Actual source code: ex9.c
petsc-3.8.4 2018-03-24
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> /* For the Kernel_*_gets_* stuff for BAIJ */
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,1,"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: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
316: }
317: return(0);
318: }
320: static PetscErrorCode PhysicsCreate_Advect(FVCtx *ctx)
321: {
323: AdvectCtx *user;
326: PetscNew(&user);
327: ctx->physics.sample = PhysicsSample_Advect;
328: ctx->physics.riemann = PhysicsRiemann_Advect;
329: ctx->physics.characteristic = PhysicsCharacteristic_Advect;
330: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
331: ctx->physics.user = user;
332: ctx->physics.dof = 1;
333: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
334: user->a = 1;
335: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for advection","");
336: {
337: PetscOptionsReal("-physics_advect_a","Speed","",user->a,&user->a,NULL);
338: }
339: PetscOptionsEnd();
340: return(0);
341: }
343: /* --------------------------------- Burgers ----------------------------------- */
345: typedef struct {
346: PetscReal lxf_speed;
347: } BurgersCtx;
349: static PetscErrorCode PhysicsSample_Burgers(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
350: {
352: if (bctype == FVBC_PERIODIC && t > 0) SETERRQ(PETSC_COMM_SELF,1,"Exact solution not implemented for periodic");
353: switch (initial) {
354: case 0: u[0] = (x < 0) ? 1 : -1; break;
355: case 1:
356: if (x < -t) u[0] = -1;
357: else if (x < t) u[0] = x/t;
358: else u[0] = 1;
359: break;
360: case 2:
361: if (x < 0) u[0] = 0;
362: else if (x <= t) u[0] = x/t;
363: else if (x < 1+0.5*t) u[0] = 1;
364: else u[0] = 0;
365: break;
366: case 3:
367: if (x < 0.2*t) u[0] = 0.2;
368: else if (x < t) u[0] = x/t;
369: else u[0] = 1;
370: break;
371: case 4:
372: if (t > 0) SETERRQ(PETSC_COMM_SELF,1,"Only initial condition available");
373: u[0] = 0.7 + 0.3*PetscSinReal(2*PETSC_PI*((x-xmin)/(xmax-xmin)));
374: break;
375: case 5: /* Pure shock solution */
376: if (x < 0.5*t) u[0] = 1;
377: else u[0] = 0;
378: break;
379: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
380: }
381: return(0);
382: }
384: static PetscErrorCode PhysicsRiemann_Burgers_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
385: {
387: if (uL[0] < uR[0]) { /* rarefaction */
388: flux[0] = (uL[0]*uR[0] < 0)
389: ? 0 /* sonic rarefaction */
390: : 0.5*PetscMin(PetscSqr(uL[0]),PetscSqr(uR[0]));
391: } else { /* shock */
392: flux[0] = 0.5*PetscMax(PetscSqr(uL[0]),PetscSqr(uR[0]));
393: }
394: *maxspeed = (PetscAbs(uL[0]) > PetscAbs(uR[0])) ? uL[0] : uR[0];
395: return(0);
396: }
398: static PetscErrorCode PhysicsRiemann_Burgers_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
399: {
400: PetscReal speed;
403: speed = 0.5*(uL[0] + uR[0]);
404: flux[0] = 0.25*(PetscSqr(uL[0]) + PetscSqr(uR[0])) - 0.5*PetscAbs(speed)*(uR[0]-uL[0]);
405: if (uL[0] <= 0 && 0 <= uR[0]) flux[0] = 0; /* Entropy fix for sonic rarefaction */
406: *maxspeed = speed;
407: return(0);
408: }
410: static PetscErrorCode PhysicsRiemann_Burgers_LxF(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
411: {
412: PetscReal c;
413: PetscScalar fL,fR;
416: c = ((BurgersCtx*)vctx)->lxf_speed;
417: fL = 0.5*PetscSqr(uL[0]);
418: fR = 0.5*PetscSqr(uR[0]);
419: flux[0] = 0.5*(fL + fR) - 0.5*c*(uR[0] - uL[0]);
420: *maxspeed = c;
421: return(0);
422: }
424: static PetscErrorCode PhysicsRiemann_Burgers_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
425: {
426: PetscReal c;
427: PetscScalar fL,fR;
430: c = PetscMax(PetscAbs(uL[0]),PetscAbs(uR[0]));
431: fL = 0.5*PetscSqr(uL[0]);
432: fR = 0.5*PetscSqr(uR[0]);
433: flux[0] = 0.5*(fL + fR) - 0.5*c*(uR[0] - uL[0]);
434: *maxspeed = c;
435: return(0);
436: }
438: static PetscErrorCode PhysicsCreate_Burgers(FVCtx *ctx)
439: {
440: BurgersCtx *user;
441: PetscErrorCode ierr;
442: RiemannFunction r;
443: PetscFunctionList rlist = 0;
444: char rname[256] = "exact";
447: PetscNew(&user);
449: ctx->physics.sample = PhysicsSample_Burgers;
450: ctx->physics.characteristic = PhysicsCharacteristic_Conservative;
451: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
452: ctx->physics.user = user;
453: ctx->physics.dof = 1;
455: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
456: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Burgers_Exact);
457: RiemannListAdd(&rlist,"roe", PhysicsRiemann_Burgers_Roe);
458: RiemannListAdd(&rlist,"lxf", PhysicsRiemann_Burgers_LxF);
459: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Burgers_Rusanov);
460: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for advection","");
461: {
462: PetscOptionsFList("-physics_burgers_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
463: }
464: PetscOptionsEnd();
465: RiemannListFind(rlist,rname,&r);
466: PetscFunctionListDestroy(&rlist);
467: ctx->physics.riemann = r;
469: /* *
470: * Hack to deal with LxF in semi-discrete form
471: * max speed is 1 for the basic initial conditions (where |u| <= 1)
472: * */
473: if (r == PhysicsRiemann_Burgers_LxF) user->lxf_speed = 1;
474: return(0);
475: }
477: /* --------------------------------- Traffic ----------------------------------- */
479: typedef struct {
480: PetscReal lxf_speed;
481: PetscReal a;
482: } TrafficCtx;
484: PETSC_STATIC_INLINE PetscScalar TrafficFlux(PetscScalar a,PetscScalar u) { return a*u*(1-u); }
486: static PetscErrorCode PhysicsSample_Traffic(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
487: {
488: PetscReal a = ((TrafficCtx*)vctx)->a;
