Actual source code: ex9.c
petsc-3.13.6 2020-09-29
1: static const char help[] = "1D periodic Finite Volume solver in slope-limiter form with semidiscrete time stepping.\n"
2: "Solves scalar and vector problems, choose the physical model with -physics\n"
3: " advection - Constant coefficient scalar advection\n"
4: " u_t + (a*u)_x = 0\n"
5: " burgers - Burgers equation\n"
6: " u_t + (u^2/2)_x = 0\n"
7: " traffic - Traffic equation\n"
8: " u_t + (u*(1-u))_x = 0\n"
9: " acoustics - Acoustic wave propagation\n"
10: " u_t + (c*z*v)_x = 0\n"
11: " v_t + (c/z*u)_x = 0\n"
12: " isogas - Isothermal gas dynamics\n"
13: " rho_t + (rho*u)_x = 0\n"
14: " (rho*u)_t + (rho*u^2 + c^2*rho)_x = 0\n"
15: " shallow - Shallow water equations\n"
16: " h_t + (h*u)_x = 0\n"
17: " (h*u)_t + (h*u^2 + g*h^2/2)_x = 0\n"
18: "Some of these physical models have multiple Riemann solvers, select these with -physics_xxx_riemann\n"
19: " exact - Exact Riemann solver which usually needs to perform a Newton iteration to connect\n"
20: " the states across shocks and rarefactions\n"
21: " roe - Linearized scheme, usually with an entropy fix inside sonic rarefactions\n"
22: "The systems provide a choice of reconstructions with -physics_xxx_reconstruct\n"
23: " characteristic - Limit the characteristic variables, this is usually preferred (default)\n"
24: " conservative - Limit the conservative variables directly, can cause undesired interaction of waves\n\n"
25: "A variety of limiters for high-resolution TVD limiters are available with -limit\n"
26: " upwind,minmod,superbee,mc,vanleer,vanalbada,koren,cada-torillhon (last two are nominally third order)\n"
27: " and non-TVD schemes lax-wendroff,beam-warming,fromm\n\n"
28: "To preserve the TVD property, one should time step with a strong stability preserving method.\n"
29: "The optimal high order explicit Runge-Kutta methods in TSSSP are recommended for non-stiff problems.\n\n"
30: "Several initial conditions can be chosen with -initial N\n\n"
31: "The problem size should be set with -da_grid_x M\n\n";
33: #include <petscts.h>
34: #include <petscdm.h>
35: #include <petscdmda.h>
36: #include <petscdraw.h>
38: #include <petsc/private/kernels/blockinvert.h>
40: PETSC_STATIC_INLINE PetscReal Sgn(PetscReal a) { return (a<0) ? -1 : 1; }
41: PETSC_STATIC_INLINE PetscReal Abs(PetscReal a) { return (a<0) ? 0 : a; }
42: PETSC_STATIC_INLINE PetscReal Sqr(PetscReal a) { return a*a; }
43: PETSC_STATIC_INLINE PetscReal MaxAbs(PetscReal a,PetscReal b) { return (PetscAbs(a) > PetscAbs(b)) ? a : b; }
44: PETSC_UNUSED PETSC_STATIC_INLINE PetscReal MinAbs(PetscReal a,PetscReal b) { return (PetscAbs(a) < PetscAbs(b)) ? a : b; }
45: PETSC_STATIC_INLINE PetscReal MinMod2(PetscReal a,PetscReal b) { return (a*b<0) ? 0 : Sgn(a)*PetscMin(PetscAbs(a),PetscAbs(b)); }
46: PETSC_STATIC_INLINE PetscReal MaxMod2(PetscReal a,PetscReal b) { return (a*b<0) ? 0 : Sgn(a)*PetscMax(PetscAbs(a),PetscAbs(b)); }
47: PETSC_STATIC_INLINE PetscReal MinMod3(PetscReal a,PetscReal b,PetscReal c) {return (a*b<0 || a*c<0) ? 0 : Sgn(a)*PetscMin(PetscAbs(a),PetscMin(PetscAbs(b),PetscAbs(c))); }
49: PETSC_STATIC_INLINE PetscReal RangeMod(PetscReal a,PetscReal xmin,PetscReal xmax) { PetscReal range = xmax-xmin; return xmin +PetscFmodReal(range+PetscFmodReal(a,range),range); }
52: /* ----------------------- Lots of limiters, these could go in a separate library ------------------------- */
53: typedef struct _LimitInfo {
54: PetscReal hx;
55: PetscInt m;
56: } *LimitInfo;
57: static void Limit_Upwind(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
58: {
59: PetscInt i;
60: for (i=0; i<info->m; i++) lmt[i] = 0;
61: }
62: static void Limit_LaxWendroff(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
63: {
64: PetscInt i;
65: for (i=0; i<info->m; i++) lmt[i] = jR[i];
66: }
67: static void Limit_BeamWarming(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
68: {
69: PetscInt i;
70: for (i=0; i<info->m; i++) lmt[i] = jL[i];
71: }
72: static void Limit_Fromm(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
73: {
74: PetscInt i;
75: for (i=0; i<info->m; i++) lmt[i] = 0.5*(jL[i] + jR[i]);
76: }
77: static void Limit_Minmod(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
78: {
79: PetscInt i;
80: for (i=0; i<info->m; i++) lmt[i] = MinMod2(jL[i],jR[i]);
81: }
82: static void Limit_Superbee(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
83: {
84: PetscInt i;
85: for (i=0; i<info->m; i++) lmt[i] = MaxMod2(MinMod2(jL[i],2*jR[i]),MinMod2(2*jL[i],jR[i]));
86: }
87: static void Limit_MC(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
88: {
89: PetscInt i;
90: for (i=0; i<info->m; i++) lmt[i] = MinMod3(2*jL[i],0.5*(jL[i]+jR[i]),2*jR[i]);
91: }
92: static void Limit_VanLeer(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
93: { /* phi = (t + abs(t)) / (1 + abs(t)) */
94: PetscInt i;
95: for (i=0; i<info->m; i++) lmt[i] = (jL[i]*Abs(jR[i]) + Abs(jL[i])*jR[i]) / (Abs(jL[i]) + Abs(jR[i]) + 1e-15);
96: }
97: static void Limit_VanAlbada(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt) /* differentiable */
98: { /* phi = (t + t^2) / (1 + t^2) */
99: PetscInt i;
100: for (i=0; i<info->m; i++) lmt[i] = (jL[i]*Sqr(jR[i]) + Sqr(jL[i])*jR[i]) / (Sqr(jL[i]) + Sqr(jR[i]) + 1e-15);
101: }
102: static void Limit_VanAlbadaTVD(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
103: { /* phi = (t + t^2) / (1 + t^2) */
104: PetscInt i;
105: for (i=0; i<info->m; i++) lmt[i] = (jL[i]*jR[i]<0) ? 0 : (jL[i]*Sqr(jR[i]) + Sqr(jL[i])*jR[i]) / (Sqr(jL[i]) + Sqr(jR[i]) + 1e-15);
106: }
107: static void Limit_Koren(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt) /* differentiable */
108: { /* phi = (t + 2*t^2) / (2 - t + 2*t^2) */
109: PetscInt i;
110: for (i=0; i<info->m; i++) lmt[i] = ((jL[i]*Sqr(jR[i]) + 2*Sqr(jL[i])*jR[i])/(2*Sqr(jL[i]) - jL[i]*jR[i] + 2*Sqr(jR[i]) + 1e-15));
111: }
112: static void Limit_KorenSym(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt) /* differentiable */
113: { /* Symmetric version of above */
114: PetscInt i;
115: for (i=0; i<info->m; i++) lmt[i] = (1.5*(jL[i]*Sqr(jR[i]) + Sqr(jL[i])*jR[i])/(2*Sqr(jL[i]) - jL[i]*jR[i] + 2*Sqr(jR[i]) + 1e-15));
116: }
117: static void Limit_Koren3(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
118: { /* Eq 11 of Cada-Torrilhon 2009 */
119: PetscInt i;
120: for (i=0; i<info->m; i++) lmt[i] = MinMod3(2*jL[i],(jL[i]+2*jR[i])/3,2*jR[i]);
121: }
122: static PetscReal CadaTorrilhonPhiHatR_Eq13(PetscReal L,PetscReal R)
123: {
124: return PetscMax(0,PetscMin((L+2*R)/3,PetscMax(-0.5*L,PetscMin(2*L,PetscMin((L+2*R)/3,1.6*R)))));
125: }
126: static void Limit_CadaTorrilhon2(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
127: { /* Cada-Torrilhon 2009, Eq 13 */
128: PetscInt i;
129: for (i=0; i<info->m; i++) lmt[i] = CadaTorrilhonPhiHatR_Eq13(jL[i],jR[i]);
130: }
131: static void Limit_CadaTorrilhon3R(PetscReal r,LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
132: { /* Cada-Torrilhon 2009, Eq 22 */
133: /* They recommend 0.001 < r < 1, but larger values are more accurate in smooth regions */
134: const PetscReal eps = 1e-7,hx = info->hx;
135: PetscInt i;
136: for (i=0; i<info->m; i++) {
137: const PetscReal eta = (Sqr(jL[i]) + Sqr(jR[i])) / Sqr(r*hx);
