERRQ(ierr); 163 ierr = DMDestroy(&da);CHKERRQ(ierr); 164 ierr = PetscFinalize(); 165 PetscFunctionReturn(0); 166 } 167 168 /* ------------------------------------------------------------------- */ 169 170 PetscErrorCode FormInitialGuess(DM da,AppCtx *ctx,Vec X) 171 { 172 PetscInt i,j,l,Mx,My,xs,ys,xm,ym; 173 PetscErrorCode ierr; 174 Field **x; 175 176 PetscFunctionBeginUser; 177 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE, 178 PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE); 179 180 ierr = DMDAVecGetArray(da,X,&x);CHKERRQ(ierr); 181 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 182 183 for (j=ys; j<ys+ym; j++) { 184 for (i=xs; i<xs+xm; i++) { 185 for (l = 0; l < N_SPECIES; l++) { 186 if (i == 0) { 187 if (l == 0) x[j][i].sp[l] = (ctx->x_inflow.sp[l]*((PetscScalar)j) / (My - 1)); 188 else if (l == 1) x[j][i].sp[l] = (ctx->x_inflow.sp[l]*(1. - ((PetscScalar)j) / (My - 1))); 189 else x[j][i].sp[l] = ctx->x_0.sp[l]; 190 } 191 } 192 } 193 } 194 ierr = DMDAVecRestoreArray(da,X,&x);CHKERRQ(ierr); 195 PetscFunctionReturn(0); 196 197 } 198 199 PetscErrorCode FormIFunctionLocal(DMDALocalInfo *info,PetscScalar ptime,Field **x,Field **xt,Field **f,AppCtx *ctx) 200 { 201 PetscErrorCode ierr; 202 PetscInt i,j,l,m; 203 PetscReal hx,hy,dhx,dhy,hxdhy,hydhx,scale; 204 PetscScalar u,uxx,uyy; 205 PetscScalar vx, vy,sxp,syp,sxm,sym,avx,vxp,vxm,avy,vyp,vym,f_advect; 206 PetscScalar rate; 207 208 PetscFunctionBeginUser; 209 hx = ctx->length[0]/((PetscReal)(info->mx-1)); 210 hy = ctx->length[1]/((PetscReal)(info->my-1)); 211 212 dhx = 1. / hx; 213 dhy = 1. / hy; 214 hxdhy = hx/hy; 215 hydhx = hy/hx; 216 scale = hx*hy; 217 218 for (j=info->ys; j<info->ys+info->ym; j++) { 219 for (i=info->xs; i<info->xs+info->xm; i++) { 220 vx = ctx->gradq_inflow*ctx->porosity*ctx->saturation; 221 vy = 0.0*dhy; 222 avx = PetscAbsScalar(vx); 223 vxp = .5*(vx+avx); vxm = .5*(vx-avx); 224 avy = PetscAbsScalar(vy); 225 vyp = .5*(vy+avy); vym = .5*(vy-avy); 226 /* chemical reactions */ 227 for (l = 0; l < N_SPECIES; l++) { 228 /* determine the velocites as the gradients of the pressure */ 229 if (i == 0) { 230 sxp = (x[j][i+1].sp[l] - x[j][i].sp[l])*dhx; 231 sxm = sxp; 232 } else if (i == info->mx - 1) { 233 sxp = (x[j][i].sp[l] - x[j][i-1].sp[l])*dhx; 234 sxm = sxp; 235 } else { 236 sxm = (x[j][i+1].sp[l] - x[j][i].sp[l])*dhx; 237 sxp = (x[j][i].sp[l] - x[j][i-1].sp[l])*dhx; 238 } 239 if (j == 0) { 240 syp = (x[j+1][i].sp[l] - x[j][i].sp[l])*dhy; 241 sym = syp; 242 } else if (j == info->my - 1) { 243 syp = (x[j][i].sp[l] - x[j-1][i].sp[l])*dhy; 244 sym = syp; 245 } else { 246 sym = (x[j+1][i].sp[l] - x[j][i].sp[l])*dhy; 247 syp = (x[j][i].sp[l] - x[j-1][i].sp[l])*dhy; 248 } /* 4 flops per species*point */ 249 250 if (i == 0) { 251 if (l == 0) f[j][i].sp[l] = (x[j][i].sp[l] - ctx->x_inflow.sp[l]*((PetscScalar)j) / (info->my - 1)); 252 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))); 253 else f[j][i].sp[l] = x[j][i].sp[l]; 254 255 } else { 256 f[j][i].sp[l] = xt[j][i].sp[l]*scale; 257 u = x[j][i].sp[l]; 258 if (j == 0) uyy = u - x[j+1][i].sp[l]; 259 else if (j == info->my - 1) uyy = u - x[j-1][i].sp[l]; 260 else uyy = (2.0*u - x[j-1][i].sp[l] - x[j+1][i].sp[l])*hxdhy; 