491: if (bctype == FVBC_PERIODIC && t > 0) SETERRQ(PETSC_COMM_SELF,1,"Exact solution not implemented for periodic");
492: switch (initial) {
493: case 0:
494: u[0] = (-a*t < x) ? 2 : 0; break;
495: case 1:
496: if (x < PetscMin(2*a*t,0.5+a*t)) u[0] = -1;
497: else if (x < 1) u[0] = 0;
498: else u[0] = 1;
499: break;
500: case 2:
501: if (t > 0) SETERRQ(PETSC_COMM_SELF,1,"Only initial condition available");
502: u[0] = 0.7 + 0.3*PetscSinReal(2*PETSC_PI*((x-xmin)/(xmax-xmin)));
503: break;
504: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
505: }
506: return(0);
507: }
509: static PetscErrorCode PhysicsRiemann_Traffic_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
510: {
511: PetscReal a = ((TrafficCtx*)vctx)->a;
514: if (uL[0] < uR[0]) {
515: flux[0] = PetscMin(TrafficFlux(a,uL[0]),TrafficFlux(a,uR[0]));
516: } else {
517: flux[0] = (uR[0] < 0.5 && 0.5 < uL[0]) ? TrafficFlux(a,0.5) : PetscMax(TrafficFlux(a,uL[0]),TrafficFlux(a,uR[0]));
518: }
519: *maxspeed = a*MaxAbs(1-2*uL[0],1-2*uR[0]);
520: return(0);
521: }
523: static PetscErrorCode PhysicsRiemann_Traffic_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
524: {
525: PetscReal a = ((TrafficCtx*)vctx)->a;
526: PetscReal speed;
529: speed = a*(1 - (uL[0] + uR[0]));
530: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*PetscAbs(speed)*(uR[0]-uL[0]);
531: *maxspeed = speed;
532: return(0);
533: }
535: static PetscErrorCode PhysicsRiemann_Traffic_LxF(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
536: {
537: TrafficCtx *phys = (TrafficCtx*)vctx;
538: PetscReal a = phys->a;
539: PetscReal speed;
542: speed = a*(1 - (uL[0] + uR[0]));
543: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*phys->lxf_speed*(uR[0]-uL[0]);
544: *maxspeed = speed;
545: return(0);
546: }
548: static PetscErrorCode PhysicsRiemann_Traffic_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
549: {
550: PetscReal a = ((TrafficCtx*)vctx)->a;
551: PetscReal speed;
554: speed = a*PetscMax(PetscAbs(1-2*uL[0]),PetscAbs(1-2*uR[0]));
555: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*speed*(uR[0]-uL[0]);
556: *maxspeed = speed;
557: return(0);
558: }
560: static PetscErrorCode PhysicsCreate_Traffic(FVCtx *ctx)
561: {
562: PetscErrorCode ierr;
563: TrafficCtx *user;
564: RiemannFunction r;
565: PetscFunctionList rlist = 0;
566: char rname[256] = "exact";
569: PetscNew(&user);
570: ctx->physics.sample = PhysicsSample_Traffic;
571: ctx->physics.characteristic = PhysicsCharacteristic_Conservative;
572: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
573: ctx->physics.user = user;
574: ctx->physics.dof = 1;
576: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
577: user->a = 0.5;
578: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Traffic_Exact);
579: RiemannListAdd(&rlist,"roe", PhysicsRiemann_Traffic_Roe);
580: RiemannListAdd(&rlist,"lxf", PhysicsRiemann_Traffic_LxF);
581: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Traffic_Rusanov);
582: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for Traffic","");
583: PetscOptionsReal("-physics_traffic_a","Flux = a*u*(1-u)","",user->a,&user->a,NULL);
584: PetscOptionsFList("-physics_traffic_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
585: PetscOptionsEnd();
587: RiemannListFind(rlist,rname,&r);
588: PetscFunctionListDestroy(&rlist);
590: ctx->physics.riemann = r;
592: /* *
593: * Hack to deal with LxF in semi-discrete form
594: * max speed is 3*a for the basic initial conditions (-1 <= u <= 2)
595: * */
596: if (r == PhysicsRiemann_Traffic_LxF) user->lxf_speed = 3*user->a;
597: return(0);
598: }
600: /* --------------------------------- Linear Acoustics ----------------------------------- */
602: /* Flux: u_t + (A u)_x
603: * z = sqrt(rho*bulk), c = sqrt(rho/bulk)
604: * Spectral decomposition: A = R * D * Rinv
605: * [ cz] = [-z z] [-c ] [-1/2z 1/2]
606: * [c/z ] = [ 1 1] [ c] [ 1/2z 1/2]
607: *
608: * We decompose this into the left-traveling waves Al = R * D^- Rinv
609: * and the right-traveling waves Ar = R * D^+ * Rinv
610: * Multiplying out these expressions produces the following two matrices
611: */
613: typedef struct {
614: PetscReal c; /* speed of sound: c = sqrt(bulk/rho) */
615: PetscReal z; /* impedence: z = sqrt(rho*bulk) */
616: } AcousticsCtx;
618: PETSC_UNUSED PETSC_STATIC_INLINE void AcousticsFlux(AcousticsCtx *ctx,const PetscScalar *u,PetscScalar *f)
619: {
620: f[0] = ctx->c*ctx->z*u[1];
621: f[1] = ctx->c/ctx->z*u[0];
622: }
624: static PetscErrorCode PhysicsCharacteristic_Acoustics(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
625: {
626: AcousticsCtx *phys = (AcousticsCtx*)vctx;
627: PetscReal z = phys->z,c = phys->c;
630: X[0*2+0] = -z;
631: X[0*2+1] = z;
632: X[1*2+0] = 1;
633: X[1*2+1] = 1;
634: Xi[0*2+0] = -1./(2*z);
635: Xi[0*2+1] = 1./2;
636: Xi[1*2+0] = 1./(2*z);
637: Xi[1*2+1] = 1./2;
638: speeds[0] = -c;
639: speeds[1] = c;
640: return(0);
641: }
643: static PetscErrorCode PhysicsSample_Acoustics_Initial(AcousticsCtx *phys,PetscInt initial,PetscReal xmin,PetscReal xmax,PetscReal x,PetscReal *u)
644: {
646: switch (initial) {
647: case 0:
648: u[0] = (PetscAbs((x - xmin)/(xmax - xmin) - 0.2) < 0.1) ? 1 : 0.5;
649: u[1] = (PetscAbs((x - xmin)/(xmax - xmin) - 0.7) < 0.1) ? 1 : -0.5;
650: break;
651: case 1:
652: u[0] = PetscCosReal(3 * 2*PETSC_PI*x/(xmax-xmin));
653: u[1] = PetscExpReal(-PetscSqr(x - (xmax + xmin)/2) / (2*PetscSqr(0.2*(xmax - xmin)))) - 0.5;
654: break;
655: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
656: }
657: return(0);
658: }
