Actual source code: ex9.c
petsc-3.7.5 2017-01-01
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;
200: PetscErrorCode RiemannListAdd(PetscFunctionList *flist,const char *name,RiemannFunction rsolve)
201: {
205: PetscFunctionListAdd(flist,name,rsolve);
206: return(0);
207: }
211: PetscErrorCode RiemannListFind(PetscFunctionList flist,const char *name,RiemannFunction *rsolve)
212: {
216: PetscFunctionListFind(flist,name,rsolve);
217: if (!*rsolve) SETERRQ1(PETSC_COMM_SELF,1,"Riemann solver \"%s\" could not be found",name);
218: return(0);
219: }
223: PetscErrorCode ReconstructListAdd(PetscFunctionList *flist,const char *name,ReconstructFunction r)
224: {
228: PetscFunctionListAdd(flist,name,r);
229: return(0);
230: }
234: PetscErrorCode ReconstructListFind(PetscFunctionList flist,const char *name,ReconstructFunction *r)
235: {
239: PetscFunctionListFind(flist,name,r);
240: if (!*r) SETERRQ1(PETSC_COMM_SELF,1,"Reconstruction \"%s\" could not be found",name);
241: return(0);
242: }
244: /* --------------------------------- Physics ----------------------------------- */
245: /**
246: * Each physical model consists of Riemann solver and a function to determine the basis to use for reconstruction. These
247: * are set with the PhysicsCreate_XXX function which allocates private storage and sets these methods as well as the
248: * number of fields and their names, and a function to deallocate private storage.
249: **/
251: /* First a few functions useful to several different physics */
254: static PetscErrorCode PhysicsCharacteristic_Conservative(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
255: {
256: PetscInt i,j;
259: for (i=0; i<m; i++) {
260: for (j=0; j<m; j++) Xi[i*m+j] = X[i*m+j] = (PetscScalar)(i==j);
261: speeds[i] = PETSC_MAX_REAL; /* Indicates invalid */
262: }
263: return(0);
264: }
268: static PetscErrorCode PhysicsDestroy_SimpleFree(void *vctx)
269: {
273: PetscFree(vctx);
274: return(0);
275: }
279: /* --------------------------------- Advection ----------------------------------- */
281: typedef struct {
282: PetscReal a; /* advective velocity */
283: } AdvectCtx;
287: static PetscErrorCode PhysicsRiemann_Advect(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
288: {
289: AdvectCtx *ctx = (AdvectCtx*)vctx;
290: PetscReal speed;
293: speed = ctx->a;
294: flux[0] = PetscMax(0,speed)*uL[0] + PetscMin(0,speed)*uR[0];
295: *maxspeed = speed;
296: return(0);
297: }
301: static PetscErrorCode PhysicsCharacteristic_Advect(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
302: {
303: AdvectCtx *ctx = (AdvectCtx*)vctx;
306: X[0] = 1.;
307: Xi[0] = 1.;
308: speeds[0] = ctx->a;
309: return(0);
310: }
314: static PetscErrorCode PhysicsSample_Advect(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
315: {
316: AdvectCtx *ctx = (AdvectCtx*)vctx;
317: PetscReal a = ctx->a,x0;
320: switch (bctype) {
321: case FVBC_OUTFLOW: x0 = x-a*t; break;
322: case FVBC_PERIODIC: x0 = RangeMod(x-a*t,xmin,xmax); break;
323: default: SETERRQ(PETSC_COMM_SELF,1,"unknown BCType");
324: }
325: switch (initial) {
326: case 0: u[0] = (x0 < 0) ? 1 : -1; break;
327: case 1: u[0] = (x0 < 0) ? -1 : 1; break;
328: case 2: u[0] = (0 < x0 && x0 < 1) ? 1 : 0; break;
329: case 3: u[0] = PetscSinReal(2*PETSC_PI*x0); break;
330: case 4: u[0] = PetscAbs(x0); break;
331: case 5: u[0] = (x0 < 0 || x0 > 0.5) ? 0 : PetscSqr(PetscSinReal(2*PETSC_PI*x0)); break;
332: case 6: u[0] = (x0 < 0) ? 0 : ((x0 < 1) ? x0 : ((x0 < 2) ? 2-x0 : 0)); break;
333: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
334: }
335: return(0);
336: }
340: static PetscErrorCode PhysicsCreate_Advect(FVCtx *ctx)
341: {
343: AdvectCtx *user;
346: PetscNew(&user);
347: ctx->physics.sample = PhysicsSample_Advect;
348: ctx->physics.riemann = PhysicsRiemann_Advect;
349: ctx->physics.characteristic = PhysicsCharacteristic_Advect;
350: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
351: ctx->physics.user = user;
352: ctx->physics.dof = 1;
353: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
354: user->a = 1;
355: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for advection","");
356: {
