1 static char help[] = "Model Equations for Advection \n"; 2 3 /* 4 Modified from ex3.c 5 Page 9, Section 1.2 Model Equations for Advection-Diffusion 6 7 u_t + a u_x = 0, 0<= x <= 1.0 8 9 The initial conditions used here different from the book. 10 11 Example: 12 ./ex6 -ts_monitor -ts_view_solution -ts_max_steps 100 -ts_monitor_solution draw -draw_pause .1 13 ./ex6 -ts_monitor -ts_max_steps 100 -ts_monitor_lg_error -draw_pause .1 14 */ 15 16 #include <petscts.h> 17 #include <petscdm.h> 18 #include <petscdmda.h> 19 20 /* 21 User-defined application context - contains data needed by the 22 application-provided call-back routines. 23 */ 24 typedef struct { 25 PetscReal a; /* advection strength */ 26 } AppCtx; 27 28 /* User-defined routines */ 29 extern PetscErrorCode InitialConditions(TS, Vec, AppCtx *); 30 extern PetscErrorCode Solution(TS, PetscReal, Vec, AppCtx *); 31 extern PetscErrorCode IFunction_LaxFriedrichs(TS, PetscReal, Vec, Vec, Vec, void *); 32 extern PetscErrorCode IFunction_LaxWendroff(TS, PetscReal, Vec, Vec, Vec, void *); 33 34 int main(int argc, char **argv) 35 { 36 AppCtx appctx; /* user-defined application context */ 37 TS ts; /* timestepping context */ 38 Vec U; /* approximate solution vector */ 39 PetscReal dt; 40 DM da; 41 PetscInt M; 42 PetscMPIInt rank; 43 PetscBool useLaxWendroff = PETSC_TRUE; 44 45 /* Initialize program and set problem parameters */ 46 PetscFunctionBeginUser; 47 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 48 PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank)); 49 50 appctx.a = -1.0; 51 PetscCall(PetscOptionsGetReal(NULL, NULL, "-a", &appctx.a, NULL)); 52 53 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da)); 54 PetscCall(DMSetFromOptions(da)); 55 PetscCall(DMSetUp(da)); 56 57 /* Create vector data structures for approximate and exact solutions */ 58 PetscCall(DMCreateGlobalVector(da, &U)); 59 60 /* Create timestepping solver context */ 61 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 62 PetscCall(TSSetDM(ts, da)); 63 64 /* Function evaluation */ 65 PetscCall(PetscOptionsGetBool(NULL, NULL, "-useLaxWendroff", &useLaxWendroff, NULL)); 66 if (useLaxWendroff) { 67 if (rank == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "... Use Lax-Wendroff finite volume\n")); 68 PetscCall(TSSetIFunction(ts, NULL, IFunction_LaxWendroff, &appctx)); 69 } else { 70 if (rank == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "... Use Lax-LaxFriedrichs finite difference\n")); 71 PetscCall(TSSetIFunction(ts, NULL, IFunction_LaxFriedrichs, &appctx)); 72 } 73 74 /* Customize timestepping solver */ 75 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 76 dt = 1.0 / (PetscAbsReal(appctx.a) * M); 77 PetscCall(TSSetTimeStep(ts, dt)); 78 PetscCall(TSSetMaxSteps(ts, 100)); 79 PetscCall(TSSetMaxTime(ts, 100.0)); 80 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 81 PetscCall(TSSetType(ts, TSBEULER)); 82 PetscCall(TSSetFromOptions(ts)); 83 84 /* Evaluate initial conditions */ 85 PetscCall(InitialConditions(ts, U, &appctx)); 86 87 /* For testing accuracy of TS with already known solution, e.g., '-ts_monitor_lg_error' */ 88 PetscCall(TSSetSolutionFunction(ts, (PetscErrorCode (*)(TS, PetscReal, Vec, void *))Solution, &appctx)); 89 90 /* Run the timestepping solver */ 91 PetscCall(TSSolve(ts, U)); 92 93 /* Free work space */ 94 PetscCall(TSDestroy(&ts)); 95 PetscCall(VecDestroy(&U)); 96 PetscCall(DMDestroy(&da)); 97 98 PetscCall(PetscFinalize()); 99 return 0; 100 } 101 /* --------------------------------------------------------------------- */ 