660: static PetscErrorCode PhysicsSample_Acoustics(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
661: {
662: AcousticsCtx *phys = (AcousticsCtx*)vctx;
663: PetscReal c = phys->c;
664: PetscReal x0a,x0b,u0a[2],u0b[2],tmp[2];
665: PetscReal X[2][2],Xi[2][2],dummy[2];
669: switch (bctype) {
670: case FVBC_OUTFLOW:
671: x0a = x+c*t;
672: x0b = x-c*t;
673: break;
674: case FVBC_PERIODIC:
675: x0a = RangeMod(x+c*t,xmin,xmax);
676: x0b = RangeMod(x-c*t,xmin,xmax);
677: break;
678: default: SETERRQ(PETSC_COMM_SELF,1,"unknown BCType");
679: }
680: PhysicsSample_Acoustics_Initial(phys,initial,xmin,xmax,x0a,u0a);
681: PhysicsSample_Acoustics_Initial(phys,initial,xmin,xmax,x0b,u0b);
682: PhysicsCharacteristic_Acoustics(vctx,2,u,&X[0][0],&Xi[0][0],dummy);
683: tmp[0] = Xi[0][0]*u0a[0] + Xi[0][1]*u0a[1];
684: tmp[1] = Xi[1][0]*u0b[0] + Xi[1][1]*u0b[1];
685: u[0] = X[0][0]*tmp[0] + X[0][1]*tmp[1];
686: u[1] = X[1][0]*tmp[0] + X[1][1]*tmp[1];
687: return(0);
688: }
690: static PetscErrorCode PhysicsRiemann_Acoustics_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
691: {
692: AcousticsCtx *phys = (AcousticsCtx*)vctx;
693: PetscReal c = phys->c,z = phys->z;
694: PetscReal
695: Al[2][2] = {{-c/2 , c*z/2 },
696: {c/(2*z) , -c/2 }}, /* Left traveling waves */
697: Ar[2][2] = {{c/2 , c*z/2 },
698: {c/(2*z) , c/2 }}; /* Right traveling waves */
701: flux[0] = Al[0][0]*uR[0] + Al[0][1]*uR[1] + Ar[0][0]*uL[0] + Ar[0][1]*uL[1];
702: flux[1] = Al[1][0]*uR[0] + Al[1][1]*uR[1] + Ar[1][0]*uL[0] + Ar[1][1]*uL[1];
703: *maxspeed = c;
704: return(0);
705: }
707: static PetscErrorCode PhysicsCreate_Acoustics(FVCtx *ctx)
708: {
709: PetscErrorCode ierr;
710: AcousticsCtx *user;
711: PetscFunctionList rlist = 0,rclist = 0;
712: char rname[256] = "exact",rcname[256] = "characteristic";
715: PetscNew(&user);
716: ctx->physics.sample = PhysicsSample_Acoustics;
717: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
718: ctx->physics.user = user;
719: ctx->physics.dof = 2;
721: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
722: PetscStrallocpy("v",&ctx->physics.fieldname[1]);
724: user->c = 1;
725: user->z = 1;
727: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Acoustics_Exact);
728: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_Acoustics);
729: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
730: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for linear Acoustics","");
731: {
732: PetscOptionsReal("-physics_acoustics_c","c = sqrt(bulk/rho)","",user->c,&user->c,NULL);
733: PetscOptionsReal("-physics_acoustics_z","z = sqrt(bulk*rho)","",user->z,&user->z,NULL);
734: PetscOptionsFList("-physics_acoustics_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
735: PetscOptionsFList("-physics_acoustics_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
736: }
737: PetscOptionsEnd();
738: RiemannListFind(rlist,rname,&ctx->physics.riemann);
739: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
740: PetscFunctionListDestroy(&rlist);
741: PetscFunctionListDestroy(&rclist);
742: return(0);
743: }
745: /* --------------------------------- Isothermal Gas Dynamics ----------------------------------- */
747: typedef struct {
748: PetscReal acoustic_speed;
749: } IsoGasCtx;
751: PETSC_STATIC_INLINE void IsoGasFlux(PetscReal c,const PetscScalar *u,PetscScalar *f)
752: {
753: f[0] = u[1];
754: f[1] = PetscSqr(u[1])/u[0] + c*c*u[0];
755: }
757: static PetscErrorCode PhysicsSample_IsoGas(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
758: {
760: if (t > 0) SETERRQ(PETSC_COMM_SELF,1,"Exact solutions not implemented for t > 0");
761: switch (initial) {
762: case 0:
763: u[0] = (x < 0) ? 1 : 0.5;
764: u[1] = (x < 0) ? 1 : 0.7;
765: break;
766: case 1:
767: u[0] = 1+0.5*PetscSinReal(2*PETSC_PI*x);
768: u[1] = 1*u[0];
769: break;
770: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
771: }
772: return(0);
773: }
775: static PetscErrorCode PhysicsRiemann_IsoGas_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
776: {
777: IsoGasCtx *phys = (IsoGasCtx*)vctx;
778: PetscReal c = phys->acoustic_speed;
779: PetscScalar ubar,du[2],a[2],fL[2],fR[2],lam[2],ustar[2],R[2][2];
780: PetscInt i;
783: ubar = (uL[1]/PetscSqrtScalar(uL[0]) + uR[1]/PetscSqrtScalar(uR[0])) / (PetscSqrtScalar(uL[0]) + PetscSqrtScalar(uR[0]));
784: /* write fluxuations in characteristic basis */
785: du[0] = uR[0] - uL[0];
786: du[1] = uR[1] - uL[1];
787: a[0] = (1/(2*c)) * ((ubar + c)*du[0] - du[1]);
788: a[1] = (1/(2*c)) * ((-ubar + c)*du[0] + du[1]);
789: /* wave speeds */
790: lam[0] = ubar - c;
791: lam[1] = ubar + c;
792: /* Right eigenvectors */
793: R[0][0] = 1; R[0][1] = ubar-c;
794: R[1][0] = 1; R[1][1] = ubar+c;
795: /* Compute state in star region (between the 1-wave and 2-wave) */
796: for (i=0; i<2; i++) ustar[i] = uL[i] + a[0]*R[0][i];
797: if (uL[1]/uL[0] < c && c < ustar[1]/ustar[0]) { /* 1-wave is sonic rarefaction */
798: PetscScalar ufan[2];
799: ufan[0] = uL[0]*PetscExpScalar(uL[1]/(uL[0]*c) - 1);
800: ufan[1] = c*ufan[0];
801: IsoGasFlux(c,ufan,flux);
802: } else if (ustar[1]/ustar[0] < -c && -c < uR[1]/uR[0]) { /* 2-wave is sonic rarefaction */
803: PetscScalar ufan[2];
804: ufan[0] = uR[0]*PetscExpScalar(-uR[1]/(uR[0]*c) - 1);
805: ufan[1] = -c*ufan[0];
806: IsoGasFlux(c,ufan,flux);
807: } else { /* Centered form */
808: IsoGasFlux(c,uL,fL);
809: IsoGasFlux(c,uR,fR);
810: for (i=0; i<2; i++) {
811: PetscScalar absdu = PetscAbsScalar(lam[0])*a[0]*R[0][i] + PetscAbsScalar(lam[1])*a[1]*R[1][i];
812: flux[i] = 0.5*(fL[i]+fR[i]) - 0.5*absdu;
813: }
814: }
815: *maxspeed = MaxAbs(lam[0],lam[1]);
816: return(0);