138: lmt[i] = ((eta < 1-eps) ? (jL[i] + 2*jR[i]) / 3 : ((eta > 1+eps) ? CadaTorrilhonPhiHatR_Eq13(jL[i],jR[i]) : 0.5*((1-(eta-1)/eps)*(jL[i]+2*jR[i])/3 + (1+(eta+1)/eps)*CadaTorrilhonPhiHatR_Eq13(jL[i],jR[i]))));
139: }
140: }
141: static void Limit_CadaTorrilhon3R0p1(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
142: {
143: Limit_CadaTorrilhon3R(0.1,info,jL,jR,lmt);
144: }
145: static void Limit_CadaTorrilhon3R1(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
146: {
147: Limit_CadaTorrilhon3R(1,info,jL,jR,lmt);
148: }
149: static void Limit_CadaTorrilhon3R10(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
150: {
151: Limit_CadaTorrilhon3R(10,info,jL,jR,lmt);
152: }
153: static void Limit_CadaTorrilhon3R100(LimitInfo info,const PetscScalar *jL,const PetscScalar *jR,PetscScalar *lmt)
154: {
155: Limit_CadaTorrilhon3R(100,info,jL,jR,lmt);
156: }
159: /* --------------------------------- Finite Volume data structures ----------------------------------- */
161: typedef enum {FVBC_PERIODIC, FVBC_OUTFLOW} FVBCType;
162: static const char *FVBCTypes[] = {"PERIODIC","OUTFLOW","FVBCType","FVBC_",0};
163: typedef PetscErrorCode (*RiemannFunction)(void*,PetscInt,const PetscScalar*,const PetscScalar*,PetscScalar*,PetscReal*);
164: typedef PetscErrorCode (*ReconstructFunction)(void*,PetscInt,const PetscScalar*,PetscScalar*,PetscScalar*,PetscReal*);
166: typedef struct {
167: PetscErrorCode (*sample)(void*,PetscInt,FVBCType,PetscReal,PetscReal,PetscReal,PetscReal,PetscReal*);
168: RiemannFunction riemann;
169: ReconstructFunction characteristic;
170: PetscErrorCode (*destroy)(void*);
171: void *user;
172: PetscInt dof;
173: char *fieldname[16];
174: } PhysicsCtx;
176: typedef struct {
177: void (*limit)(LimitInfo,const PetscScalar*,const PetscScalar*,PetscScalar*);
178: PhysicsCtx physics;
179: MPI_Comm comm;
180: char prefix[256];
182: /* Local work arrays */
183: PetscScalar *R,*Rinv; /* Characteristic basis, and it's inverse. COLUMN-MAJOR */
184: PetscScalar *cjmpLR; /* Jumps at left and right edge of cell, in characteristic basis, len=2*dof */
185: PetscScalar *cslope; /* Limited slope, written in characteristic basis */
186: PetscScalar *uLR; /* Solution at left and right of interface, conservative variables, len=2*dof */
187: PetscScalar *flux; /* Flux across interface */
188: PetscReal *speeds; /* Speeds of each wave */
190: PetscReal cfl_idt; /* Max allowable value of 1/Delta t */
191: PetscReal cfl;
192: PetscReal xmin,xmax;
193: PetscInt initial;
194: PetscBool exact;
195: FVBCType bctype;
196: } FVCtx;
198: PetscErrorCode RiemannListAdd(PetscFunctionList *flist,const char *name,RiemannFunction rsolve)
199: {
203: PetscFunctionListAdd(flist,name,rsolve);
204: return(0);
205: }
207: PetscErrorCode RiemannListFind(PetscFunctionList flist,const char *name,RiemannFunction *rsolve)
208: {
212: PetscFunctionListFind(flist,name,rsolve);
213: if (!*rsolve) SETERRQ1(PETSC_COMM_SELF,1,"Riemann solver \"%s\" could not be found",name);
214: return(0);
215: }
217: PetscErrorCode ReconstructListAdd(PetscFunctionList *flist,const char *name,ReconstructFunction r)
218: {
222: PetscFunctionListAdd(flist,name,r);
223: return(0);
224: }
226: PetscErrorCode ReconstructListFind(PetscFunctionList flist,const char *name,ReconstructFunction *r)
227: {
231: PetscFunctionListFind(flist,name,r);
232: if (!*r) SETERRQ1(PETSC_COMM_SELF,1,"Reconstruction \"%s\" could not be found",name);
233: return(0);
234: }
236: /* --------------------------------- Physics ----------------------------------- */
237: /**
238: * Each physical model consists of Riemann solver and a function to determine the basis to use for reconstruction. These
239: * are set with the PhysicsCreate_XXX function which allocates private storage and sets these methods as well as the
240: * number of fields and their names, and a function to deallocate private storage.
241: **/
243: /* First a few functions useful to several different physics */
244: static PetscErrorCode PhysicsCharacteristic_Conservative(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
245: {
246: PetscInt i,j;
249: for (i=0; i<m; i++) {
250: for (j=0; j<m; j++) Xi[i*m+j] = X[i*m+j] = (PetscScalar)(i==j);
251: speeds[i] = PETSC_MAX_REAL; /* Indicates invalid */
252: }
253: return(0);
254: }
256: static PetscErrorCode PhysicsDestroy_SimpleFree(void *vctx)
257: {
261: PetscFree(vctx);
262: return(0);
263: }
267: /* --------------------------------- Advection ----------------------------------- */
269: typedef struct {
270: PetscReal a; /* advective velocity */
271: } AdvectCtx;
273: static PetscErrorCode PhysicsRiemann_Advect(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
274: {
275: AdvectCtx *ctx = (AdvectCtx*)vctx;
276: PetscReal speed;
279: speed = ctx->a;
280: flux[0] = PetscMax(0,speed)*uL[0] + PetscMin(0,speed)*uR[0];
281: *maxspeed = speed;
282: return(0);
283: }
285: static PetscErrorCode PhysicsCharacteristic_Advect(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
286: {
287: AdvectCtx *ctx = (AdvectCtx*)vctx;
290: X[0] = 1.;
291: Xi[0] = 1.;
292: speeds[0] = ctx->a;
293: return(0);
294: }
296: static PetscErrorCode PhysicsSample_Advect(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
297: {
298: AdvectCtx *ctx = (AdvectCtx*)vctx;
299: PetscReal a = ctx->a,x0;
302: switch (bctype) {
303: case FVBC_OUTFLOW: x0 = x-a*t; break;
304: case FVBC_PERIODIC: x0 = RangeMod(x-a*t,xmin,xmax); break;
305: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown BCType");
306: }
307: switch (initial) {
308: case 0: u[0] = (x0 < 0) ? 1 : -1; break;
309: case 1: u[0] = (x0 < 0) ? -1 : 1; break;
310: case 2: u[0] = (0 < x0 && x0 < 1) ? 1 : 0; break;
311: case 3: u[0] = PetscSinReal(2*PETSC_PI*x0); break;
312: case 4: u[0] = PetscAbs(x0); break;
313: case 5: u[0] = (x0 < 0 || x0 > 0.5) ? 0 : PetscSqr(PetscSinReal(2*PETSC_PI*x0)); break;
314: case 6: u[0] = (x0 < 0) ? 0 : ((x0 < 1) ? x0 : ((x0 < 2) ? 2-x0 : 0)); break;
315: case 7: u[0] = PetscPowReal(PetscSinReal(PETSC_PI*x0),10.0);break;
316: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown initial condition");
317: }
318: return(0);
319: }
321: static PetscErrorCode PhysicsCreate_Advect(FVCtx *ctx)
322: {
324: AdvectCtx *user;
327: PetscNew(&user);
328: ctx->physics.sample = PhysicsSample_Advect;
329: ctx->physics.riemann = PhysicsRiemann_Advect;
330: ctx->physics.characteristic = PhysicsCharacteristic_Advect;
331: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
332: ctx->physics.user = user;
333: ctx->physics.dof = 1;
334: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
335: user->a = 1;
336: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for advection","");
337: {
338: PetscOptionsReal("-physics_advect_a","Speed","",user->a,&user->a,NULL);
339: }
340: PetscOptionsEnd();
341: return(0);
342: }
344: /* --------------------------------- Burgers ----------------------------------- */
346: typedef struct {
347: PetscReal lxf_speed;
348: } BurgersCtx;
350: static PetscErrorCode PhysicsSample_Burgers(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
351: {
353: if (bctype == FVBC_PERIODIC && t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Exact solution not implemented for periodic");
354: switch (initial) {
355: case 0: u[0] = (x < 0) ? 1 : -1; break;
356: case 1:
357: if (x < -t) u[0] = -1;
358: else if (x < t) u[0] = x/t;
359: else u[0] = 1;
360: break;
361: case 2:
362: if (x < 0) u[0] = 0;