357: PetscOptionsReal("-physics_advect_a","Speed","",user->a,&user->a,NULL);
358: }
359: PetscOptionsEnd();
360: return(0);
361: }
363: /* --------------------------------- Burgers ----------------------------------- */
365: typedef struct {
366: PetscReal lxf_speed;
367: } BurgersCtx;
371: static PetscErrorCode PhysicsSample_Burgers(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
372: {
374: if (bctype == FVBC_PERIODIC && t > 0) SETERRQ(PETSC_COMM_SELF,1,"Exact solution not implemented for periodic");
375: switch (initial) {
376: case 0: u[0] = (x < 0) ? 1 : -1; break;
377: case 1:
378: if (x < -t) u[0] = -1;
379: else if (x < t) u[0] = x/t;
380: else u[0] = 1;
381: break;
382: case 2:
383: if (x < 0) u[0] = 0;
384: else if (x <= t) u[0] = x/t;
385: else if (x < 1+0.5*t) u[0] = 1;
386: else u[0] = 0;
387: break;
388: case 3:
389: if (x < 0.2*t) u[0] = 0.2;
390: else if (x < t) u[0] = x/t;
391: else u[0] = 1;
392: break;
393: case 4:
394: if (t > 0) SETERRQ(PETSC_COMM_SELF,1,"Only initial condition available");
395: u[0] = 0.7 + 0.3*PetscSinReal(2*PETSC_PI*((x-xmin)/(xmax-xmin)));
396: break;
397: case 5: /* Pure shock solution */
398: if (x < 0.5*t) u[0] = 1;
399: else u[0] = 0;
400: break;
401: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
402: }
403: return(0);
404: }
408: static PetscErrorCode PhysicsRiemann_Burgers_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
409: {
411: if (uL[0] < uR[0]) { /* rarefaction */
412: flux[0] = (uL[0]*uR[0] < 0)
413: ? 0 /* sonic rarefaction */
414: : 0.5*PetscMin(PetscSqr(uL[0]),PetscSqr(uR[0]));
415: } else { /* shock */
416: flux[0] = 0.5*PetscMax(PetscSqr(uL[0]),PetscSqr(uR[0]));
417: }
418: *maxspeed = (PetscAbs(uL[0]) > PetscAbs(uR[0])) ? uL[0] : uR[0];
419: return(0);
420: }
424: static PetscErrorCode PhysicsRiemann_Burgers_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
425: {
426: PetscReal speed;
429: speed = 0.5*(uL[0] + uR[0]);
430: flux[0] = 0.25*(PetscSqr(uL[0]) + PetscSqr(uR[0])) - 0.5*PetscAbs(speed)*(uR[0]-uL[0]);
431: if (uL[0] <= 0 && 0 <= uR[0]) flux[0] = 0; /* Entropy fix for sonic rarefaction */
432: *maxspeed = speed;
433: return(0);
434: }
438: static PetscErrorCode PhysicsRiemann_Burgers_LxF(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
439: {
440: PetscReal c;
441: PetscScalar fL,fR;
444: c = ((BurgersCtx*)vctx)->lxf_speed;
445: fL = 0.5*PetscSqr(uL[0]);
446: fR = 0.5*PetscSqr(uR[0]);
447: flux[0] = 0.5*(fL + fR) - 0.5*c*(uR[0] - uL[0]);
448: *maxspeed = c;
449: return(0);
450: }
454: static PetscErrorCode PhysicsRiemann_Burgers_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
455: {
456: PetscReal c;
457: PetscScalar fL,fR;
460: c = PetscMax(PetscAbs(uL[0]),PetscAbs(uR[0]));
461: fL = 0.5*PetscSqr(uL[0]);
462: fR = 0.5*PetscSqr(uR[0]);
463: flux[0] = 0.5*(fL + fR) - 0.5*c*(uR[0] - uL[0]);
464: *maxspeed = c;
465: return(0);
466: }
470: static PetscErrorCode PhysicsCreate_Burgers(FVCtx *ctx)
471: {
472: BurgersCtx *user;
473: PetscErrorCode ierr;
474: RiemannFunction r;
475: PetscFunctionList rlist = 0;
476: char rname[256] = "exact";
479: PetscNew(&user);
481: ctx->physics.sample = PhysicsSample_Burgers;
482: ctx->physics.characteristic = PhysicsCharacteristic_Conservative;
483: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
484: ctx->physics.user = user;
485: ctx->physics.dof = 1;
487: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
488: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Burgers_Exact);
489: RiemannListAdd(&rlist,"roe", PhysicsRiemann_Burgers_Roe);
490: RiemannListAdd(&rlist,"lxf", PhysicsRiemann_Burgers_LxF);
491: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Burgers_Rusanov);
492: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for advection","");
493: {
494: PetscOptionsFList("-physics_burgers_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
495: }
496: PetscOptionsEnd();
497: RiemannListFind(rlist,rname,&r);
498: PetscFunctionListDestroy(&rlist);
499: ctx->physics.riemann = r;
501: /* *
502: * Hack to deal with LxF in semi-discrete form
503: * max speed is 1 for the basic initial conditions (where |u| <= 1)
504: * */