102 /* 103 InitialConditions - Computes the solution at the initial time. 104 105 Input Parameter: 106 u - uninitialized solution vector (global) 107 appctx - user-defined application context 108 109 Output Parameter: 110 u - vector with solution at initial time (global) 111 */ 112 PetscErrorCode InitialConditions(TS ts, Vec U, AppCtx *appctx) 113 { 114 PetscScalar *u; 115 PetscInt i, mstart, mend, um, M; 116 DM da; 117 PetscReal h; 118 119 PetscFunctionBeginUser; 120 PetscCall(TSGetDM(ts, &da)); 121 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &um, 0, 0)); 122 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 123 h = 1.0 / M; 124 mend = mstart + um; 125 /* 126 Get a pointer to vector data. 127 - For default PETSc vectors, VecGetArray() returns a pointer to 128 the data array. Otherwise, the routine is implementation dependent. 129 - You MUST call VecRestoreArray() when you no longer need access to 130 the array. 131 - Note that the Fortran interface to VecGetArray() differs from the 132 C version. See the users manual for details. 133 */ 134 PetscCall(DMDAVecGetArray(da, U, &u)); 135 136 /* 137 We initialize the solution array by simply writing the solution 138 directly into the array locations. Alternatively, we could use 139 VecSetValues() or VecSetValuesLocal(). 140 */ 141 for (i = mstart; i < mend; i++) u[i] = PetscSinReal(PETSC_PI * i * 6. * h) + 3. * PetscSinReal(PETSC_PI * i * 2. * h); 142 143 /* Restore vector */ 144 PetscCall(DMDAVecRestoreArray(da, U, &u)); 145 PetscFunctionReturn(PETSC_SUCCESS); 146 } 147 /* --------------------------------------------------------------------- */ 148 /* 149 Solution - Computes the exact solution at a given time 150 151 Input Parameters: 152 t - current time 153 solution - vector in which exact solution will be computed 154 appctx - user-defined application context 155 156 Output Parameter: 157 solution - vector with the newly computed exact solution 158 u(x,t) = sin(6*PI*(x - a*t)) + 3 * sin(2*PI*(x - a*t)) 159 */ 160 PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *appctx) 161 { 162 PetscScalar *u; 163 PetscReal a = appctx->a, h, PI6, PI2; 164 PetscInt i, mstart, mend, um, M; 165 DM da; 166 167 PetscFunctionBeginUser; 168 PetscCall(TSGetDM(ts, &da)); 169 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &um, 0, 0)); 170 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 171 h = 1.0 / M; 172 mend = mstart + um; 173 174 /* Get a pointer to vector data. */ 175 PetscCall(DMDAVecGetArray(da, U, &u)); 176 177 /* u[i] = sin(6*PI*(x[i] - a*t)) + 3 * sin(2*PI*(x[i] - a*t)) */ 178 PI6 = PETSC_PI * 6.; 179 PI2 = PETSC_PI * 2.; 180 for (i = mstart; i < mend; i++) u[i] = PetscSinReal(PI6 * (i * h - a * t)) + 3. * PetscSinReal(PI2 * (i * h - a * t)); 181 182 /* Restore vector */ 183 PetscCall(DMDAVecRestoreArray(da, U, &u)); 184 PetscFunctionReturn(PETSC_SUCCESS); 185 } 186 187 /* --------------------------------------------------------------------- */ 188 /* 189 Use Lax-Friedrichs method to evaluate F(u,t) = du/dt + a * du/dx 190 191 See https://en.wikipedia.org/wiki/Lax%E2%80%93Friedrichs_method 192 */ 193 PetscErrorCode IFunction_LaxFriedrichs(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx) 194 { 195 AppCtx *appctx = (AppCtx *)ctx; 196 PetscInt mstart, mend, M, i, um; 197 DM da; 198 Vec Uold, localUold; 199 PetscScalar *uarray, *f, *uoldarray, h, uave, c; 200 PetscReal dt; 201 202 PetscFunctionBegin; 203 PetscCall(TSGetTimeStep(ts, &dt)); 204 PetscCall(TSGetSolution(ts, &Uold)); 205 206 PetscCall(TSGetDM(ts, &da)); 