363: else if (x <= t) u[0] = x/t;
364: else if (x < 1+0.5*t) u[0] = 1;
365: else u[0] = 0;
366: break;
367: case 3:
368: if (x < 0.2*t) u[0] = 0.2;
369: else if (x < t) u[0] = x/t;
370: else u[0] = 1;
371: break;
372: case 4:
373: if (t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only initial condition available");
374: u[0] = 0.7 + 0.3*PetscSinReal(2*PETSC_PI*((x-xmin)/(xmax-xmin)));
375: break;
376: case 5: /* Pure shock solution */
377: if (x < 0.5*t) u[0] = 1;
378: else u[0] = 0;
379: break;
380: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown initial condition");
381: }
382: return(0);
383: }
385: static PetscErrorCode PhysicsRiemann_Burgers_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
386: {
388: if (uL[0] < uR[0]) { /* rarefaction */
389: flux[0] = (uL[0]*uR[0] < 0)
390: ? 0 /* sonic rarefaction */
391: : 0.5*PetscMin(PetscSqr(uL[0]),PetscSqr(uR[0]));
392: } else { /* shock */
393: flux[0] = 0.5*PetscMax(PetscSqr(uL[0]),PetscSqr(uR[0]));
394: }
395: *maxspeed = (PetscAbs(uL[0]) > PetscAbs(uR[0])) ? uL[0] : uR[0];
396: return(0);
397: }
399: static PetscErrorCode PhysicsRiemann_Burgers_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
400: {
401: PetscReal speed;
404: speed = 0.5*(uL[0] + uR[0]);
405: flux[0] = 0.25*(PetscSqr(uL[0]) + PetscSqr(uR[0])) - 0.5*PetscAbs(speed)*(uR[0]-uL[0]);
406: if (uL[0] <= 0 && 0 <= uR[0]) flux[0] = 0; /* Entropy fix for sonic rarefaction */
407: *maxspeed = speed;
408: return(0);
409: }
411: static PetscErrorCode PhysicsRiemann_Burgers_LxF(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
412: {
413: PetscReal c;
414: PetscScalar fL,fR;
417: c = ((BurgersCtx*)vctx)->lxf_speed;
418: fL = 0.5*PetscSqr(uL[0]);
419: fR = 0.5*PetscSqr(uR[0]);
420: flux[0] = 0.5*(fL + fR) - 0.5*c*(uR[0] - uL[0]);
421: *maxspeed = c;
422: return(0);
423: }
425: static PetscErrorCode PhysicsRiemann_Burgers_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
426: {
427: PetscReal c;
428: PetscScalar fL,fR;
431: c = PetscMax(PetscAbs(uL[0]),PetscAbs(uR[0]));
432: fL = 0.5*PetscSqr(uL[0]);
433: fR = 0.5*PetscSqr(uR[0]);
434: flux[0] = 0.5*(fL + fR) - 0.5*c*(uR[0] - uL[0]);
435: *maxspeed = c;
436: return(0);
437: }
439: static PetscErrorCode PhysicsCreate_Burgers(FVCtx *ctx)
440: {
441: BurgersCtx *user;
442: PetscErrorCode ierr;
443: RiemannFunction r;
444: PetscFunctionList rlist = 0;
445: char rname[256] = "exact";
448: PetscNew(&user);
450: ctx->physics.sample = PhysicsSample_Burgers;
451: ctx->physics.characteristic = PhysicsCharacteristic_Conservative;
452: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
453: ctx->physics.user = user;
454: ctx->physics.dof = 1;
456: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
457: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Burgers_Exact);
458: RiemannListAdd(&rlist,"roe", PhysicsRiemann_Burgers_Roe);
459: RiemannListAdd(&rlist,"lxf", PhysicsRiemann_Burgers_LxF);
460: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Burgers_Rusanov);
461: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for advection","");
462: {
463: PetscOptionsFList("-physics_burgers_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
464: }
465: PetscOptionsEnd();
466: RiemannListFind(rlist,rname,&r);
467: PetscFunctionListDestroy(&rlist);
468: ctx->physics.riemann = r;
470: /* *
471: * Hack to deal with LxF in semi-discrete form
472: * max speed is 1 for the basic initial conditions (where |u| <= 1)
473: * */
474: if (r == PhysicsRiemann_Burgers_LxF) user->lxf_speed = 1;
475: return(0);
476: }
478: /* --------------------------------- Traffic ----------------------------------- */
480: typedef struct {
481: PetscReal lxf_speed;
482: PetscReal a;
483: } TrafficCtx;
485: PETSC_STATIC_INLINE PetscScalar TrafficFlux(PetscScalar a,PetscScalar u) { return a*u*(1-u); }
487: static PetscErrorCode PhysicsSample_Traffic(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
488: {
489: PetscReal a = ((TrafficCtx*)vctx)->a;
492: if (bctype == FVBC_PERIODIC && t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Exact solution not implemented for periodic");
493: switch (initial) {
494: case 0:
495: u[0] = (-a*t < x) ? 2 : 0; break;
496: case 1:
497: if (x < PetscMin(2*a*t,0.5+a*t)) u[0] = -1;
498: else if (x < 1) u[0] = 0;
499: else u[0] = 1;
500: break;
501: case 2:
502: if (t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only initial condition available");
503: u[0] = 0.7 + 0.3*PetscSinReal(2*PETSC_PI*((x-xmin)/(xmax-xmin)));
504: break;
505: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown initial condition");
506: }
507: return(0);
508: }
510: static PetscErrorCode PhysicsRiemann_Traffic_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
511: {
512: PetscReal a = ((TrafficCtx*)vctx)->a;
515: if (uL[0] < uR[0]) {
516: flux[0] = PetscMin(TrafficFlux(a,uL[0]),TrafficFlux(a,uR[0]));
517: } else {
518: flux[0] = (uR[0] < 0.5 && 0.5 < uL[0]) ? TrafficFlux(a,0.5) : PetscMax(TrafficFlux(a,uL[0]),TrafficFlux(a,uR[0]));
519: }
520: *maxspeed = a*MaxAbs(1-2*uL[0],1-2*uR[0]);
521: return(0);
522: }
524: static PetscErrorCode PhysicsRiemann_Traffic_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
525: {
526: PetscReal a = ((TrafficCtx*)vctx)->a;
527: PetscReal speed;
530: speed = a*(1 - (uL[0] + uR[0]));
531: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*PetscAbs(speed)*(uR[0]-uL[0]);
532: *maxspeed = speed;
533: return(0);
534: }
536: static PetscErrorCode PhysicsRiemann_Traffic_LxF(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
537: {
538: TrafficCtx *phys = (TrafficCtx*)vctx;
539: PetscReal a = phys->a;
540: PetscReal speed;
543: speed = a*(1 - (uL[0] + uR[0]));
544: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*phys->lxf_speed*(uR[0]-uL[0]);
545: *maxspeed = speed;
546: return(0);
547: }
549: static PetscErrorCode PhysicsRiemann_Traffic_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
550: {
551: PetscReal a = ((TrafficCtx*)vctx)->a;
552: PetscReal speed;
555: speed = a*PetscMax(PetscAbs(1-2*uL[0]),PetscAbs(1-2*uR[0]));
556: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*speed*(uR[0]-uL[0]);
557: *maxspeed = speed;
558: return(0);
559: }
561: static PetscErrorCode PhysicsCreate_Traffic(FVCtx *ctx)
562: {
563: PetscErrorCode ierr;
564: TrafficCtx *user;
565: RiemannFunction r;
566: PetscFunctionList rlist = 0;
567: char rname[256] = "exact";
570: PetscNew(&user);
571: ctx->physics.sample = PhysicsSample_Traffic;
572: ctx->physics.characteristic = PhysicsCharacteristic_Conservative;
573: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
574: ctx->physics.user = user;
575: ctx->physics.dof = 1;
577: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
578: user->a = 0.5;
579: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Traffic_Exact);
580: RiemannListAdd(&rlist,"roe", PhysicsRiemann_Traffic_Roe);
581: RiemannListAdd(&rlist,"lxf", PhysicsRiemann_Traffic_LxF);
582: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Traffic_Rusanov);
583: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for Traffic","");
584: PetscOptionsReal("-physics_traffic_a","Flux = a*u*(1-u)","",user->a,&user->a,NULL);
585: PetscOptionsFList("-physics_traffic_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
586: PetscOptionsEnd();
588: RiemannListFind(rlist,rname,&r);