505: if (r == PhysicsRiemann_Burgers_LxF) user->lxf_speed = 1;
506: return(0);
507: }
509: /* --------------------------------- Traffic ----------------------------------- */
511: typedef struct {
512: PetscReal lxf_speed;
513: PetscReal a;
514: } TrafficCtx;
516: PETSC_STATIC_INLINE PetscScalar TrafficFlux(PetscScalar a,PetscScalar u) { return a*u*(1-u); }
520: static PetscErrorCode PhysicsSample_Traffic(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
521: {
522: PetscReal a = ((TrafficCtx*)vctx)->a;
525: if (bctype == FVBC_PERIODIC && t > 0) SETERRQ(PETSC_COMM_SELF,1,"Exact solution not implemented for periodic");
526: switch (initial) {
527: case 0:
528: u[0] = (-a*t < x) ? 2 : 0; break;
529: case 1:
530: if (x < PetscMin(2*a*t,0.5+a*t)) u[0] = -1;
531: else if (x < 1) u[0] = 0;
532: else u[0] = 1;
533: break;
534: case 2:
535: if (t > 0) SETERRQ(PETSC_COMM_SELF,1,"Only initial condition available");
536: u[0] = 0.7 + 0.3*PetscSinReal(2*PETSC_PI*((x-xmin)/(xmax-xmin)));
537: break;
538: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
539: }
540: return(0);
541: }
545: static PetscErrorCode PhysicsRiemann_Traffic_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
546: {
547: PetscReal a = ((TrafficCtx*)vctx)->a;
550: if (uL[0] < uR[0]) {
551: flux[0] = PetscMin(TrafficFlux(a,uL[0]),TrafficFlux(a,uR[0]));
552: } else {
553: flux[0] = (uR[0] < 0.5 && 0.5 < uL[0]) ? TrafficFlux(a,0.5) : PetscMax(TrafficFlux(a,uL[0]),TrafficFlux(a,uR[0]));
554: }
555: *maxspeed = a*MaxAbs(1-2*uL[0],1-2*uR[0]);
556: return(0);
557: }
561: static PetscErrorCode PhysicsRiemann_Traffic_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
562: {
563: PetscReal a = ((TrafficCtx*)vctx)->a;
564: PetscReal speed;
567: speed = a*(1 - (uL[0] + uR[0]));
568: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*PetscAbs(speed)*(uR[0]-uL[0]);
569: *maxspeed = speed;
570: return(0);
571: }
575: static PetscErrorCode PhysicsRiemann_Traffic_LxF(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
576: {
577: TrafficCtx *phys = (TrafficCtx*)vctx;
578: PetscReal a = phys->a;
579: PetscReal speed;
582: speed = a*(1 - (uL[0] + uR[0]));
583: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*phys->lxf_speed*(uR[0]-uL[0]);
584: *maxspeed = speed;
585: return(0);
586: }
590: static PetscErrorCode PhysicsRiemann_Traffic_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
591: {
592: PetscReal a = ((TrafficCtx*)vctx)->a;
593: PetscReal speed;
596: speed = a*PetscMax(PetscAbs(1-2*uL[0]),PetscAbs(1-2*uR[0]));
597: flux[0] = 0.5*(TrafficFlux(a,uL[0]) + TrafficFlux(a,uR[0])) - 0.5*speed*(uR[0]-uL[0]);
598: *maxspeed = speed;
599: return(0);
600: }
604: static PetscErrorCode PhysicsCreate_Traffic(FVCtx *ctx)
605: {
606: PetscErrorCode ierr;
607: TrafficCtx *user;
608: RiemannFunction r;
609: PetscFunctionList rlist = 0;
610: char rname[256] = "exact";
613: PetscNew(&user);
614: ctx->physics.sample = PhysicsSample_Traffic;
615: ctx->physics.characteristic = PhysicsCharacteristic_Conservative;
616: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
617: ctx->physics.user = user;
618: ctx->physics.dof = 1;
620: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
621: user->a = 0.5;
622: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Traffic_Exact);
623: RiemannListAdd(&rlist,"roe", PhysicsRiemann_Traffic_Roe);
624: RiemannListAdd(&rlist,"lxf", PhysicsRiemann_Traffic_LxF);
625: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Traffic_Rusanov);
626: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for Traffic","");
627: PetscOptionsReal("-physics_traffic_a","Flux = a*u*(1-u)","",user->a,&user->a,NULL);
628: PetscOptionsFList("-physics_traffic_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
629: PetscOptionsEnd();
631: RiemannListFind(rlist,rname,&r);
632: PetscFunctionListDestroy(&rlist);
634: ctx->physics.riemann = r;
636: /* *
637: * Hack to deal with LxF in semi-discrete form
638: * max speed is 3*a for the basic initial conditions (-1 <= u <= 2)
639: * */
640: if (r == PhysicsRiemann_Traffic_LxF) user->lxf_speed = 3*user->a;
641: return(0);
642: }