207 PetscCall(DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 208 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &um, 0, 0)); 209 h = 1.0 / M; 210 mend = mstart + um; 211 /* printf(" mstart %d, um %d\n",mstart,um); */ 212 213 PetscCall(DMGetLocalVector(da, &localUold)); 214 PetscCall(DMGlobalToLocalBegin(da, Uold, INSERT_VALUES, localUold)); 215 PetscCall(DMGlobalToLocalEnd(da, Uold, INSERT_VALUES, localUold)); 216 217 /* Get pointers to vector data */ 218 PetscCall(DMDAVecGetArrayRead(da, U, &uarray)); 219 PetscCall(DMDAVecGetArrayRead(da, localUold, &uoldarray)); 220 PetscCall(DMDAVecGetArray(da, F, &f)); 221 222 /* advection */ 223 c = appctx->a * dt / h; /* Courant-Friedrichs-Lewy number (CFL number) */ 224 225 for (i = mstart; i < mend; i++) { 226 uave = 0.5 * (uoldarray[i - 1] + uoldarray[i + 1]); 227 f[i] = uarray[i] - uave + c * 0.5 * (uoldarray[i + 1] - uoldarray[i - 1]); 228 } 229 230 /* Restore vectors */ 231 PetscCall(DMDAVecRestoreArrayRead(da, U, &uarray)); 232 PetscCall(DMDAVecRestoreArrayRead(da, localUold, &uoldarray)); 233 PetscCall(DMDAVecRestoreArray(da, F, &f)); 234 PetscCall(DMRestoreLocalVector(da, &localUold)); 235 PetscFunctionReturn(PETSC_SUCCESS); 236 } 237 238 /* 239 Use Lax-Wendroff method to evaluate F(u,t) = du/dt + a * du/dx 240 */ 241 PetscErrorCode IFunction_LaxWendroff(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx) 242 { 243 AppCtx *appctx = (AppCtx *)ctx; 244 PetscInt mstart, mend, M, i, um; 245 DM da; 246 Vec Uold, localUold; 247 PetscScalar *uarray, *f, *uoldarray, h, RFlux, LFlux, lambda; 248 PetscReal dt, a; 249 250 PetscFunctionBegin; 251 PetscCall(TSGetTimeStep(ts, &dt)); 252 PetscCall(TSGetSolution(ts, &Uold)); 253 254 PetscCall(TSGetDM(ts, &da)); 255 PetscCall(DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 256 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &um, 0, 0)); 257 h = 1.0 / M; 258 mend = mstart + um; 259 /* printf(" mstart %d, um %d\n",mstart,um); */ 260 261 PetscCall(DMGetLocalVector(da, &localUold)); 262 PetscCall(DMGlobalToLocalBegin(da, Uold, INSERT_VALUES, localUold)); 263 PetscCall(DMGlobalToLocalEnd(da, Uold, INSERT_VALUES, localUold)); 264 265 /* Get pointers to vector data */ 266 PetscCall(DMDAVecGetArrayRead(da, U, &uarray)); 267 PetscCall(DMDAVecGetArrayRead(da, localUold, &uoldarray)); 268 PetscCall(DMDAVecGetArray(da, F, &f)); 269 270 /* advection -- finite volume (appctx->a < 0 -- can be relaxed?) */ 271 lambda = dt / h; 272 a = appctx->a; 273 274 for (i = mstart; i < mend; i++) { 275 RFlux = 0.5 * a * (uoldarray[i + 1] + uoldarray[i]) - a * a * 0.5 * lambda * (uoldarray[i + 1] - uoldarray[i]); 276 LFlux = 0.5 * a * (uoldarray[i - 1] + uoldarray[i]) - a * a * 0.5 * lambda * (uoldarray[i] - uoldarray[i - 1]); 277 f[i] = uarray[i] - uoldarray[i] + lambda * (RFlux - LFlux); 278 } 279 280 /* Restore vectors */ 281 PetscCall(DMDAVecRestoreArrayRead(da, U, &uarray)); 282 PetscCall(DMDAVecRestoreArrayRead(da, localUold, &uoldarray)); 283 PetscCall(DMDAVecRestoreArray(da, F, &f)); 284 PetscCall(DMRestoreLocalVector(da, &localUold)); 285 PetscFunctionReturn(PETSC_SUCCESS); 286 } 287 288 /*TEST 289 290 test: 291 args: -ts_max_steps 10 -ts_monitor 292 293 test: 294 suffix: 2 295 nsize: 3 296 args: -ts_max_steps 10 -ts_monitor 297 output_file: output/ex6_1.out 298 299 test: 300 suffix: 3 301 args: -ts_max_steps 10 -ts_monitor -useLaxWendroff false 302 303 test: 304 suffix: 4 305 nsize: 3 306 args: -ts_max_steps 10 -ts_monitor -useLaxWendroff false 307 output_file: output/ex6_3.out 308 309 TEST*/ 310