817: }
819: static PetscErrorCode PhysicsRiemann_IsoGas_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
820: {
821: IsoGasCtx *phys = (IsoGasCtx*)vctx;
822: PetscReal c = phys->acoustic_speed;
823: PetscScalar ustar[2];
824: struct {PetscScalar rho,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]},star;
825: PetscInt i;
828: if (!(L.rho > 0 && R.rho > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed density is negative");
829: {
830: /* Solve for star state */
831: PetscScalar res,tmp,rho = 0.5*(L.rho + R.rho); /* initial guess */
832: for (i=0; i<20; i++) {
833: PetscScalar fr,fl,dfr,dfl;
834: fl = (L.rho < rho)
835: ? (rho-L.rho)/PetscSqrtScalar(L.rho*rho) /* shock */
836: : PetscLogScalar(rho) - PetscLogScalar(L.rho); /* rarefaction */
837: fr = (R.rho < rho)
838: ? (rho-R.rho)/PetscSqrtScalar(R.rho*rho) /* shock */
839: : PetscLogScalar(rho) - PetscLogScalar(R.rho); /* rarefaction */
840: res = R.u-L.u + c*(fr+fl);
841: if (PetscIsInfOrNanScalar(res)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Infinity or Not-a-Number generated in computation");
842: if (PetscAbsScalar(res) < 1e-10) {
843: star.rho = rho;
844: star.u = L.u - c*fl;
845: goto converged;
846: }
847: dfl = (L.rho < rho) ? 1/PetscSqrtScalar(L.rho*rho)*(1 - 0.5*(rho-L.rho)/rho) : 1/rho;
848: dfr = (R.rho < rho) ? 1/PetscSqrtScalar(R.rho*rho)*(1 - 0.5*(rho-R.rho)/rho) : 1/rho;
849: tmp = rho - res/(c*(dfr+dfl));
850: if (tmp <= 0) rho /= 2; /* Guard against Newton shooting off to a negative density */
851: else rho = tmp;
852: if (!((rho > 0) && PetscIsNormalScalar(rho))) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP,"non-normal iterate rho=%g",(double)PetscRealPart(rho));
853: }
854: SETERRQ1(PETSC_COMM_SELF,1,"Newton iteration for star.rho diverged after %D iterations",i);
855: }
856: converged:
857: if (L.u-c < 0 && 0 < star.u-c) { /* 1-wave is sonic rarefaction */
858: PetscScalar ufan[2];
859: ufan[0] = L.rho*PetscExpScalar(L.u/c - 1);
860: ufan[1] = c*ufan[0];
861: IsoGasFlux(c,ufan,flux);
862: } else if (star.u+c < 0 && 0 < R.u+c) { /* 2-wave is sonic rarefaction */
863: PetscScalar ufan[2];
864: ufan[0] = R.rho*PetscExpScalar(-R.u/c - 1);
865: ufan[1] = -c*ufan[0];
866: IsoGasFlux(c,ufan,flux);
867: } 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)) {
868: /* 1-wave is supersonic rarefaction, or supersonic shock */
869: IsoGasFlux(c,uL,flux);
870: } 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)) {
871: /* 2-wave is supersonic rarefaction or supersonic shock */
872: IsoGasFlux(c,uR,flux);
873: } else {
874: ustar[0] = star.rho;
875: ustar[1] = star.rho*star.u;
876: IsoGasFlux(c,ustar,flux);
877: }
878: *maxspeed = MaxAbs(MaxAbs(star.u-c,star.u+c),MaxAbs(L.u-c,R.u+c));
879: return(0);
880: }
882: static PetscErrorCode PhysicsRiemann_IsoGas_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
883: {
884: IsoGasCtx *phys = (IsoGasCtx*)vctx;
885: PetscScalar c = phys->acoustic_speed,fL[2],fR[2],s;
886: struct {PetscScalar rho,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]};
889: if (!(L.rho > 0 && R.rho > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed density is negative");
890: IsoGasFlux(c,uL,fL);
891: IsoGasFlux(c,uR,fR);
892: s = PetscMax(PetscAbs(L.u),PetscAbs(R.u))+c;
893: flux[0] = 0.5*(fL[0] + fR[0]) + 0.5*s*(uL[0] - uR[0]);
894: flux[1] = 0.5*(fL[1] + fR[1]) + 0.5*s*(uL[1] - uR[1]);
895: *maxspeed = s;
896: return(0);
897: }
899: static PetscErrorCode PhysicsCharacteristic_IsoGas(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
900: {
901: IsoGasCtx *phys = (IsoGasCtx*)vctx;
902: PetscReal c = phys->acoustic_speed;
906: speeds[0] = u[1]/u[0] - c;
907: speeds[1] = u[1]/u[0] + c;
908: X[0*2+0] = 1;
909: X[0*2+1] = speeds[0];
910: X[1*2+0] = 1;
911: X[1*2+1] = speeds[1];
912: PetscMemcpy(Xi,X,4*sizeof(X[0]));
913: PetscKernel_A_gets_inverse_A_2(Xi,0,PETSC_FALSE,NULL);
914: return(0);
915: }
917: static PetscErrorCode PhysicsCreate_IsoGas(FVCtx *ctx)
918: {
919: PetscErrorCode ierr;
920: IsoGasCtx *user;
921: PetscFunctionList rlist = 0,rclist = 0;
922: char rname[256] = "exact",rcname[256] = "characteristic";
925: PetscNew(&user);
926: ctx->physics.sample = PhysicsSample_IsoGas;
927: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
928: ctx->physics.user = user;
929: ctx->physics.dof = 2;
931: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
932: PetscStrallocpy("momentum",&ctx->physics.fieldname[1]);
934: user->acoustic_speed = 1;
936: RiemannListAdd(&rlist,"exact", PhysicsRiemann_IsoGas_Exact);
937: RiemannListAdd(&rlist,"roe", PhysicsRiemann_IsoGas_Roe);
938: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_IsoGas_Rusanov);
939: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_IsoGas);
940: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
941: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for IsoGas","");
942: PetscOptionsReal("-physics_isogas_acoustic_speed","Acoustic speed","",user->acoustic_speed,&user->acoustic_speed,NULL);
943: PetscOptionsFList("-physics_isogas_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
944: PetscOptionsFList("-physics_isogas_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
945: PetscOptionsEnd();
946: RiemannListFind(rlist,rname,&ctx->physics.riemann);
947: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
948: PetscFunctionListDestroy(&rlist);
949: PetscFunctionListDestroy(&rclist);
950: return(0);
951: }
953: /* --------------------------------- Shallow Water ----------------------------------- */
954: typedef struct {
955: PetscReal gravity;