644: /* --------------------------------- Linear Acoustics ----------------------------------- */
646: /* Flux: u_t + (A u)_x
647: * z = sqrt(rho*bulk), c = sqrt(rho/bulk)
648: * Spectral decomposition: A = R * D * Rinv
649: * [ cz] = [-z z] [-c ] [-1/2z 1/2]
650: * [c/z ] = [ 1 1] [ c] [ 1/2z 1/2]
651: *
652: * We decompose this into the left-traveling waves Al = R * D^- Rinv
653: * and the right-traveling waves Ar = R * D^+ * Rinv
654: * Multiplying out these expressions produces the following two matrices
655: */
657: typedef struct {
658: PetscReal c; /* speed of sound: c = sqrt(bulk/rho) */
659: PetscReal z; /* impedence: z = sqrt(rho*bulk) */
660: } AcousticsCtx;
662: PETSC_UNUSED PETSC_STATIC_INLINE void AcousticsFlux(AcousticsCtx *ctx,const PetscScalar *u,PetscScalar *f)
663: {
664: f[0] = ctx->c*ctx->z*u[1];
665: f[1] = ctx->c/ctx->z*u[0];
666: }
670: static PetscErrorCode PhysicsCharacteristic_Acoustics(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
671: {
672: AcousticsCtx *phys = (AcousticsCtx*)vctx;
673: PetscReal z = phys->z,c = phys->c;
676: X[0*2+0] = -z;
677: X[0*2+1] = z;
678: X[1*2+0] = 1;
679: X[1*2+1] = 1;
680: Xi[0*2+0] = -1./(2*z);
681: Xi[0*2+1] = 1./2;
682: Xi[1*2+0] = 1./(2*z);
683: Xi[1*2+1] = 1./2;
684: speeds[0] = -c;
685: speeds[1] = c;
686: return(0);
687: }
691: static PetscErrorCode PhysicsSample_Acoustics_Initial(AcousticsCtx *phys,PetscInt initial,PetscReal xmin,PetscReal xmax,PetscReal x,PetscReal *u)
692: {
694: switch (initial) {
695: case 0:
696: u[0] = (PetscAbs((x - xmin)/(xmax - xmin) - 0.2) < 0.1) ? 1 : 0.5;
697: u[1] = (PetscAbs((x - xmin)/(xmax - xmin) - 0.7) < 0.1) ? 1 : -0.5;
698: break;
699: case 1:
700: u[0] = PetscCosReal(3 * 2*PETSC_PI*x/(xmax-xmin));
701: u[1] = PetscExpReal(-PetscSqr(x - (xmax + xmin)/2) / (2*PetscSqr(0.2*(xmax - xmin)))) - 0.5;
702: break;
703: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
704: }
705: return(0);
706: }
710: static PetscErrorCode PhysicsSample_Acoustics(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
711: {
712: AcousticsCtx *phys = (AcousticsCtx*)vctx;
713: PetscReal c = phys->c;
714: PetscReal x0a,x0b,u0a[2],u0b[2],tmp[2];
715: PetscReal X[2][2],Xi[2][2],dummy[2];
719: switch (bctype) {
720: case FVBC_OUTFLOW:
721: x0a = x+c*t;
722: x0b = x-c*t;
723: break;
724: case FVBC_PERIODIC:
725: x0a = RangeMod(x+c*t,xmin,xmax);
726: x0b = RangeMod(x-c*t,xmin,xmax);
727: break;
728: default: SETERRQ(PETSC_COMM_SELF,1,"unknown BCType");
729: }
730: PhysicsSample_Acoustics_Initial(phys,initial,xmin,xmax,x0a,u0a);
731: PhysicsSample_Acoustics_Initial(phys,initial,xmin,xmax,x0b,u0b);
732: PhysicsCharacteristic_Acoustics(vctx,2,u,&X[0][0],&Xi[0][0],dummy);
733: tmp[0] = Xi[0][0]*u0a[0] + Xi[0][1]*u0a[1];
734: tmp[1] = Xi[1][0]*u0b[0] + Xi[1][1]*u0b[1];
735: u[0] = X[0][0]*tmp[0] + X[0][1]*tmp[1];
736: u[1] = X[1][0]*tmp[0] + X[1][1]*tmp[1];
737: return(0);
738: }
742: static PetscErrorCode PhysicsRiemann_Acoustics_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
743: {
744: AcousticsCtx *phys = (AcousticsCtx*)vctx;
745: PetscReal c = phys->c,z = phys->z;
746: PetscReal
747: Al[2][2] = {{-c/2 , c*z/2 },
748: {c/(2*z) , -c/2 }}, /* Left traveling waves */
749: Ar[2][2] = {{c/2 , c*z/2 },
750: {c/(2*z) , c/2 }}; /* Right traveling waves */
753: flux[0] = Al[0][0]*uR[0] + Al[0][1]*uR[1] + Ar[0][0]*uL[0] + Ar[0][1]*uL[1];
754: flux[1] = Al[1][0]*uR[0] + Al[1][1]*uR[1] + Ar[1][0]*uL[0] + Ar[1][1]*uL[1];
755: *maxspeed = c;
756: return(0);
757: }
761: static PetscErrorCode PhysicsCreate_Acoustics(FVCtx *ctx)
762: {
763: PetscErrorCode ierr;
764: AcousticsCtx *user;
765: PetscFunctionList rlist = 0,rclist = 0;
766: char rname[256] = "exact",rcname[256] = "characteristic";
769: PetscNew(&user);
770: ctx->physics.sample = PhysicsSample_Acoustics;
771: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
772: ctx->physics.user = user;
773: ctx->physics.dof = 2;
775: PetscStrallocpy("u",&ctx->physics.fieldname[0]);
776: PetscStrallocpy("v",&ctx->physics.fieldname[1]);
778: user->c = 1;
779: user->z = 1;
781: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Acoustics_Exact);