589: PetscFunctionListDestroy(&rlist);
591: ctx->physics.riemann = r;
593: /* *
594: * Hack to deal with LxF in semi-discrete form
595: * max speed is 3*a for the basic initial conditions (-1 <= u <= 2)
596: * */
597: if (r == PhysicsRiemann_Traffic_LxF) user->lxf_speed = 3*user->a;
598: return(0);
599: }
601: /* --------------------------------- Linear Acoustics ----------------------------------- */
603: /* Flux: u_t + (A u)_x
604: * z = sqrt(rho*bulk), c = sqrt(rho/bulk)
605: * Spectral decomposition: A = R * D * Rinv
606: * [ cz] = [-z z] [-c ] [-1/2z 1/2]
607: * [c/z ] = [ 1 1] [ c] [ 1/2z 1/2]
608: *
609: * We decompose this into the left-traveling waves Al = R * D^- Rinv
610: * and the right-traveling waves Ar = R * D^+ * Rinv
611: * Multiplying out these expressions produces the following two matrices
612: */
614: typedef struct {
615: PetscReal c; /* speed of sound: c = sqrt(bulk/rho) */
616: PetscReal z; /* impedence: z = sqrt(rho*bulk) */
617: } AcousticsCtx;
619: PETSC_UNUSED PETSC_STATIC_INLINE void AcousticsFlux(AcousticsCtx *ctx,const PetscScalar *u,PetscScalar *f)
620: {
621: f[0] = ctx->c*ctx->z*u[1];
622: f[1] = ctx->c/ctx->z*u[0];
623: }
625: static PetscErrorCode PhysicsCharacteristic_Acoustics(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
626: {
627: AcousticsCtx *phys = (AcousticsCtx*)vctx;
628: PetscReal z = phys->z,c = phys->c;
631: X[0*2+0] = -z;
632: X[0*2+1] = z;
633: X[1*2+0] = 1;
634: X[1*2+1] = 1;
635: Xi[0*2+0] = -1./(2*z);
636: Xi[0*2+1] = 1./2;
637: Xi[1*2+0] = 1./(2*z);
638: Xi[1*2+1] = 1./2;
639: speeds[0] = -c;
640: speeds[1] = c;
641: return(0);
642: }
644: static PetscErrorCode PhysicsSample_Acoustics_Initial(AcousticsCtx *phys,PetscInt initial,PetscReal xmin,PetscReal xmax,PetscReal x,PetscReal *u)
645: {
647: switch (initial) {
648: case 0:
649: u[0] = (PetscAbs((x - xmin)/(xmax - xmin) - 0.2) < 0.1) ? 1 : 0.5;
650: u[1] = (PetscAbs((x - xmin)/(xmax - xmin) - 0.7) < 0.1) ? 1 : -0.5;
651: break;
652: case 1:
653: u[0] = PetscCosReal(3 * 2*PETSC_PI*x/(xmax-xmin));
654: u[1] = PetscExpReal(-PetscSqr(x - (xmax + xmin)/2) / (2*PetscSqr(0.2*(xmax - xmin)))) - 0.5;
655: break;
656: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown initial condition");
657: }
658: return(0);
659: }
661: static PetscErrorCode PhysicsSample_Acoustics(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
662: {
663: AcousticsCtx *phys = (AcousticsCtx*)vctx;
664: PetscReal c = phys->c;
665: PetscReal x0a,x0b,u0a[2],u0b[2],tmp[2];
666: PetscReal X[2][2],Xi[2][2],dummy[2];
670: switch (bctype) {
671: case FVBC_OUTFLOW:
672: x0a = x+c*t;
673: x0b = x-c*t;
674: break;
675: case FVBC_PERIODIC:
676: x0a = RangeMod(x+c*t,xmin,xmax);
677: x0b = RangeMod(x-c*t,xmin,xmax);
678: break;
679: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown BCType");
680: }
681: PhysicsSample_Acoustics_Initial(phys,initial,xmin,xmax,x0a,u0a);
682: PhysicsSample_Acoustics_Initial(phys,initial,xmin,xmax,x0b,u0b);
683: PhysicsCharacteristic_Acoustics(vctx,2,u,&X[0][0],&Xi[0][0],dummy);
684: tmp[0] = Xi[0][0]*u0a[0] + Xi[0][1]*u0a[1];
685: tmp[1] = Xi[1][0]*u0b[0] + Xi[1][1]*u0b[1];
686: u[0] = X[0][0]*tmp[0] + X[0][1]*tmp[1];
687: u[1] = X[1][0]*tmp[0] + X[1][1]*tmp[1];
688: return(0);
689: }
691: static PetscErrorCode PhysicsRiemann_Acoustics_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
692: {
693: AcousticsCtx *phys = (AcousticsCtx*)vctx;
694: PetscReal c = phys->c,z = phys->z;
695: PetscReal
696: Al[2][2] = {{-c/2 , c*z/2 },
697: {c/(2*z) , -c/2 }}, /* Left traveling waves */
698: Ar[2][2] = {{c/2 , c*z/2 },
699: {c/(2*z) , c/2 }}; /* Right traveling waves */
702: flux[0] = Al[0][0]*uR[0] + Al[0][1]*uR[1] + Ar[0][0]*uL[0] + Ar[0][1]*uL[1];
703: flux[1] = Al[1][0]*uR[0] + Al[1][1]*uR[1] + Ar[1][0]*uL[0] + Ar[1][1]*uL[1];
704: *maxspeed = c;
705: return(0);
706: }
708: static PetscErrorCode PhysicsCreate_Acoustics(FVCtx *ctx)
709: {
710: PetscErrorCode ierr;
711: AcousticsCtx *user;
712: PetscFunctionList rlist = 0,rclist = 0;
713: char rname[256] = "exact",rcname[256] = "characteristic";
716: PetscNew(&user);
717: ctx->physics.sample = PhysicsSample_Acoustics;
718: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
719: ctx->physics.user = user;
720: ctx->physics.dof = 2;
722: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
723: PetscStrallocpy("v",&ctx->physics.fieldname[1]);
725: user->c = 1;
726: user->z = 1;
728: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Acoustics_Exact);
729: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_Acoustics);
730: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
731: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for linear Acoustics","");
732: {
733: PetscOptionsReal("-physics_acoustics_c","c = sqrt(bulk/rho)","",user->c,&user->c,NULL);
734: PetscOptionsReal("-physics_acoustics_z","z = sqrt(bulk*rho)","",user->z,&user->z,NULL);
735: PetscOptionsFList("-physics_acoustics_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
736: PetscOptionsFList("-physics_acoustics_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
737: }
738: PetscOptionsEnd();
739: RiemannListFind(rlist,rname,&ctx->physics.riemann);
740: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
741: PetscFunctionListDestroy(&rlist);
742: PetscFunctionListDestroy(&rclist);
743: return(0);
744: }
746: /* --------------------------------- Isothermal Gas Dynamics ----------------------------------- */
748: typedef struct {
749: PetscReal acoustic_speed;
750: } IsoGasCtx;
752: PETSC_STATIC_INLINE void IsoGasFlux(PetscReal c,const PetscScalar *u,PetscScalar *f)
753: {
754: f[0] = u[1];
755: f[1] = PetscSqr(u[1])/u[0] + c*c*u[0];
756: }
758: static PetscErrorCode PhysicsSample_IsoGas(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
759: {
761: if (t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Exact solutions not implemented for t > 0");
762: switch (initial) {
763: case 0:
764: u[0] = (x < 0) ? 1 : 0.5;
765: u[1] = (x < 0) ? 1 : 0.7;
766: break;
767: case 1:
768: u[0] = 1+0.5*PetscSinReal(2*PETSC_PI*x);
769: u[1] = 1*u[0];
770: break;
771: default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"unknown initial condition");
772: }
773: return(0);
774: }
776: static PetscErrorCode PhysicsRiemann_IsoGas_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
777: {
778: IsoGasCtx *phys = (IsoGasCtx*)vctx;
779: PetscReal c = phys->acoustic_speed;
780: PetscScalar ubar,du[2],a[2],fL[2],fR[2],lam[2],ustar[2],R[2][2];
781: PetscInt i;
784: ubar = (uL[1]/PetscSqrtScalar(uL[0]) + uR[1]/PetscSqrtScalar(uR[0])) / (PetscSqrtScalar(uL[0]) + PetscSqrtScalar(uR[0]));
785: /* write fluxuations in characteristic basis */
786: du[0] = uR[0] - uL[0];
787: du[1] = uR[1] - uL[1];
788: a[0] = (1/(2*c)) * ((ubar + c)*du[0] - du[1]);
789: a[1] = (1/(2*c)) * ((-ubar + c)*du[0] + du[1]);
790: /* wave speeds */
791: lam[0] = ubar - c;
792: lam[1] = ubar + c;
793: /* Right eigenvectors */
794: R[0][0] = 1; R[0][1] = ubar-c;
795: R[1][0] = 1; R[1][1] = ubar+c;
796: /* Compute state in star region (between the 1-wave and 2-wave) */
797: for (i=0; i<2; i++) ustar[i] = uL[i] + a[0]*R[0][i];
798: if (uL[1]/uL[0] < c && c < ustar[1]/ustar[0]) { /* 1-wave is sonic rarefaction */
799: PetscScalar ufan[2];
800: ufan[0] = uL[0]*PetscExpScalar(uL[1]/(uL[0]*c) - 1);
801: ufan[1] = c*ufan[0];