956: } ShallowCtx;
958: PETSC_STATIC_INLINE void ShallowFlux(ShallowCtx *phys,const PetscScalar *u,PetscScalar *f)
959: {
960: f[0] = u[1];
961: f[1] = PetscSqr(u[1])/u[0] + 0.5*phys->gravity*PetscSqr(u[0]);
962: }
964: static PetscErrorCode PhysicsRiemann_Shallow_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
965: {
966: ShallowCtx *phys = (ShallowCtx*)vctx;
967: PetscScalar g = phys->gravity,ustar[2],cL,cR,c,cstar;
968: struct {PetscScalar h,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]},star;
969: PetscInt i;
972: if (!(L.h > 0 && R.h > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed thickness is negative");
973: cL = PetscSqrtScalar(g*L.h);
974: cR = PetscSqrtScalar(g*R.h);
975: c = PetscMax(cL,cR);
976: {
977: /* Solve for star state */
978: const PetscInt maxits = 50;
979: PetscScalar tmp,res,res0=0,h0,h = 0.5*(L.h + R.h); /* initial guess */
980: h0 = h;
981: for (i=0; i<maxits; i++) {
982: PetscScalar fr,fl,dfr,dfl;
983: fl = (L.h < h)
984: ? PetscSqrtScalar(0.5*g*(h*h - L.h*L.h)*(1/L.h - 1/h)) /* shock */
985: : 2*PetscSqrtScalar(g*h) - 2*PetscSqrtScalar(g*L.h); /* rarefaction */
986: fr = (R.h < h)
987: ? PetscSqrtScalar(0.5*g*(h*h - R.h*R.h)*(1/R.h - 1/h)) /* shock */
988: : 2*PetscSqrtScalar(g*h) - 2*PetscSqrtScalar(g*R.h); /* rarefaction */
989: res = R.u - L.u + fr + fl;
990: if (PetscIsInfOrNanScalar(res)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Infinity or Not-a-Number generated in computation");
991: if (PetscAbsScalar(res) < 1e-8 || (i > 0 && PetscAbsScalar(h-h0) < 1e-8)) {
992: star.h = h;
993: star.u = L.u - fl;
994: goto converged;
995: } else if (i > 0 && PetscAbsScalar(res) >= PetscAbsScalar(res0)) { /* Line search */
996: h = 0.8*h0 + 0.2*h;
997: continue;
998: }
999: /* Accept the last step and take another */
1000: res0 = res;
1001: h0 = h;
1002: dfl = (L.h < h) ? 0.5/fl*0.5*g*(-L.h*L.h/(h*h) - 1 + 2*h/L.h) : PetscSqrtScalar(g/h);
1003: dfr = (R.h < h) ? 0.5/fr*0.5*g*(-R.h*R.h/(h*h) - 1 + 2*h/R.h) : PetscSqrtScalar(g/h);
1004: tmp = h - res/(dfr+dfl);
1005: if (tmp <= 0) h /= 2; /* Guard against Newton shooting off to a negative thickness */
1006: else h = tmp;
1007: if (!((h > 0) && PetscIsNormalScalar(h))) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP,"non-normal iterate h=%g",(double)h);
1008: }
1009: SETERRQ1(PETSC_COMM_SELF,1,"Newton iteration for star.h diverged after %D iterations",i);
1010: }
1011: converged:
1012: cstar = PetscSqrtScalar(g*star.h);
1013: if (L.u-cL < 0 && 0 < star.u-cstar) { /* 1-wave is sonic rarefaction */
1014: PetscScalar ufan[2];
1015: ufan[0] = 1/g*PetscSqr(L.u/3 + 2./3*cL);
1016: ufan[1] = PetscSqrtScalar(g*ufan[0])*ufan[0];
1017: ShallowFlux(phys,ufan,flux);
1018: } else if (star.u+cstar < 0 && 0 < R.u+cR) { /* 2-wave is sonic rarefaction */
1019: PetscScalar ufan[2];
1020: ufan[0] = 1/g*PetscSqr(R.u/3 - 2./3*cR);
1021: ufan[1] = -PetscSqrtScalar(g*ufan[0])*ufan[0];
1022: ShallowFlux(phys,ufan,flux);
1023: } 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)) {
1024: /* 1-wave is right-travelling shock (supersonic) */
1025: ShallowFlux(phys,uL,flux);
1026: } 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)) {
1027: /* 2-wave is left-travelling shock (supersonic) */
1028: ShallowFlux(phys,uR,flux);
1029: } else {
1030: ustar[0] = star.h;
1031: ustar[1] = star.h*star.u;
1032: ShallowFlux(phys,ustar,flux);
1033: }
1034: *maxspeed = MaxAbs(MaxAbs(star.u-cstar,star.u+cstar),MaxAbs(L.u-cL,R.u+cR));
1035: return(0);
1036: }
1038: static PetscErrorCode PhysicsRiemann_Shallow_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
1039: {
1040: ShallowCtx *phys = (ShallowCtx*)vctx;
1041: PetscScalar g = phys->gravity,fL[2],fR[2],s;
1042: struct {PetscScalar h,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]};
1045: if (!(L.h > 0 && R.h > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed thickness is negative");
1046: ShallowFlux(phys,uL,fL);
1047: ShallowFlux(phys,uR,fR);
1048: s = PetscMax(PetscAbs(L.u)+PetscSqrtScalar(g*L.h),PetscAbs(R.u)+PetscSqrtScalar(g*R.h));
1049: flux[0] = 0.5*(fL[0] + fR[0]) + 0.5*s*(uL[0] - uR[0]);
1050: flux[1] = 0.5*(fL[1] + fR[1]) + 0.5*s*(uL[1] - uR[1]);
1051: *maxspeed = s;
1052: return(0);
1053: }
1055: static PetscErrorCode PhysicsCharacteristic_Shallow(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
1056: {
1057: ShallowCtx *phys = (ShallowCtx*)vctx;
1058: PetscReal c;
1062: c = PetscSqrtScalar(u[0]*phys->gravity);
1063: speeds[0] = u[1]/u[0] - c;
1064: speeds[1] = u[1]/u[0] + c;
1065: X[0*2+0] = 1;
1066: X[0*2+1] = speeds[0];
1067: X[1*2+0] = 1;
1068: X[1*2+1] = speeds[1];
1069: PetscMemcpy(Xi,X,4*sizeof(X[0]));
1070: PetscKernel_A_gets_inverse_A_2(Xi,0,PETSC_FALSE,NULL);
1071: return(0);
1072: }
1074: static PetscErrorCode PhysicsCreate_Shallow(FVCtx *ctx)
1075: {
1076: PetscErrorCode ierr;
1077: ShallowCtx *user;
1078: PetscFunctionList rlist = 0,rclist = 0;
1079: char rname[256] = "exact",rcname[256] = "characteristic";
1082: PetscNew(&user);
1083: /* Shallow water and Isothermal Gas dynamics are similar so we reuse initial conditions for now */
1084: ctx->physics.sample = PhysicsSample_IsoGas;
1085: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
1086: ctx->physics.user = user;
1087: ctx->physics.dof = 2;
1089: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
1090: PetscStrallocpy("momentum",&ctx->physics.fieldname[1]);
1092: user->gravity = 1;
1094: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Shallow_Exact);
1095: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Shallow_Rusanov);