782: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_Acoustics);
783: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
784: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for linear Acoustics","");
785: {
786: PetscOptionsReal("-physics_acoustics_c","c = sqrt(bulk/rho)","",user->c,&user->c,NULL);
787: PetscOptionsReal("-physics_acoustics_z","z = sqrt(bulk*rho)","",user->z,&user->z,NULL);
788: PetscOptionsFList("-physics_acoustics_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
789: PetscOptionsFList("-physics_acoustics_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
790: }
791: PetscOptionsEnd();
792: RiemannListFind(rlist,rname,&ctx->physics.riemann);
793: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
794: PetscFunctionListDestroy(&rlist);
795: PetscFunctionListDestroy(&rclist);
796: return(0);
797: }
799: /* --------------------------------- Isothermal Gas Dynamics ----------------------------------- */
801: typedef struct {
802: PetscReal acoustic_speed;
803: } IsoGasCtx;
805: PETSC_STATIC_INLINE void IsoGasFlux(PetscReal c,const PetscScalar *u,PetscScalar *f)
806: {
807: f[0] = u[1];
808: f[1] = PetscSqr(u[1])/u[0] + c*c*u[0];
809: }
813: static PetscErrorCode PhysicsSample_IsoGas(void *vctx,PetscInt initial,FVBCType bctype,PetscReal xmin,PetscReal xmax,PetscReal t,PetscReal x,PetscReal *u)
814: {
816: if (t > 0) SETERRQ(PETSC_COMM_SELF,1,"Exact solutions not implemented for t > 0");
817: switch (initial) {
818: case 0:
819: u[0] = (x < 0) ? 1 : 0.5;
820: u[1] = (x < 0) ? 1 : 0.7;
821: break;
822: case 1:
823: u[0] = 1+0.5*PetscSinReal(2*PETSC_PI*x);
824: u[1] = 1*u[0];
825: break;
826: default: SETERRQ(PETSC_COMM_SELF,1,"unknown initial condition");
827: }
828: return(0);
829: }
833: static PetscErrorCode PhysicsRiemann_IsoGas_Roe(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
834: {
835: IsoGasCtx *phys = (IsoGasCtx*)vctx;
836: PetscReal c = phys->acoustic_speed;
837: PetscScalar ubar,du[2],a[2],fL[2],fR[2],lam[2],ustar[2],R[2][2];
838: PetscInt i;
841: ubar = (uL[1]/PetscSqrtScalar(uL[0]) + uR[1]/PetscSqrtScalar(uR[0])) / (PetscSqrtScalar(uL[0]) + PetscSqrtScalar(uR[0]));
842: /* write fluxuations in characteristic basis */
843: du[0] = uR[0] - uL[0];
844: du[1] = uR[1] - uL[1];
845: a[0] = (1/(2*c)) * ((ubar + c)*du[0] - du[1]);
846: a[1] = (1/(2*c)) * ((-ubar + c)*du[0] + du[1]);
847: /* wave speeds */
848: lam[0] = ubar - c;
849: lam[1] = ubar + c;
850: /* Right eigenvectors */
851: R[0][0] = 1; R[0][1] = ubar-c;
852: R[1][0] = 1; R[1][1] = ubar+c;
853: /* Compute state in star region (between the 1-wave and 2-wave) */
854: for (i=0; i<2; i++) ustar[i] = uL[i] + a[0]*R[0][i];
855: if (uL[1]/uL[0] < c && c < ustar[1]/ustar[0]) { /* 1-wave is sonic rarefaction */
856: PetscScalar ufan[2];
857: ufan[0] = uL[0]*PetscExpScalar(uL[1]/(uL[0]*c) - 1);
858: ufan[1] = c*ufan[0];
859: IsoGasFlux(c,ufan,flux);
860: } else if (ustar[1]/ustar[0] < -c && -c < uR[1]/uR[0]) { /* 2-wave is sonic rarefaction */
861: PetscScalar ufan[2];
862: ufan[0] = uR[0]*PetscExpScalar(-uR[1]/(uR[0]*c) - 1);
863: ufan[1] = -c*ufan[0];
864: IsoGasFlux(c,ufan,flux);
865: } else { /* Centered form */
866: IsoGasFlux(c,uL,fL);
867: IsoGasFlux(c,uR,fR);
868: for (i=0; i<2; i++) {
869: PetscScalar absdu = PetscAbsScalar(lam[0])*a[0]*R[0][i] + PetscAbsScalar(lam[1])*a[1]*R[1][i];
870: flux[i] = 0.5*(fL[i]+fR[i]) - 0.5*absdu;
871: }
872: }
873: *maxspeed = MaxAbs(lam[0],lam[1]);
874: return(0);
875: }
879: static PetscErrorCode PhysicsRiemann_IsoGas_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
880: {
881: IsoGasCtx *phys = (IsoGasCtx*)vctx;
882: PetscReal c = phys->acoustic_speed;
883: PetscScalar ustar[2];
884: struct {PetscScalar rho,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]},star;
885: PetscInt i;
886: PetscErrorCode ierr;
889: if (!(L.rho > 0 && R.rho > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed density is negative");
890: {
891: /* Solve for star state */
892: PetscScalar res,tmp,rho = 0.5*(L.rho + R.rho); /* initial guess */
893: for (i=0; i<20; i++) {
894: PetscScalar fr,fl,dfr,dfl;
895: fl = (L.rho < rho)
896: ? (rho-L.rho)/PetscSqrtScalar(L.rho*rho) /* shock */