802: IsoGasFlux(c,ufan,flux);
803: } else if (ustar[1]/ustar[0] < -c && -c < uR[1]/uR[0]) { /* 2-wave is sonic rarefaction */
804: PetscScalar ufan[2];
805: ufan[0] = uR[0]*PetscExpScalar(-uR[1]/(uR[0]*c) - 1);
806: ufan[1] = -c*ufan[0];
807: IsoGasFlux(c,ufan,flux);
808: } else { /* Centered form */
809: IsoGasFlux(c,uL,fL);
810: IsoGasFlux(c,uR,fR);
811: for (i=0; i<2; i++) {
812: PetscScalar absdu = PetscAbsScalar(lam[0])*a[0]*R[0][i] + PetscAbsScalar(lam[1])*a[1]*R[1][i];
813: flux[i] = 0.5*(fL[i]+fR[i]) - 0.5*absdu;
814: }
815: }
816: *maxspeed = MaxAbs(lam[0],lam[1]);
817: return(0);
818: }
820: static PetscErrorCode PhysicsRiemann_IsoGas_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
821: {
822: IsoGasCtx *phys = (IsoGasCtx*)vctx;
823: PetscReal c = phys->acoustic_speed;
824: PetscScalar ustar[2];
825: struct {PetscScalar rho,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]},star;
826: PetscInt i;
829: if (!(L.rho > 0 && R.rho > 0)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed density is negative");
830: {
831: /* Solve for star state */
832: PetscScalar res,tmp,rho = 0.5*(L.rho + R.rho); /* initial guess */
833: for (i=0; i<20; i++) {
834: PetscScalar fr,fl,dfr,dfl;
835: fl = (L.rho < rho)
836: ? (rho-L.rho)/PetscSqrtScalar(L.rho*rho) /* shock */
837: : PetscLogScalar(rho) - PetscLogScalar(L.rho); /* rarefaction */
838: fr = (R.rho < rho)
839: ? (rho-R.rho)/PetscSqrtScalar(R.rho*rho) /* shock */
840: : PetscLogScalar(rho) - PetscLogScalar(R.rho); /* rarefaction */
841: res = R.u-L.u + c*(fr+fl);
842: if (PetscIsInfOrNanScalar(res)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Infinity or Not-a-Number generated in computation");
843: if (PetscAbsScalar(res) < 1e-10) {
844: star.rho = rho;
845: star.u = L.u - c*fl;
846: goto converged;
847: }
848: dfl = (L.rho < rho) ? 1/PetscSqrtScalar(L.rho*rho)*(1 - 0.5*(rho-L.rho)/rho) : 1/rho;
849: dfr = (R.rho < rho) ? 1/PetscSqrtScalar(R.rho*rho)*(1 - 0.5*(rho-R.rho)/rho) : 1/rho;
850: tmp = rho - res/(c*(dfr+dfl));
851: if (tmp <= 0) rho /= 2; /* Guard against Newton shooting off to a negative density */
852: else rho = tmp;
853: if (!((rho > 0) && PetscIsNormalScalar(rho))) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP,"non-normal iterate rho=%g",(double)PetscRealPart(rho));
854: }
855: SETERRQ1(PETSC_COMM_SELF,1,"Newton iteration for star.rho diverged after %D iterations",i);
856: }
857: converged:
858: if (L.u-c < 0 && 0 < star.u-c) { /* 1-wave is sonic rarefaction */
859: PetscScalar ufan[2];
860: ufan[0] = L.rho*PetscExpScalar(L.u/c - 1);
861: ufan[1] = c*ufan[0];
862: IsoGasFlux(c,ufan,flux);
863: } else if (star.u+c < 0 && 0 < R.u+c) { /* 2-wave is sonic rarefaction */
864: PetscScalar ufan[2];
865: ufan[0] = R.rho*PetscExpScalar(-R.u/c - 1);
866: ufan[1] = -c*ufan[0];
867: IsoGasFlux(c,ufan,flux);
868: } else if ((L.rho >= star.rho && L.u-c >= 0) || (L.rho < star.rho && (star.rho*star.u-L.rho*L.u)/(star.rho-L.rho) > 0)) {
869: /* 1-wave is supersonic rarefaction, or supersonic shock */
870: IsoGasFlux(c,uL,flux);
871: } else if ((star.rho <= R.rho && R.u+c <= 0) || (star.rho > R.rho && (R.rho*R.u-star.rho*star.u)/(R.rho-star.rho) < 0)) {
872: /* 2-wave is supersonic rarefaction or supersonic shock */
873: IsoGasFlux(c,uR,flux);
874: } else {
875: ustar[0] = star.rho;
876: ustar[1] = star.rho*star.u;
877: IsoGasFlux(c,ustar,flux);
878: }
879: *maxspeed = MaxAbs(MaxAbs(star.u-c,star.u+c),MaxAbs(L.u-c,R.u+c));
880: return(0);
881: }
883: static PetscErrorCode PhysicsRiemann_IsoGas_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
884: {
885: IsoGasCtx *phys = (IsoGasCtx*)vctx;
886: PetscScalar c = phys->acoustic_speed,fL[2],fR[2],s;
887: struct {PetscScalar rho,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]};
890: if (!(L.rho > 0 && R.rho > 0)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed density is negative");
891: IsoGasFlux(c,uL,fL);
892: IsoGasFlux(c,uR,fR);
893: s = PetscMax(PetscAbs(L.u),PetscAbs(R.u))+c;
894: flux[0] = 0.5*(fL[0] + fR[0]) + 0.5*s*(uL[0] - uR[0]);
895: flux[1] = 0.5*(fL[1] + fR[1]) + 0.5*s*(uL[1] - uR[1]);
896: *maxspeed = s;
897: return(0);
898: }
900: static PetscErrorCode PhysicsCharacteristic_IsoGas(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
901: {
902: IsoGasCtx *phys = (IsoGasCtx*)vctx;
903: PetscReal c = phys->acoustic_speed;
907: speeds[0] = u[1]/u[0] - c;
908: speeds[1] = u[1]/u[0] + c;
909: X[0*2+0] = 1;
910: X[0*2+1] = speeds[0];
911: X[1*2+0] = 1;
912: X[1*2+1] = speeds[1];
913: PetscArraycpy(Xi,X,4);
914: PetscKernel_A_gets_inverse_A_2(Xi,0,PETSC_FALSE,NULL);
915: return(0);
916: }
918: static PetscErrorCode PhysicsCreate_IsoGas(FVCtx *ctx)
919: {
920: PetscErrorCode ierr;
921: IsoGasCtx *user;
922: PetscFunctionList rlist = 0,rclist = 0;
923: char rname[256] = "exact",rcname[256] = "characteristic";
926: PetscNew(&user);
927: ctx->physics.sample = PhysicsSample_IsoGas;
928: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
929: ctx->physics.user = user;
930: ctx->physics.dof = 2;
932: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
933: PetscStrallocpy("momentum",&ctx->physics.fieldname[1]);
935: user->acoustic_speed = 1;
937: RiemannListAdd(&rlist,"exact", PhysicsRiemann_IsoGas_Exact);
938: RiemannListAdd(&rlist,"roe", PhysicsRiemann_IsoGas_Roe);
939: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_IsoGas_Rusanov);
940: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_IsoGas);
941: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
942: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for IsoGas","");
943: PetscOptionsReal("-physics_isogas_acoustic_speed","Acoustic speed","",user->acoustic_speed,&user->acoustic_speed,NULL);
944: PetscOptionsFList("-physics_isogas_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
945: PetscOptionsFList("-physics_isogas_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
946: PetscOptionsEnd();
947: RiemannListFind(rlist,rname,&ctx->physics.riemann);
948: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
949: PetscFunctionListDestroy(&rlist);
950: PetscFunctionListDestroy(&rclist);
951: return(0);
952: }
954: /* --------------------------------- Shallow Water ----------------------------------- */
955: typedef struct {
956: PetscReal gravity;
957: } ShallowCtx;
959: PETSC_STATIC_INLINE void ShallowFlux(ShallowCtx *phys,const PetscScalar *u,PetscScalar *f)
960: {
961: f[0] = u[1];
962: f[1] = PetscSqr(u[1])/u[0] + 0.5*phys->gravity*PetscSqr(u[0]);
963: }
965: static PetscErrorCode PhysicsRiemann_Shallow_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
966: {
967: ShallowCtx *phys = (ShallowCtx*)vctx;
968: PetscScalar g = phys->gravity,ustar[2],cL,cR,c,cstar;
969: struct {PetscScalar h,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]},star;
970: PetscInt i;
973: if (!(L.h > 0 && R.h > 0)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative");
974: cL = PetscSqrtScalar(g*L.h);
975: cR = PetscSqrtScalar(g*R.h);
976: c = PetscMax(cL,cR);
977: {
978: /* Solve for star state */
979: const PetscInt maxits = 50;
980: PetscScalar tmp,res,res0=0,h0,h = 0.5*(L.h + R.h); /* initial guess */
981: h0 = h;
982: for (i=0; i<maxits; i++) {
983: PetscScalar fr,fl,dfr,dfl;
984: fl = (L.h < h)
985: ? PetscSqrtScalar(0.5*g*(h*h - L.h*L.h)*(1/L.h - 1/h)) /* shock */