1096: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_Shallow);
1097: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
1098: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for Shallow","");
1099: PetscOptionsReal("-physics_shallow_gravity","Gravity","",user->gravity,&user->gravity,NULL);
1100: PetscOptionsFList("-physics_shallow_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
1101: PetscOptionsFList("-physics_shallow_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
1102: PetscOptionsEnd();
1103: RiemannListFind(rlist,rname,&ctx->physics.riemann);
1104: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
1105: PetscFunctionListDestroy(&rlist);
1106: PetscFunctionListDestroy(&rclist);
1107: return(0);
1108: }
1110: /* --------------------------------- Finite Volume Solver ----------------------------------- */
1112: static PetscErrorCode FVRHSFunction(TS ts,PetscReal time,Vec X,Vec F,void *vctx)
1113: {
1114: FVCtx *ctx = (FVCtx*)vctx;
1115: PetscErrorCode ierr;
1116: PetscInt i,j,k,Mx,dof,xs,xm;
1117: PetscReal hx,cfl_idt = 0;
1118: PetscScalar *x,*f,*slope;
1119: Vec Xloc;
1120: DM da;
1123: TSGetDM(ts,&da);
1124: DMGetLocalVector(da,&Xloc);
1125: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1126: hx = (ctx->xmax - ctx->xmin)/Mx;
1127: DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
1128: DMGlobalToLocalEnd (da,X,INSERT_VALUES,Xloc);
1130: VecZeroEntries(F);
1132: DMDAVecGetArray(da,Xloc,&x);
1133: DMDAVecGetArray(da,F,&f);
1134: DMDAGetArray(da,PETSC_TRUE,&slope);
1136: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1138: if (ctx->bctype == FVBC_OUTFLOW) {
1139: for (i=xs-2; i<0; i++) {
1140: for (j=0; j<dof; j++) x[i*dof+j] = x[j];
1141: }
1142: for (i=Mx; i<xs+xm+2; i++) {
1143: for (j=0; j<dof; j++) x[i*dof+j] = x[(xs+xm-1)*dof+j];
1144: }
1145: }
1146: for (i=xs-1; i<xs+xm+1; i++) {
1147: struct _LimitInfo info;
1148: PetscScalar *cjmpL,*cjmpR;
1149: /* Determine the right eigenvectors R, where A = R \Lambda R^{-1} */
1150: (*ctx->physics.characteristic)(ctx->physics.user,dof,&x[i*dof],ctx->R,ctx->Rinv,ctx->speeds);
1151: /* Evaluate jumps across interfaces (i-1, i) and (i, i+1), put in characteristic basis */
1152: PetscMemzero(ctx->cjmpLR,2*dof*sizeof(ctx->cjmpLR[0]));
1153: cjmpL = &ctx->cjmpLR[0];
1154: cjmpR = &ctx->cjmpLR[dof];
1155: for (j=0; j<dof; j++) {
1156: PetscScalar jmpL,jmpR;
1157: jmpL = x[(i+0)*dof+j] - x[(i-1)*dof+j];
1158: jmpR = x[(i+1)*dof+j] - x[(i+0)*dof+j];
1159: for (k=0; k<dof; k++) {
1160: cjmpL[k] += ctx->Rinv[k+j*dof] * jmpL;
1161: cjmpR[k] += ctx->Rinv[k+j*dof] * jmpR;
1162: }
1163: }
1164: /* Apply limiter to the left and right characteristic jumps */
1165: info.m = dof;
1166: info.hx = hx;
1167: (*ctx->limit)(&info,cjmpL,cjmpR,ctx->cslope);
1168: for (j=0; j<dof; j++) ctx->cslope[j] /= hx; /* rescale to a slope */
1169: for (j=0; j<dof; j++) {
1170: PetscScalar tmp = 0;
1171: for (k=0; k<dof; k++) tmp += ctx->R[j+k*dof] * ctx->cslope[k];
1172: slope[i*dof+j] = tmp;
1173: }
1174: }
1176: for (i=xs; i<xs+xm+1; i++) {
1177: PetscReal maxspeed;
1178: PetscScalar *uL,*uR;
1179: uL = &ctx->uLR[0];
1180: uR = &ctx->uLR[dof];
1181: for (j=0; j<dof; j++) {
1182: uL[j] = x[(i-1)*dof+j] + slope[(i-1)*dof+j]*hx/2;
1183: uR[j] = x[(i-0)*dof+j] - slope[(i-0)*dof+j]*hx/2;
1184: }
1185: (*ctx->physics.riemann)(ctx->physics.user,dof,uL,uR,ctx->flux,&maxspeed);
1186: cfl_idt = PetscMax(cfl_idt,PetscAbsScalar(maxspeed/hx)); /* Max allowable value of 1/Delta t */
1188: if (i > xs) {
1189: for (j=0; j<dof; j++) f[(i-1)*dof+j] -= ctx->flux[j]/hx;
1190: }
1191: if (i < xs+xm) {
1192: for (j=0; j<dof; j++) f[i*dof+j] += ctx->flux[j]/hx;
1193: }
1194: }
1196: DMDAVecRestoreArray(da,Xloc,&x);
1197: DMDAVecRestoreArray(da,F,&f);
1198: DMDARestoreArray(da,PETSC_TRUE,&slope);
1199: DMRestoreLocalVector(da,&Xloc);
1201: MPI_Allreduce(&cfl_idt,&ctx->cfl_idt,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
1202: if (0) {
1203: /* We need to a way to inform the TS of a CFL constraint, this is a debugging fragment */
1204: PetscReal dt,tnow;
1205: TSGetTimeStep(ts,&dt);
1206: TSGetTime(ts,&tnow);
1207: if (dt > 0.5/ctx->cfl_idt) {
1208: if (1) {
1209: PetscPrintf(ctx->comm,"Stability constraint exceeded at t=%g, dt %g > %g\n",(double)tnow,(double)dt,(double)(0.5/ctx->cfl_idt));
1210: } else SETERRQ2(PETSC_COMM_SELF,1,"Stability constraint exceeded, %g > %g",(double)dt,(double)(ctx->cfl/ctx->cfl_idt));
1211: }
1212: }
1213: return(0);
1214: }
1216: static PetscErrorCode SmallMatMultADB(PetscScalar *C,PetscInt bs,const PetscScalar *A,const PetscReal *D,const PetscScalar *B)
1217: {
1218: PetscInt i,j,k;
1221: for (i=0; i<bs; i++) {
1222: for (j=0; j<bs; j++) {
1223: PetscScalar tmp = 0;
1224: for (k=0; k<bs; k++) tmp += A[i*bs+k] * D[k] * B[k*bs+j];
1225: C[i*bs+j] = tmp;
1226: }
1227: }
1228: return(0);
1229: }
1232: static PetscErrorCode FVIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat A,Mat B,void *vctx)
1233: {
1234: FVCtx *ctx = (FVCtx*)vctx;
1235: PetscErrorCode ierr;
1236: PetscInt i,j,dof = ctx->physics.dof;
1237: PetscScalar *J;
1238: const PetscScalar *x;
1239: PetscReal hx;
1240: DM da;
1241: DMDALocalInfo dainfo;
1244: TSGetDM(ts,&da);
1245: DMDAVecGetArrayRead(da,X,(void*)&x);
1246: DMDAGetLocalInfo(da,&dainfo);
1247: hx = (ctx->xmax - ctx->xmin)/dainfo.mx;
1248: PetscMalloc1(dof*dof,&J);
1249: for (i=dainfo.xs; i<dainfo.xs+dainfo.xm; i++) {
1250: (*ctx->physics.characteristic)(ctx->physics.user,dof,&x[i*dof],ctx->R,ctx->Rinv,ctx->speeds);
1251: for (j=0; j<dof; j++) ctx->speeds[j] = PetscAbs(ctx->speeds[j]);