897: : PetscLogScalar(rho) - PetscLogScalar(L.rho); /* rarefaction */
898: fr = (R.rho < rho)
899: ? (rho-R.rho)/PetscSqrtScalar(R.rho*rho) /* shock */
900: : PetscLogScalar(rho) - PetscLogScalar(R.rho); /* rarefaction */
901: res = R.u-L.u + c*(fr+fl);
902: PetscIsInfOrNanScalar(res);
903: if (PetscAbsScalar(res) < 1e-10) {
904: star.rho = rho;
905: star.u = L.u - c*fl;
906: goto converged;
907: }
908: dfl = (L.rho < rho) ? 1/PetscSqrtScalar(L.rho*rho)*(1 - 0.5*(rho-L.rho)/rho) : 1/rho;
909: dfr = (R.rho < rho) ? 1/PetscSqrtScalar(R.rho*rho)*(1 - 0.5*(rho-R.rho)/rho) : 1/rho;
910: tmp = rho - res/(c*(dfr+dfl));
911: if (tmp <= 0) rho /= 2; /* Guard against Newton shooting off to a negative density */
912: else rho = tmp;
913: if (!((rho > 0) && PetscIsNormalScalar(rho))) SETERRQ1(PETSC_COMM_SELF,1,"non-normal iterate rho=%g",(double)PetscRealPart(rho));
914: }
915: SETERRQ1(PETSC_COMM_SELF,1,"Newton iteration for star.rho diverged after %D iterations",i);
916: }
917: converged:
918: if (L.u-c < 0 && 0 < star.u-c) { /* 1-wave is sonic rarefaction */
919: PetscScalar ufan[2];
920: ufan[0] = L.rho*PetscExpScalar(L.u/c - 1);
921: ufan[1] = c*ufan[0];
922: IsoGasFlux(c,ufan,flux);
923: } else if (star.u+c < 0 && 0 < R.u+c) { /* 2-wave is sonic rarefaction */
924: PetscScalar ufan[2];
925: ufan[0] = R.rho*PetscExpScalar(-R.u/c - 1);
926: ufan[1] = -c*ufan[0];
927: IsoGasFlux(c,ufan,flux);
928: } 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)) {
929: /* 1-wave is supersonic rarefaction, or supersonic shock */
930: IsoGasFlux(c,uL,flux);
931: } 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)) {
932: /* 2-wave is supersonic rarefaction or supersonic shock */
933: IsoGasFlux(c,uR,flux);
934: } else {
935: ustar[0] = star.rho;
936: ustar[1] = star.rho*star.u;
937: IsoGasFlux(c,ustar,flux);
938: }
939: *maxspeed = MaxAbs(MaxAbs(star.u-c,star.u+c),MaxAbs(L.u-c,R.u+c));
940: return(0);
941: }
945: static PetscErrorCode PhysicsRiemann_IsoGas_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
946: {
947: IsoGasCtx *phys = (IsoGasCtx*)vctx;
948: PetscScalar c = phys->acoustic_speed,fL[2],fR[2],s;
949: struct {PetscScalar rho,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]};
952: if (!(L.rho > 0 && R.rho > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed density is negative");
953: IsoGasFlux(c,uL,fL);
954: IsoGasFlux(c,uR,fR);
955: s = PetscMax(PetscAbs(L.u),PetscAbs(R.u))+c;
956: flux[0] = 0.5*(fL[0] + fR[0]) + 0.5*s*(uL[0] - uR[0]);
957: flux[1] = 0.5*(fL[1] + fR[1]) + 0.5*s*(uL[1] - uR[1]);
958: *maxspeed = s;
959: return(0);
960: }
964: static PetscErrorCode PhysicsCharacteristic_IsoGas(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
965: {
966: IsoGasCtx *phys = (IsoGasCtx*)vctx;
967: PetscReal c = phys->acoustic_speed;
971: speeds[0] = u[1]/u[0] - c;
972: speeds[1] = u[1]/u[0] + c;
973: X[0*2+0] = 1;
974: X[0*2+1] = speeds[0];
975: X[1*2+0] = 1;
976: X[1*2+1] = speeds[1];
977: PetscMemcpy(Xi,X,4*sizeof(X[0]));
978: PetscKernel_A_gets_inverse_A_2(Xi,0,PETSC_FALSE,NULL);
979: return(0);
980: }
984: static PetscErrorCode PhysicsCreate_IsoGas(FVCtx *ctx)
985: {
986: PetscErrorCode ierr;
987: IsoGasCtx *user;
988: PetscFunctionList rlist = 0,rclist = 0;
989: char rname[256] = "exact",rcname[256] = "characteristic";
992: PetscNew(&user);
993: ctx->physics.sample = PhysicsSample_IsoGas;
994: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
995: ctx->physics.user = user;
996: ctx->physics.dof = 2;
998: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
999: PetscStrallocpy("momentum",&ctx->physics.fieldname[1]);
1001: user->acoustic_speed = 1;
1003: RiemannListAdd(&rlist,"exact", PhysicsRiemann_IsoGas_Exact);
1004: RiemannListAdd(&rlist,"roe", PhysicsRiemann_IsoGas_Roe);
1005: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_IsoGas_Rusanov);
1006: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_IsoGas);
1007: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
1008: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for IsoGas","");
1009: PetscOptionsReal("-physics_isogas_acoustic_speed","Acoustic speed","",user->acoustic_speed,&user->acoustic_speed,NULL);