986: : 2*PetscSqrtScalar(g*h) - 2*PetscSqrtScalar(g*L.h); /* rarefaction */
987: fr = (R.h < h)
988: ? PetscSqrtScalar(0.5*g*(h*h - R.h*R.h)*(1/R.h - 1/h)) /* shock */
989: : 2*PetscSqrtScalar(g*h) - 2*PetscSqrtScalar(g*R.h); /* rarefaction */
990: res = R.u - L.u + fr + fl;
991: if (PetscIsInfOrNanScalar(res)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Infinity or Not-a-Number generated in computation");
992: if (PetscAbsScalar(res) < 1e-8 || (i > 0 && PetscAbsScalar(h-h0) < 1e-8)) {
993: star.h = h;
994: star.u = L.u - fl;
995: goto converged;
996: } else if (i > 0 && PetscAbsScalar(res) >= PetscAbsScalar(res0)) { /* Line search */
997: h = 0.8*h0 + 0.2*h;
998: continue;
999: }
1000: /* Accept the last step and take another */
1001: res0 = res;
1002: h0 = h;
1003: dfl = (L.h < h) ? 0.5/fl*0.5*g*(-L.h*L.h/(h*h) - 1 + 2*h/L.h) : PetscSqrtScalar(g/h);
1004: dfr = (R.h < h) ? 0.5/fr*0.5*g*(-R.h*R.h/(h*h) - 1 + 2*h/R.h) : PetscSqrtScalar(g/h);
1005: tmp = h - res/(dfr+dfl);
1006: if (tmp <= 0) h /= 2; /* Guard against Newton shooting off to a negative thickness */
1007: else h = tmp;
1008: if (!((h > 0) && PetscIsNormalScalar(h))) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP,"non-normal iterate h=%g",(double)h);
1009: }
1010: SETERRQ1(PETSC_COMM_SELF,1,"Newton iteration for star.h diverged after %D iterations",i);
1011: }
1012: converged:
1013: cstar = PetscSqrtScalar(g*star.h);
1014: if (L.u-cL < 0 && 0 < star.u-cstar) { /* 1-wave is sonic rarefaction */
1015: PetscScalar ufan[2];
1016: ufan[0] = 1/g*PetscSqr(L.u/3 + 2./3*cL);
1017: ufan[1] = PetscSqrtScalar(g*ufan[0])*ufan[0];
1018: ShallowFlux(phys,ufan,flux);
1019: } else if (star.u+cstar < 0 && 0 < R.u+cR) { /* 2-wave is sonic rarefaction */
1020: PetscScalar ufan[2];
1021: ufan[0] = 1/g*PetscSqr(R.u/3 - 2./3*cR);
1022: ufan[1] = -PetscSqrtScalar(g*ufan[0])*ufan[0];
1023: ShallowFlux(phys,ufan,flux);
1024: } else if ((L.h >= star.h && L.u-c >= 0) || (L.h<star.h && (star.h*star.u-L.h*L.u)/(star.h-L.h) > 0)) {
1025: /* 1-wave is right-travelling shock (supersonic) */
1026: ShallowFlux(phys,uL,flux);
1027: } else if ((star.h <= R.h && R.u+c <= 0) || (star.h>R.h && (R.h*R.u-star.h*star.h)/(R.h-star.h) < 0)) {
1028: /* 2-wave is left-travelling shock (supersonic) */
1029: ShallowFlux(phys,uR,flux);
1030: } else {
1031: ustar[0] = star.h;
1032: ustar[1] = star.h*star.u;
1033: ShallowFlux(phys,ustar,flux);
1034: }
1035: *maxspeed = MaxAbs(MaxAbs(star.u-cstar,star.u+cstar),MaxAbs(L.u-cL,R.u+cR));
1036: return(0);
1037: }
1039: static PetscErrorCode PhysicsRiemann_Shallow_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
1040: {
1041: ShallowCtx *phys = (ShallowCtx*)vctx;
1042: PetscScalar g = phys->gravity,fL[2],fR[2],s;
1043: struct {PetscScalar h,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]};
1046: if (!(L.h > 0 && R.h > 0)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative");
1047: ShallowFlux(phys,uL,fL);
1048: ShallowFlux(phys,uR,fR);
1049: s = PetscMax(PetscAbs(L.u)+PetscSqrtScalar(g*L.h),PetscAbs(R.u)+PetscSqrtScalar(g*R.h));
1050: flux[0] = 0.5*(fL[0] + fR[0]) + 0.5*s*(uL[0] - uR[0]);
1051: flux[1] = 0.5*(fL[1] + fR[1]) + 0.5*s*(uL[1] - uR[1]);
1052: *maxspeed = s;
1053: return(0);
1054: }
1056: static PetscErrorCode PhysicsCharacteristic_Shallow(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
1057: {
1058: ShallowCtx *phys = (ShallowCtx*)vctx;
1059: PetscReal c;
1063: c = PetscSqrtScalar(u[0]*phys->gravity);
1064: speeds[0] = u[1]/u[0] - c;
1065: speeds[1] = u[1]/u[0] + c;
1066: X[0*2+0] = 1;
1067: X[0*2+1] = speeds[0];
1068: X[1*2+0] = 1;
1069: X[1*2+1] = speeds[1];
1070: PetscArraycpy(Xi,X,4);
1071: PetscKernel_A_gets_inverse_A_2(Xi,0,PETSC_FALSE,NULL);
1072: return(0);
1073: }
1075: static PetscErrorCode PhysicsCreate_Shallow(FVCtx *ctx)
1076: {
1077: PetscErrorCode ierr;
1078: ShallowCtx *user;
1079: PetscFunctionList rlist = 0,rclist = 0;
1080: char rname[256] = "exact",rcname[256] = "characteristic";
1083: PetscNew(&user);
1084: /* Shallow water and Isothermal Gas dynamics are similar so we reuse initial conditions for now */
1085: ctx->physics.sample = PhysicsSample_IsoGas;
1086: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
1087: ctx->physics.user = user;
1088: ctx->physics.dof = 2;
1090: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
1091: PetscStrallocpy("momentum",&ctx->physics.fieldname[1]);
1093: user->gravity = 1;
1095: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Shallow_Exact);
1096: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Shallow_Rusanov);
1097: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_Shallow);
1098: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
1099: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for Shallow","");
1100: PetscOptionsReal("-physics_shallow_gravity","Gravity","",user->gravity,&user->gravity,NULL);
1101: PetscOptionsFList("-physics_shallow_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
1102: PetscOptionsFList("-physics_shallow_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
1103: PetscOptionsEnd();
1104: RiemannListFind(rlist,rname,&ctx->physics.riemann);
1105: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
1106: PetscFunctionListDestroy(&rlist);
1107: PetscFunctionListDestroy(&rclist);
1108: return(0);
1109: }
1111: /* --------------------------------- Finite Volume Solver ----------------------------------- */
1113: static PetscErrorCode FVRHSFunction(TS ts,PetscReal time,Vec X,Vec F,void *vctx)
1114: {
1115: FVCtx *ctx = (FVCtx*)vctx;
1116: PetscErrorCode ierr;
1117: PetscInt i,j,k,Mx,dof,xs,xm;
1118: PetscReal hx,cfl_idt = 0;
1119: PetscScalar *x,*f,*slope;
1120: Vec Xloc;
1121: DM da;
1124: TSGetDM(ts,&da);
1125: DMGetLocalVector(da,&Xloc);
1126: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1127: hx = (ctx->xmax - ctx->xmin)/Mx;
1128: DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
1129: DMGlobalToLocalEnd (da,X,INSERT_VALUES,Xloc);
1131: VecZeroEntries(F);
1133: DMDAVecGetArray(da,Xloc,&x);
1134: DMDAVecGetArray(da,F,&f);
1135: DMDAGetArray(da,PETSC_TRUE,&slope);
1137: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1139: if (ctx->bctype == FVBC_OUTFLOW) {
1140: for (i=xs-2; i<0; i++) {
1141: for (j=0; j<dof; j++) x[i*dof+j] = x[j];
1142: }
1143: for (i=Mx; i<xs+xm+2; i++) {
1144: for (j=0; j<dof; j++) x[i*dof+j] = x[(xs+xm-1)*dof+j];
1145: }
1146: }
1147: for (i=xs-1; i<xs+xm+1; i++) {
1148: struct _LimitInfo info;
1149: PetscScalar *cjmpL,*cjmpR;
1150: /* Determine the right eigenvectors R, where A = R \Lambda R^{-1} */
1151: (*ctx->physics.characteristic)(ctx->physics.user,dof,&x[i*dof],ctx->R,ctx->Rinv,ctx->speeds);
1152: /* Evaluate jumps across interfaces (i-1, i) and (i, i+1), put in characteristic basis */
1153: PetscArrayzero(ctx->cjmpLR,2*dof);
1154: cjmpL = &ctx->cjmpLR[0];
1155: cjmpR = &ctx->cjmpLR[dof];
1156: for (j=0; j<dof; j++) {
1157: PetscScalar jmpL,jmpR;
1158: jmpL = x[(i+0)*dof+j] - x[(i-1)*dof+j];
1159: jmpR = x[(i+1)*dof+j] - x[(i+0)*dof+j];
1160: for (k=0; k<dof; k++) {
1161: cjmpL[k] += ctx->Rinv[k+j*dof] * jmpL;
1162: cjmpR[k] += ctx->Rinv[k+j*dof] * jmpR;
1163: }
1164: }
1165: /* Apply limiter to the left and right characteristic jumps */
1166: info.m = dof;
1167: info.hx = hx;
1168: (*ctx->limit)(&info,cjmpL,cjmpR,ctx->cslope);
1169: for (j=0; j<dof; j++) ctx->cslope[j] /= hx; /* rescale to a slope */