1252: SmallMatMultADB(J,dof,ctx->R,ctx->speeds,ctx->Rinv);
1253: for (j=0; j<dof*dof; j++) J[j] = J[j]/hx + shift*(j/dof == j%dof);
1254: MatSetValuesBlocked(B,1,&i,1,&i,J,INSERT_VALUES);
1255: }
1256: PetscFree(J);
1257: DMDAVecRestoreArrayRead(da,X,(void*)&x);
1259: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1260: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1261: if (A != B) {
1262: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1263: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1264: }
1265: return(0);
1266: }
1268: static PetscErrorCode FVSample(FVCtx *ctx,DM da,PetscReal time,Vec U)
1269: {
1271: PetscScalar *u,*uj;
1272: PetscInt i,j,k,dof,xs,xm,Mx;
1275: if (!ctx->physics.sample) SETERRQ(PETSC_COMM_SELF,1,"Physics has not provided a sampling function");
1276: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1277: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1278: DMDAVecGetArray(da,U,&u);
1279: PetscMalloc1(dof,&uj);
1280: for (i=xs; i<xs+xm; i++) {
1281: const PetscReal h = (ctx->xmax-ctx->xmin)/Mx,xi = ctx->xmin+h/2+i*h;
1282: const PetscInt N = 200;
1283: /* Integrate over cell i using trapezoid rule with N points. */
1284: for (k=0; k<dof; k++) u[i*dof+k] = 0;
1285: for (j=0; j<N+1; j++) {
1286: PetscScalar xj = xi+h*(j-N/2)/(PetscReal)N;
1287: (*ctx->physics.sample)(ctx->physics.user,ctx->initial,ctx->bctype,ctx->xmin,ctx->xmax,time,xj,uj);
1288: for (k=0; k<dof; k++) u[i*dof+k] += ((j==0 || j==N) ? 0.5 : 1.0)*uj[k]/N;
1289: }
1290: }
1291: DMDAVecRestoreArray(da,U,&u);
1292: PetscFree(uj);
1293: return(0);
1294: }
1296: static PetscErrorCode SolutionStatsView(DM da,Vec X,PetscViewer viewer)
1297: {
1298: PetscErrorCode ierr;
1299: PetscReal xmin,xmax;
1300: PetscScalar sum,tvsum,tvgsum;
1301: const PetscScalar *x;
1302: PetscInt imin,imax,Mx,i,j,xs,xm,dof;
1303: Vec Xloc;
1304: PetscBool iascii;
1307: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1308: if (iascii) {
1309: /* PETSc lacks a function to compute total variation norm (difficult in multiple dimensions), we do it here */
1310: DMGetLocalVector(da,&Xloc);
1311: DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
1312: DMGlobalToLocalEnd (da,X,INSERT_VALUES,Xloc);
1313: DMDAVecGetArrayRead(da,Xloc,(void*)&x);
1314: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1315: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1316: tvsum = 0;
1317: for (i=xs; i<xs+xm; i++) {
1318: for (j=0; j<dof; j++) tvsum += PetscAbsScalar(x[i*dof+j] - x[(i-1)*dof+j]);
1319: }
1320: MPI_Allreduce(&tvsum,&tvgsum,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
1321: DMDAVecRestoreArrayRead(da,Xloc,(void*)&x);
1322: DMRestoreLocalVector(da,&Xloc);
1324: VecMin(X,&imin,&xmin);
1325: VecMax(X,&imax,&xmax);
1326: VecSum(X,&sum);
1327: 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));
1328: } else SETERRQ(PETSC_COMM_SELF,1,"Viewer type not supported");
1329: return(0);
1330: }
1332: static PetscErrorCode SolutionErrorNorms(FVCtx *ctx,DM da,PetscReal t,Vec X,PetscReal *nrm1,PetscReal *nrmsup)
1333: {
1335: Vec Y;
1336: PetscInt Mx;
1339: VecGetSize(X,&Mx);
1340: VecDuplicate(X,&Y);
1341: FVSample(ctx,da,t,Y);
1342: VecAYPX(Y,-1,X);
1343: VecNorm(Y,NORM_1,nrm1);
1344: VecNorm(Y,NORM_INFINITY,nrmsup);
1345: *nrm1 /= Mx;
1346: VecDestroy(&Y);
1347: return(0);
1348: }
1350: int main(int argc,char *argv[])
1351: {
1352: char lname[256] = "mc",physname[256] = "advect",final_fname[256] = "solution.m";
1353: PetscFunctionList limiters = 0,physics = 0;
1354: MPI_Comm comm;
1355: TS ts;
1356: DM da;
1357: Vec X,X0,R;
1358: Mat B;
1359: FVCtx ctx;
1360: PetscInt i,dof,xs,xm,Mx,draw = 0;
1361: PetscBool view_final = PETSC_FALSE;
1362: PetscReal ptime;
1363: PetscErrorCode ierr;
1365: PetscInitialize(&argc,&argv,0,help);
1366: comm = PETSC_COMM_WORLD;
1367: PetscMemzero(&ctx,sizeof(ctx));
1369: /* Register limiters to be available on the command line */
1370: PetscFunctionListAdd(&limiters,"upwind" ,Limit_Upwind);
1371: PetscFunctionListAdd(&limiters,"lax-wendroff" ,Limit_LaxWendroff);
1372: PetscFunctionListAdd(&limiters,"beam-warming" ,Limit_BeamWarming);
1373: PetscFunctionListAdd(&limiters,"fromm" ,Limit_Fromm);
1374: PetscFunctionListAdd(&limiters,"minmod" ,Limit_Minmod);
1375: PetscFunctionListAdd(&limiters,"superbee" ,Limit_Superbee);
1376: PetscFunctionListAdd(&limiters,"mc" ,Limit_MC);
1377: PetscFunctionListAdd(&limiters,"vanleer" ,Limit_VanLeer);
1378: PetscFunctionListAdd(&limiters,"vanalbada" ,Limit_VanAlbada);
1379: PetscFunctionListAdd(&limiters,"vanalbadatvd" ,Limit_VanAlbadaTVD);
1380: PetscFunctionListAdd(&limiters,"koren" ,Limit_Koren);
1381: PetscFunctionListAdd(&limiters,"korensym" ,Limit_KorenSym);
1382: PetscFunctionListAdd(&limiters,"koren3" ,Limit_Koren3);
1383: PetscFunctionListAdd(&limiters,"cada-torrilhon2" ,Limit_CadaTorrilhon2);
1384: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r0p1",Limit_CadaTorrilhon3R0p1);
1385: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r1" ,Limit_CadaTorrilhon3R1);
1386: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r10" ,Limit_CadaTorrilhon3R10);
1387: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r100",Limit_CadaTorrilhon3R100);
1389: /* Register physical models to be available on the command line */
1390: PetscFunctionListAdd(&physics,"advect" ,PhysicsCreate_Advect);
1391: PetscFunctionListAdd(&physics,"burgers" ,PhysicsCreate_Burgers);
1392: PetscFunctionListAdd(&physics,"traffic" ,PhysicsCreate_Traffic);
1393: PetscFunctionListAdd(&physics,"acoustics" ,PhysicsCreate_Acoustics);