1010: PetscOptionsFList("-physics_isogas_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
1011: PetscOptionsFList("-physics_isogas_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
1012: PetscOptionsEnd();
1013: RiemannListFind(rlist,rname,&ctx->physics.riemann);
1014: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
1015: PetscFunctionListDestroy(&rlist);
1016: PetscFunctionListDestroy(&rclist);
1017: return(0);
1018: }
1020: /* --------------------------------- Shallow Water ----------------------------------- */
1021: typedef struct {
1022: PetscReal gravity;
1023: } ShallowCtx;
1025: PETSC_STATIC_INLINE void ShallowFlux(ShallowCtx *phys,const PetscScalar *u,PetscScalar *f)
1026: {
1027: f[0] = u[1];
1028: f[1] = PetscSqr(u[1])/u[0] + 0.5*phys->gravity*PetscSqr(u[0]);
1029: }
1033: static PetscErrorCode PhysicsRiemann_Shallow_Exact(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
1034: {
1035: ShallowCtx *phys = (ShallowCtx*)vctx;
1036: PetscScalar g = phys->gravity,ustar[2],cL,cR,c,cstar;
1037: struct {PetscScalar h,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]},star;
1038: PetscInt i;
1039: PetscErrorCode ierr;
1042: if (!(L.h > 0 && R.h > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed thickness is negative");
1043: cL = PetscSqrtScalar(g*L.h);
1044: cR = PetscSqrtScalar(g*R.h);
1045: c = PetscMax(cL,cR);
1046: {
1047: /* Solve for star state */
1048: const PetscInt maxits = 50;
1049: PetscScalar tmp,res,res0=0,h0,h = 0.5*(L.h + R.h); /* initial guess */
1050: h0 = h;
1051: for (i=0; i<maxits; i++) {
1052: PetscScalar fr,fl,dfr,dfl;
1053: fl = (L.h < h)
1054: ? PetscSqrtScalar(0.5*g*(h*h - L.h*L.h)*(1/L.h - 1/h)) /* shock */
1055: : 2*PetscSqrtScalar(g*h) - 2*PetscSqrtScalar(g*L.h); /* rarefaction */
1056: fr = (R.h < h)
1057: ? PetscSqrtScalar(0.5*g*(h*h - R.h*R.h)*(1/R.h - 1/h)) /* shock */
1058: : 2*PetscSqrtScalar(g*h) - 2*PetscSqrtScalar(g*R.h); /* rarefaction */
1059: res = R.u - L.u + fr + fl;
1060: PetscIsInfOrNanScalar(res);
1061: if (PetscAbsScalar(res) < 1e-8 || (i > 0 && PetscAbsScalar(h-h0) < 1e-8)) {
1062: star.h = h;
1063: star.u = L.u - fl;
1064: goto converged;
1065: } else if (i > 0 && PetscAbsScalar(res) >= PetscAbsScalar(res0)) { /* Line search */
1066: h = 0.8*h0 + 0.2*h;
1067: continue;
1068: }
1069: /* Accept the last step and take another */
1070: res0 = res;
1071: h0 = h;
1072: dfl = (L.h < h) ? 0.5/fl*0.5*g*(-L.h*L.h/(h*h) - 1 + 2*h/L.h) : PetscSqrtScalar(g/h);
1073: dfr = (R.h < h) ? 0.5/fr*0.5*g*(-R.h*R.h/(h*h) - 1 + 2*h/R.h) : PetscSqrtScalar(g/h);
1074: tmp = h - res/(dfr+dfl);
1075: if (tmp <= 0) h /= 2; /* Guard against Newton shooting off to a negative thickness */
1076: else h = tmp;
1077: if (!((h > 0) && PetscIsNormalScalar(h))) SETERRQ1(PETSC_COMM_SELF,1,"non-normal iterate h=%g",(double)h);
1078: }
1079: SETERRQ1(PETSC_COMM_SELF,1,"Newton iteration for star.h diverged after %D iterations",i);
1080: }
1081: converged:
1082: cstar = PetscSqrtScalar(g*star.h);
1083: if (L.u-cL < 0 && 0 < star.u-cstar) { /* 1-wave is sonic rarefaction */
1084: PetscScalar ufan[2];
1085: ufan[0] = 1/g*PetscSqr(L.u/3 + 2./3*cL);
1086: ufan[1] = PetscSqrtScalar(g*ufan[0])*ufan[0];
1087: ShallowFlux(phys,ufan,flux);
1088: } else if (star.u+cstar < 0 && 0 < R.u+cR) { /* 2-wave is sonic rarefaction */
1089: PetscScalar ufan[2];
1090: ufan[0] = 1/g*PetscSqr(R.u/3 - 2./3*cR);
1091: ufan[1] = -PetscSqrtScalar(g*ufan[0])*ufan[0];
1092: ShallowFlux(phys,ufan,flux);
1093: } 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)) {
1094: /* 1-wave is right-travelling shock (supersonic) */
1095: ShallowFlux(phys,uL,flux);
1096: } 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)) {
1097: /* 2-wave is left-travelling shock (supersonic) */
1098: ShallowFlux(phys,uR,flux);
1099: } else {
1100: ustar[0] = star.h;
1101: ustar[1] = star.h*star.u;
1102: ShallowFlux(phys,ustar,flux);
1103: }
1104: *maxspeed = MaxAbs(MaxAbs(star.u-cstar,star.u+cstar),MaxAbs(L.u-cL,R.u+cR));
1105: return(0);
1106: }