1170: for (j=0; j<dof; j++) {
1171: PetscScalar tmp = 0;
1172: for (k=0; k<dof; k++) tmp += ctx->R[j+k*dof] * ctx->cslope[k];
1173: slope[i*dof+j] = tmp;
1174: }
1175: }
1177: for (i=xs; i<xs+xm+1; i++) {
1178: PetscReal maxspeed;
1179: PetscScalar *uL,*uR;
1180: uL = &ctx->uLR[0];
1181: uR = &ctx->uLR[dof];
1182: for (j=0; j<dof; j++) {
1183: uL[j] = x[(i-1)*dof+j] + slope[(i-1)*dof+j]*hx/2;
1184: uR[j] = x[(i-0)*dof+j] - slope[(i-0)*dof+j]*hx/2;
1185: }
1186: (*ctx->physics.riemann)(ctx->physics.user,dof,uL,uR,ctx->flux,&maxspeed);
1187: cfl_idt = PetscMax(cfl_idt,PetscAbsScalar(maxspeed/hx)); /* Max allowable value of 1/Delta t */
1189: if (i > xs) {
1190: for (j=0; j<dof; j++) f[(i-1)*dof+j] -= ctx->flux[j]/hx;
1191: }
1192: if (i < xs+xm) {
1193: for (j=0; j<dof; j++) f[i*dof+j] += ctx->flux[j]/hx;
1194: }
1195: }
1197: DMDAVecRestoreArray(da,Xloc,&x);
1198: DMDAVecRestoreArray(da,F,&f);
1199: DMDARestoreArray(da,PETSC_TRUE,&slope);
1200: DMRestoreLocalVector(da,&Xloc);
1202: MPI_Allreduce(&cfl_idt,&ctx->cfl_idt,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
1203: if (0) {
1204: /* We need to a way to inform the TS of a CFL constraint, this is a debugging fragment */
1205: PetscReal dt,tnow;
1206: TSGetTimeStep(ts,&dt);
1207: TSGetTime(ts,&tnow);
1208: if (dt > 0.5/ctx->cfl_idt) {
1209: if (1) {
1210: PetscPrintf(ctx->comm,"Stability constraint exceeded at t=%g, dt %g > %g\n",(double)tnow,(double)dt,(double)(0.5/ctx->cfl_idt));
1211: } else SETERRQ2(PETSC_COMM_SELF,1,"Stability constraint exceeded, %g > %g",(double)dt,(double)(ctx->cfl/ctx->cfl_idt));
1212: }
1213: }
1214: return(0);
1215: }
1217: static PetscErrorCode SmallMatMultADB(PetscScalar *C,PetscInt bs,const PetscScalar *A,const PetscReal *D,const PetscScalar *B)
1218: {
1219: PetscInt i,j,k;
1222: for (i=0; i<bs; i++) {
1223: for (j=0; j<bs; j++) {
1224: PetscScalar tmp = 0;
1225: for (k=0; k<bs; k++) tmp += A[i*bs+k] * D[k] * B[k*bs+j];
1226: C[i*bs+j] = tmp;
1227: }
1228: }
1229: return(0);
1230: }
1233: static PetscErrorCode FVIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat A,Mat B,void *vctx)
1234: {
1235: FVCtx *ctx = (FVCtx*)vctx;
1236: PetscErrorCode ierr;
1237: PetscInt i,j,dof = ctx->physics.dof;
1238: PetscScalar *J;
1239: const PetscScalar *x;
1240: PetscReal hx;
1241: DM da;
1242: DMDALocalInfo dainfo;
1245: TSGetDM(ts,&da);
1246: DMDAVecGetArrayRead(da,X,(void*)&x);
1247: DMDAGetLocalInfo(da,&dainfo);
1248: hx = (ctx->xmax - ctx->xmin)/dainfo.mx;
1249: PetscMalloc1(dof*dof,&J);
1250: for (i=dainfo.xs; i<dainfo.xs+dainfo.xm; i++) {
1251: (*ctx->physics.characteristic)(ctx->physics.user,dof,&x[i*dof],ctx->R,ctx->Rinv,ctx->speeds);
1252: for (j=0; j<dof; j++) ctx->speeds[j] = PetscAbs(ctx->speeds[j]);
1253: SmallMatMultADB(J,dof,ctx->R,ctx->speeds,ctx->Rinv);
1254: for (j=0; j<dof*dof; j++) J[j] = J[j]/hx + shift*(j/dof == j%dof);
1255: MatSetValuesBlocked(B,1,&i,1,&i,J,INSERT_VALUES);
1256: }
1257: PetscFree(J);
1258: DMDAVecRestoreArrayRead(da,X,(void*)&x);
1260: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1261: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1262: if (A != B) {
1263: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1264: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1265: }
1266: return(0);
1267: }
1269: static PetscErrorCode FVSample(FVCtx *ctx,DM da,PetscReal time,Vec U)
1270: {
1272: PetscScalar *u,*uj;
1273: PetscInt i,j,k,dof,xs,xm,Mx;
1276: if (!ctx->physics.sample) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Physics has not provided a sampling function");
1277: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1278: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1279: DMDAVecGetArray(da,U,&u);
1280: PetscMalloc1(dof,&uj);
1281: for (i=xs; i<xs+xm; i++) {
1282: const PetscReal h = (ctx->xmax-ctx->xmin)/Mx,xi = ctx->xmin+h/2+i*h;
1283: const PetscInt N = 200;
1284: /* Integrate over cell i using trapezoid rule with N points. */
1285: for (k=0; k<dof; k++) u[i*dof+k] = 0;
1286: for (j=0; j<N+1; j++) {
1287: PetscScalar xj = xi+h*(j-N/2)/(PetscReal)N;
1288: (*ctx->physics.sample)(ctx->physics.user,ctx->initial,ctx->bctype,ctx->xmin,ctx->xmax,time,xj,uj);
1289: for (k=0; k<dof; k++) u[i*dof+k] += ((j==0 || j==N) ? 0.5 : 1.0)*uj[k]/N;
1290: }
1291: }
1292: DMDAVecRestoreArray(da,U,&u);
1293: PetscFree(uj);
1294: return(0);
1295: }
1297: static PetscErrorCode SolutionStatsView(DM da,Vec X,PetscViewer viewer)
1298: {
1299: PetscErrorCode ierr;
1300: PetscReal xmin,xmax;
1301: PetscScalar sum,tvsum,tvgsum;
1302: const PetscScalar *x;
1303: PetscInt imin,imax,Mx,i,j,xs,xm,dof;
1304: Vec Xloc;
1305: PetscBool iascii;
1308: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1309: if (iascii) {
1310: /* PETSc lacks a function to compute total variation norm (difficult in multiple dimensions), we do it here */
1311: DMGetLocalVector(da,&Xloc);
1312: DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
1313: DMGlobalToLocalEnd (da,X,INSERT_VALUES,Xloc);
1314: DMDAVecGetArrayRead(da,Xloc,(void*)&x);
1315: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1316: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1317: tvsum = 0;
1318: for (i=xs; i<xs+xm; i++) {
1319: for (j=0; j<dof; j++) tvsum += PetscAbsScalar(x[i*dof+j] - x[(i-1)*dof+j]);
1320: }
1321: MPI_Allreduce(&tvsum,&tvgsum,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)da));
1322: DMDAVecRestoreArrayRead(da,Xloc,(void*)&x);
1323: DMRestoreLocalVector(da,&Xloc);
1325: VecMin(X,&imin,&xmin);
1326: VecMax(X,&imax,&xmax);
1327: VecSum(X,&sum);
1328: PetscViewerASCIIPrintf(viewer,"Solution range [%8.5f,%8.5f] with extrema at %D and %D, mean %8.5f, ||x||_TV %8.5f\n",(double)xmin,(double)xmax,imin,imax,(double)(sum/Mx),(double)(tvgsum/Mx));
1329: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type not supported");
1330: return(0);
1331: }
1333: static PetscErrorCode SolutionErrorNorms(FVCtx *ctx,DM da,PetscReal t,Vec X,PetscReal *nrm1,PetscReal *nrmsup)
1334: {
1336: Vec Y;
1337: PetscInt Mx;
1340: VecGetSize(X,&Mx);
1341: VecDuplicate(X,&Y);
1342: FVSample(ctx,da,t,Y);
1343: VecAYPX(Y,-1,X);
1344: VecNorm(Y,NORM_1,nrm1);
1345: VecNorm(Y,NORM_INFINITY,nrmsup);
1346: *nrm1 /= Mx;
1347: VecDestroy(&Y);
1348: return(0);
1349: }
1351: int main(int argc,char *argv[])
1352: {
1353: char lname[256] = "mc",physname[256] = "advect",final_fname[256] = "solution.m";
1354: PetscFunctionList limiters = 0,physics = 0;
1355: MPI_Comm comm;
1356: TS ts;
1357: DM da;
1358: Vec X,X0,R;
1359: Mat B;
1360: FVCtx ctx;
1361: PetscInt i,dof,xs,xm,Mx,draw = 0;
1362: PetscBool view_final = PETSC_FALSE;
1363: PetscReal ptime;
1364: PetscErrorCode ierr;
1366: PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
1367: comm = PETSC_COMM_WORLD;
1368: PetscMemzero(&ctx,sizeof(ctx));
1370: /* Register limiters to be available on the command line */
1371: PetscFunctionListAdd(&limiters,"upwind" ,Limit_Upwind);
1372: PetscFunctionListAdd(&limiters,"lax-wendroff" ,Limit_LaxWendroff);
1373: PetscFunctionListAdd(&limiters,"beam-warming" ,Limit_BeamWarming);
1374: PetscFunctionListAdd(&limiters,"fromm" ,Limit_Fromm);
1375: PetscFunctionListAdd(&limiters,"minmod" ,Limit_Minmod);
1376: PetscFunctionListAdd(&limiters,"superbee" ,Limit_Superbee);
1377: PetscFunctionListAdd(&limiters,"mc" ,Limit_MC);