1394: PetscFunctionListAdd(&physics,"isogas" ,PhysicsCreate_IsoGas);
1395: PetscFunctionListAdd(&physics,"shallow" ,PhysicsCreate_Shallow);
1397: ctx.comm = comm;
1398: ctx.cfl = 0.9; ctx.bctype = FVBC_PERIODIC;
1399: ctx.xmin = -1; ctx.xmax = 1;
1400: PetscOptionsBegin(comm,NULL,"Finite Volume solver options","");
1401: PetscOptionsReal("-xmin","X min","",ctx.xmin,&ctx.xmin,NULL);
1402: PetscOptionsReal("-xmax","X max","",ctx.xmax,&ctx.xmax,NULL);
1403: PetscOptionsFList("-limit","Name of flux limiter to use","",limiters,lname,lname,sizeof(lname),NULL);
1404: PetscOptionsFList("-physics","Name of physics (Riemann solver and characteristics) to use","",physics,physname,physname,sizeof(physname),NULL);
1405: PetscOptionsInt("-draw","Draw solution vector, bitwise OR of (1=initial,2=final,4=final error)","",draw,&draw,NULL);
1406: PetscOptionsString("-view_final","Write final solution in ASCII MATLAB format to given file name","",final_fname,final_fname,sizeof(final_fname),&view_final);
1407: PetscOptionsInt("-initial","Initial condition (depends on the physics)","",ctx.initial,&ctx.initial,NULL);
1408: PetscOptionsBool("-exact","Compare errors with exact solution","",ctx.exact,&ctx.exact,NULL);
1409: PetscOptionsReal("-cfl","CFL number to time step at","",ctx.cfl,&ctx.cfl,NULL);
1410: PetscOptionsEnum("-bc_type","Boundary condition","",FVBCTypes,(PetscEnum)ctx.bctype,(PetscEnum*)&ctx.bctype,NULL);
1411: PetscOptionsEnd();
1413: /* Choose the limiter from the list of registered limiters */
1414: PetscFunctionListFind(limiters,lname,&ctx.limit);
1415: if (!ctx.limit) SETERRQ1(PETSC_COMM_SELF,1,"Limiter '%s' not found",lname);
1417: /* Choose the physics from the list of registered models */
1418: {
1419: PetscErrorCode (*r)(FVCtx*);
1420: PetscFunctionListFind(physics,physname,&r);
1421: if (!r) SETERRQ1(PETSC_COMM_SELF,1,"Physics '%s' not found",physname);
1422: /* Create the physics, will set the number of fields and their names */
1423: (*r)(&ctx);
1424: }
1426: /* Create a DMDA to manage the parallel grid */
1427: DMDACreate1d(comm,DM_BOUNDARY_PERIODIC,50,ctx.physics.dof,2,NULL,&da);
1428: DMSetFromOptions(da);
1429: DMSetUp(da);
1430: /* Inform the DMDA of the field names provided by the physics. */
1431: /* The names will be shown in the title bars when run with -ts_monitor_draw_solution */
1432: for (i=0; i<ctx.physics.dof; i++) {
1433: DMDASetFieldName(da,i,ctx.physics.fieldname[i]);
1434: }
1435: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1436: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1438: /* Set coordinates of cell centers */
1439: DMDASetUniformCoordinates(da,ctx.xmin+0.5*(ctx.xmax-ctx.xmin)/Mx,ctx.xmax+0.5*(ctx.xmax-ctx.xmin)/Mx,0,0,0,0);
1441: /* Allocate work space for the Finite Volume solver (so it doesn't have to be reallocated on each function evaluation) */
1442: PetscMalloc4(dof*dof,&ctx.R,dof*dof,&ctx.Rinv,2*dof,&ctx.cjmpLR,1*dof,&ctx.cslope);
1443: PetscMalloc3(2*dof,&ctx.uLR,dof,&ctx.flux,dof,&ctx.speeds);
1445: /* Create a vector to store the solution and to save the initial state */
1446: DMCreateGlobalVector(da,&X);
1447: VecDuplicate(X,&X0);
1448: VecDuplicate(X,&R);
1450: DMCreateMatrix(da,&B);
1452: /* Create a time-stepping object */
1453: TSCreate(comm,&ts);
1454: TSSetDM(ts,da);
1455: TSSetRHSFunction(ts,R,FVRHSFunction,&ctx);
1456: TSSetIJacobian(ts,B,B,FVIJacobian,&ctx);
1457: TSSetType(ts,TSSSP);
1458: TSSetMaxTime(ts,10);
1459: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1461: /* Compute initial conditions and starting time step */
1462: FVSample(&ctx,da,0,X0);
1463: FVRHSFunction(ts,0,X0,X,(void*)&ctx); /* Initial function evaluation, only used to determine max speed */
1464: VecCopy(X0,X); /* The function value was not used so we set X=X0 again */
1465: TSSetTimeStep(ts,ctx.cfl/ctx.cfl_idt);
1466: TSSetFromOptions(ts); /* Take runtime options */
1467: SolutionStatsView(da,X,PETSC_VIEWER_STDOUT_WORLD);
1468: {
1469: PetscReal nrm1,nrmsup;
1470: PetscInt steps;
1472: TSSolve(ts,X);
1473: TSGetSolveTime(ts,&ptime);
1474: TSGetStepNumber(ts,&steps);
1476: PetscPrintf(comm,"Final time %8.5f, steps %D\n",(double)ptime,steps);
1477: if (ctx.exact) {
1478: SolutionErrorNorms(&ctx,da,ptime,X,&nrm1,&nrmsup);
1479: PetscPrintf(comm,"Error ||x-x_e||_1 %8.4e ||x-x_e||_sup %8.4e\n",(double)nrm1,(double)nrmsup);
1480: }
1481: }
1483: SolutionStatsView(da,X,PETSC_VIEWER_STDOUT_WORLD);
1484: if (draw & 0x1) {VecView(X0,PETSC_VIEWER_DRAW_WORLD);}
1485: if (draw & 0x2) {VecView(X,PETSC_VIEWER_DRAW_WORLD);}
1486: if (draw & 0x4) {
1487: Vec Y;
1488: VecDuplicate(X,&Y);
1489: FVSample(&ctx,da,ptime,Y);
1490: VecAYPX(Y,-1,X);
1491: VecView(Y,PETSC_VIEWER_DRAW_WORLD);
1492: VecDestroy(&Y);
1493: }
1495: if (view_final) {
1496: PetscViewer viewer;
1497: PetscViewerASCIIOpen(PETSC_COMM_WORLD,final_fname,&viewer);
1498: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
1499: VecView(X,viewer);
1500: PetscViewerPopFormat(viewer);
1501: PetscViewerDestroy(&viewer);
1502: }
1504: /* Clean up */
1505: (*ctx.physics.destroy)(ctx.physics.user);
1506: for (i=0; i<ctx.physics.dof; i++) {PetscFree(ctx.physics.fieldname[i]);}
1507: PetscFree4(ctx.R,ctx.Rinv,ctx.cjmpLR,ctx.cslope);
1508: PetscFree3(ctx.uLR,ctx.flux,ctx.speeds);
1509: VecDestroy(&X);
1510: VecDestroy(&X0);
1511: VecDestroy(&R);
1512: MatDestroy(&B);
1513: DMDestroy(&da);
1514: TSDestroy(&ts);
1515: PetscFunctionListDestroy(&limiters);
1516: PetscFunctionListDestroy(&physics);
1517: PetscFinalize();
1518: return ierr;
1519: }