261 262 if (i != info->mx - 1) uxx = (2.0*u - x[j][i-1].sp[l] - x[j][i+1].sp[l])*hydhx; 263 else uxx = u - x[j][i-1].sp[l]; 264 /* 10 flops per species*point */ 265 266 f_advect = 0.; 267 f_advect += scale*(vxp*sxp + vxm*sxm); 268 f_advect += scale*(vyp*syp + vym*sym); 269 f[j][i].sp[l] += f_advect + ctx->dispersivity*(uxx + uyy); 270 /* 14 flops per species*point */ 271 } 272 } 273 /* reaction */ 274 if (i != 0) { 275 for (m = 0; m < N_REACTIONS; m++) { 276 rate = ctx->rate_constant[m]; 277 for (l = 0; l < N_SPECIES; l++) { 278 if (stoich(m, l) < 0) { 279 /* assume an elementary reaction */ 280 rate *= PetscPowScalar(x[j][i].sp[l], PetscAbsScalar(stoich(m, l))); 281 /* ~10 flops per reaction per species per point */ 282 } 283 } 284 for (l = 0; l < N_SPECIES; l++) { 285 f[j][i].sp[l] += -scale*stoich(m, l)*rate; /* Reaction term */ 286 /* 3 flops per reaction per species per point */ 287 } 288 } 289 } 290 } 291 } 292 ierr = PetscLogFlops((N_SPECIES*(28.0 + 13.0*N_REACTIONS))*info->ym*info->xm);CHKERRQ(ierr); 293 PetscFunctionReturn(0); 294 } 295 296 PetscErrorCode ReactingFlowPostCheck(SNESLineSearch linesearch, Vec X, Vec Y, Vec W, PetscBool *changed_y, PetscBool *changed_w, void *vctx) 297 { 298 PetscInt i,j,l,Mx,My,xs,ys,xm,ym; 299 PetscErrorCode ierr; 300 Field **x; 301 SNES snes; 302 DM da; 303 PetscScalar min; 304 305 PetscFunctionBeginUser; 306 *changed_w = PETSC_FALSE; 307 ierr = VecMin(X,NULL,&min);CHKERRQ(ierr); 308 if (min >= 0.) PetscFunctionReturn(0); 309 310 *changed_w = PETSC_TRUE; 311 ierr = SNESLineSearchGetSNES(linesearch, &snes);CHKERRQ(ierr); 312 ierr = SNESGetDM(snes,&da);CHKERRQ(ierr); 313 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE, 314 PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE); 315 ierr = DMDAVecGetArray(da,W,&x);CHKERRQ(ierr); 316 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 317 for (j=ys; j<ys+ym; j++) { 318 for (i=xs; i<xs+xm; i++) { 319 for (l = 0; l < N_SPECIES; l++) { 320 if (x[j][i].sp[l] < 0.) x[j][i].sp[l] = 0.; 321 } 322 } 323 } 324 ierr = DMDAVecRestoreArray(da,W,&x);CHKERRQ(ierr); 325 PetscFunctionReturn(0); 326 } 327 328 PetscErrorCode FormIFunction(TS ts,PetscReal ptime,Vec X,Vec Xdot,Vec F,void *user) 329 { 330 DMDALocalInfo info; 331 Field **u,**udot,**fu; 332 PetscErrorCode ierr; 333 Vec localX; 334 DM da; 335 336 PetscFunctionBeginUser; 337 ierr = TSGetDM(ts,(DM*)&da);CHKERRQ(ierr); 338 ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr); 339 ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr); 340 ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr); 341 ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr); 342 ierr = DMDAVecGetArrayRead(da,localX,&u);CHKERRQ(ierr); 343 ierr = DMDAVecGetArrayRead(da,Xdot,&udot);CHKERRQ(ierr); 344 ierr = DMDAVecGetArray(da,F,&fu);CHKERRQ(ierr); 345 ierr = FormIFunctionLocal(&info,ptime,u,udot,fu,(AppCtx*)user);CHKERRQ(ierr); 346 ierr = DMDAVecRestoreArrayRead(da,localX,&u);CHKERRQ(ierr); 347 ierr = DMDAVecRestoreArrayRead(da,Xdot,&udot);CHKERRQ(ierr); 348 ierr = DMDAVecRestoreArray(da,F,&fu);CHKERRQ(ierr); 349 ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr); 350 PetscFunctionReturn(0); 351 } 352