1378: PetscFunctionListAdd(&limiters,"vanleer" ,Limit_VanLeer);
1379: PetscFunctionListAdd(&limiters,"vanalbada" ,Limit_VanAlbada);
1380: PetscFunctionListAdd(&limiters,"vanalbadatvd" ,Limit_VanAlbadaTVD);
1381: PetscFunctionListAdd(&limiters,"koren" ,Limit_Koren);
1382: PetscFunctionListAdd(&limiters,"korensym" ,Limit_KorenSym);
1383: PetscFunctionListAdd(&limiters,"koren3" ,Limit_Koren3);
1384: PetscFunctionListAdd(&limiters,"cada-torrilhon2" ,Limit_CadaTorrilhon2);
1385: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r0p1",Limit_CadaTorrilhon3R0p1);
1386: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r1" ,Limit_CadaTorrilhon3R1);
1387: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r10" ,Limit_CadaTorrilhon3R10);
1388: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r100",Limit_CadaTorrilhon3R100);
1390: /* Register physical models to be available on the command line */
1391: PetscFunctionListAdd(&physics,"advect" ,PhysicsCreate_Advect);
1392: PetscFunctionListAdd(&physics,"burgers" ,PhysicsCreate_Burgers);
1393: PetscFunctionListAdd(&physics,"traffic" ,PhysicsCreate_Traffic);
1394: PetscFunctionListAdd(&physics,"acoustics" ,PhysicsCreate_Acoustics);
1395: PetscFunctionListAdd(&physics,"isogas" ,PhysicsCreate_IsoGas);
1396: PetscFunctionListAdd(&physics,"shallow" ,PhysicsCreate_Shallow);
1398: ctx.comm = comm;
1399: ctx.cfl = 0.9; ctx.bctype = FVBC_PERIODIC;
1400: ctx.xmin = -1; ctx.xmax = 1;
1401: PetscOptionsBegin(comm,NULL,"Finite Volume solver options","");
1402: PetscOptionsReal("-xmin","X min","",ctx.xmin,&ctx.xmin,NULL);
1403: PetscOptionsReal("-xmax","X max","",ctx.xmax,&ctx.xmax,NULL);
1404: PetscOptionsFList("-limit","Name of flux limiter to use","",limiters,lname,lname,sizeof(lname),NULL);
1405: PetscOptionsFList("-physics","Name of physics (Riemann solver and characteristics) to use","",physics,physname,physname,sizeof(physname),NULL);
1406: PetscOptionsInt("-draw","Draw solution vector, bitwise OR of (1=initial,2=final,4=final error)","",draw,&draw,NULL);
1407: PetscOptionsString("-view_final","Write final solution in ASCII MATLAB format to given file name","",final_fname,final_fname,sizeof(final_fname),&view_final);
1408: PetscOptionsInt("-initial","Initial condition (depends on the physics)","",ctx.initial,&ctx.initial,NULL);
1409: PetscOptionsBool("-exact","Compare errors with exact solution","",ctx.exact,&ctx.exact,NULL);
1410: PetscOptionsReal("-cfl","CFL number to time step at","",ctx.cfl,&ctx.cfl,NULL);
1411: PetscOptionsEnum("-bc_type","Boundary condition","",FVBCTypes,(PetscEnum)ctx.bctype,(PetscEnum*)&ctx.bctype,NULL);
1412: PetscOptionsEnd();
1414: /* Choose the limiter from the list of registered limiters */
1415: PetscFunctionListFind(limiters,lname,&ctx.limit);
1416: if (!ctx.limit) SETERRQ1(PETSC_COMM_SELF,1,"Limiter '%s' not found",lname);
1418: /* Choose the physics from the list of registered models */
1419: {
1420: PetscErrorCode (*r)(FVCtx*);
1421: PetscFunctionListFind(physics,physname,&r);
1422: if (!r) SETERRQ1(PETSC_COMM_SELF,1,"Physics '%s' not found",physname);
1423: /* Create the physics, will set the number of fields and their names */
1424: (*r)(&ctx);
1425: }
1427: /* Create a DMDA to manage the parallel grid */
1428: DMDACreate1d(comm,DM_BOUNDARY_PERIODIC,50,ctx.physics.dof,2,NULL,&da);
1429: DMSetFromOptions(da);
1430: DMSetUp(da);
1431: /* Inform the DMDA of the field names provided by the physics. */
1432: /* The names will be shown in the title bars when run with -ts_monitor_draw_solution */
1433: for (i=0; i<ctx.physics.dof; i++) {
1434: DMDASetFieldName(da,i,ctx.physics.fieldname[i]);
1435: }
1436: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1437: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1439: /* Set coordinates of cell centers */
1440: DMDASetUniformCoordinates(da,ctx.xmin+0.5*(ctx.xmax-ctx.xmin)/Mx,ctx.xmax+0.5*(ctx.xmax-ctx.xmin)/Mx,0,0,0,0);
1442: /* Allocate work space for the Finite Volume solver (so it doesn't have to be reallocated on each function evaluation) */
1443: PetscMalloc4(dof*dof,&ctx.R,dof*dof,&ctx.Rinv,2*dof,&ctx.cjmpLR,1*dof,&ctx.cslope);
1444: PetscMalloc3(2*dof,&ctx.uLR,dof,&ctx.flux,dof,&ctx.speeds);
1446: /* Create a vector to store the solution and to save the initial state */
1447: DMCreateGlobalVector(da,&X);
1448: VecDuplicate(X,&X0);
1449: VecDuplicate(X,&R);
1451: DMCreateMatrix(da,&B);
1453: /* Create a time-stepping object */
1454: TSCreate(comm,&ts);
1455: TSSetDM(ts,da);
1456: TSSetRHSFunction(ts,R,FVRHSFunction,&ctx);
1457: TSSetIJacobian(ts,B,B,FVIJacobian,&ctx);
1458: TSSetType(ts,TSSSP);
1459: TSSetMaxTime(ts,10);
1460: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1462: /* Compute initial conditions and starting time step */
1463: FVSample(&ctx,da,0,X0);
1464: FVRHSFunction(ts,0,X0,X,(void*)&ctx); /* Initial function evaluation, only used to determine max speed */
1465: VecCopy(X0,X); /* The function value was not used so we set X=X0 again */
1466: TSSetTimeStep(ts,ctx.cfl/ctx.cfl_idt);
1467: TSSetFromOptions(ts); /* Take runtime options */
1468: SolutionStatsView(da,X,PETSC_VIEWER_STDOUT_WORLD);
1469: {
1470: PetscReal nrm1,nrmsup;
1471: PetscInt steps;
1473: TSSolve(ts,X);
1474: TSGetSolveTime(ts,&ptime);
1475: TSGetStepNumber(ts,&steps);
1477: PetscPrintf(comm,"Final time %8.5f, steps %D\n",(double)ptime,steps);
1478: if (ctx.exact) {
1479: SolutionErrorNorms(&ctx,da,ptime,X,&nrm1,&nrmsup);
1480: PetscPrintf(comm,"Error ||x-x_e||_1 %8.4e ||x-x_e||_sup %8.4e\n",(double)nrm1,(double)nrmsup);
1481: }
1482: }
1484: SolutionStatsView(da,X,PETSC_VIEWER_STDOUT_WORLD);
1485: if (draw & 0x1) {VecView(X0,PETSC_VIEWER_DRAW_WORLD);}
1486: if (draw & 0x2) {VecView(X,PETSC_VIEWER_DRAW_WORLD);}
1487: if (draw & 0x4) {
1488: Vec Y;
1489: VecDuplicate(X,&Y);
1490: FVSample(&ctx,da,ptime,Y);
1491: VecAYPX(Y,-1,X);
1492: VecView(Y,PETSC_VIEWER_DRAW_WORLD);
1493: VecDestroy(&Y);
1494: }
1496: if (view_final) {
1497: PetscViewer viewer;
1498: PetscViewerASCIIOpen(PETSC_COMM_WORLD,final_fname,&viewer);
1499: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
1500: VecView(X,viewer);
1501: PetscViewerPopFormat(viewer);
1502: PetscViewerDestroy(&viewer);
1503: }
1505: /* Clean up */
1506: (*ctx.physics.destroy)(ctx.physics.user);
1507: for (i=0; i<ctx.physics.dof; i++) {PetscFree(ctx.physics.fieldname[i]);}
1508: PetscFree4(ctx.R,ctx.Rinv,ctx.cjmpLR,ctx.cslope);
1509: PetscFree3(ctx.uLR,ctx.flux,ctx.speeds);
1510: VecDestroy(&X);
1511: VecDestroy(&X0);
1512: VecDestroy(&R);
1513: MatDestroy(&B);
1514: DMDestroy(&da);
1515: TSDestroy(&ts);
1516: PetscFunctionListDestroy(&limiters);
1517: PetscFunctionListDestroy(&physics);
1518: PetscFinalize();
1519: return ierr;
1520: }
1522: /*TEST
1524: build:
1525: requires: !complex c99
1527: test:
1528: args: -da_grid_x 100 -initial 1 -xmin -2 -xmax 5 -exact -limit mc
1529: requires: !complex !single
1531: test:
1532: suffix: 2
1533: args: -da_grid_x 100 -initial 2 -xmin -2 -xmax 2 -exact -limit mc -physics burgers -bc_type outflow -ts_max_time 1
1534: filter: sed "s/at 48/at 0/g"
1535: requires: !complex !single
1537: test:
1538: suffix: 3
1539: args: -da_grid_x 100 -initial 2 -xmin -2 -xmax 2 -exact -limit mc -physics burgers -bc_type outflow -ts_max_time 1
1540: nsize: 3
1541: filter: sed "s/at 48/at 0/g"
1542: requires: !complex !single
1544: TEST*/