1110: static PetscErrorCode PhysicsRiemann_Shallow_Rusanov(void *vctx,PetscInt m,const PetscScalar *uL,const PetscScalar *uR,PetscScalar *flux,PetscReal *maxspeed)
1111: {
1112: ShallowCtx *phys = (ShallowCtx*)vctx;
1113: PetscScalar g = phys->gravity,fL[2],fR[2],s;
1114: struct {PetscScalar h,u;} L = {uL[0],uL[1]/uL[0]},R = {uR[0],uR[1]/uR[0]};
1117: if (!(L.h > 0 && R.h > 0)) SETERRQ(PETSC_COMM_SELF,1,"Reconstructed thickness is negative");
1118: ShallowFlux(phys,uL,fL);
1119: ShallowFlux(phys,uR,fR);
1120: s = PetscMax(PetscAbs(L.u)+PetscSqrtScalar(g*L.h),PetscAbs(R.u)+PetscSqrtScalar(g*R.h));
1121: flux[0] = 0.5*(fL[0] + fR[0]) + 0.5*s*(uL[0] - uR[0]);
1122: flux[1] = 0.5*(fL[1] + fR[1]) + 0.5*s*(uL[1] - uR[1]);
1123: *maxspeed = s;
1124: return(0);
1125: }
1129: static PetscErrorCode PhysicsCharacteristic_Shallow(void *vctx,PetscInt m,const PetscScalar *u,PetscScalar *X,PetscScalar *Xi,PetscReal *speeds)
1130: {
1131: ShallowCtx *phys = (ShallowCtx*)vctx;
1132: PetscReal c;
1136: c = PetscSqrtScalar(u[0]*phys->gravity);
1137: speeds[0] = u[1]/u[0] - c;
1138: speeds[1] = u[1]/u[0] + c;
1139: X[0*2+0] = 1;
1140: X[0*2+1] = speeds[0];
1141: X[1*2+0] = 1;
1142: X[1*2+1] = speeds[1];
1143: PetscMemcpy(Xi,X,4*sizeof(X[0]));
1144: PetscKernel_A_gets_inverse_A_2(Xi,0,PETSC_FALSE,NULL);
1145: return(0);
1146: }
1150: static PetscErrorCode PhysicsCreate_Shallow(FVCtx *ctx)
1151: {
1152: PetscErrorCode ierr;
1153: ShallowCtx *user;
1154: PetscFunctionList rlist = 0,rclist = 0;
1155: char rname[256] = "exact",rcname[256] = "characteristic";
1158: PetscNew(&user);
1159: /* Shallow water and Isothermal Gas dynamics are similar so we reuse initial conditions for now */
1160: ctx->physics.sample = PhysicsSample_IsoGas;
1161: ctx->physics.destroy = PhysicsDestroy_SimpleFree;
1162: ctx->physics.user = user;
1163: ctx->physics.dof = 2;
1165: PetscStrallocpy("density",&ctx->physics.fieldname[0]);
1166: PetscStrallocpy("momentum",&ctx->physics.fieldname[1]);
1168: user->gravity = 1;
1170: RiemannListAdd(&rlist,"exact", PhysicsRiemann_Shallow_Exact);
1171: RiemannListAdd(&rlist,"rusanov",PhysicsRiemann_Shallow_Rusanov);
1172: ReconstructListAdd(&rclist,"characteristic",PhysicsCharacteristic_Shallow);
1173: ReconstructListAdd(&rclist,"conservative",PhysicsCharacteristic_Conservative);
1174: PetscOptionsBegin(ctx->comm,ctx->prefix,"Options for Shallow","");
1175: PetscOptionsReal("-physics_shallow_gravity","Gravity","",user->gravity,&user->gravity,NULL);
1176: PetscOptionsFList("-physics_shallow_riemann","Riemann solver","",rlist,rname,rname,sizeof(rname),NULL);
1177: PetscOptionsFList("-physics_shallow_reconstruct","Reconstruction","",rclist,rcname,rcname,sizeof(rcname),NULL);
1178: PetscOptionsEnd();
1179: RiemannListFind(rlist,rname,&ctx->physics.riemann);
1180: ReconstructListFind(rclist,rcname,&ctx->physics.characteristic);
1181: PetscFunctionListDestroy(&rlist);
1182: PetscFunctionListDestroy(&rclist);
1183: return(0);
1184: }
1186: /* --------------------------------- Finite Volume Solver ----------------------------------- */
1190: static PetscErrorCode FVRHSFunction(TS ts,PetscReal time,Vec X,Vec F,void *vctx)
1191: {
1192: FVCtx *ctx = (FVCtx*)vctx;
1193: PetscErrorCode ierr;
1194: PetscInt i,j,k,Mx,dof,xs,xm;
1195: PetscReal hx,cfl_idt = 0;
1196: PetscScalar *x,*f,*slope;
1197: Vec Xloc;
1198: DM da;
1201: TSGetDM(ts,&da);
1202: DMGetLocalVector(da,&Xloc);
1203: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1204: hx = (ctx->xmax - ctx->xmin)/Mx;
1205: DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
1206: DMGlobalToLocalEnd (da,X,INSERT_VALUES,Xloc);
1208: VecZeroEntries(F);
1210: DMDAVecGetArray(da,Xloc,&x);
1211: DMDAVecGetArray(da,F,&f);
1212: DMDAGetArray(da,PETSC_TRUE,&slope);
1214: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1216: if (ctx->bctype == FVBC_OUTFLOW) {
1217: for (i=xs-2; i<0; i++) {
1218: for (j=0; j<dof; j++) x[i*dof+j] = x[j];
1219: }
1220: for (i=Mx; i<xs+xm+2; i++) {
1221: for (j=0; j<dof; j++) x[i*dof+j] = x[(xs+xm-1)*dof+j];
1222: }
1223: }
1224: for (i=xs-1; i<xs+xm+1; i++) {
1225: struct _LimitInfo info;
1226: PetscScalar *cjmpL,*cjmpR;
1227: /* Determine the right eigenvectors R, where A = R \Lambda R^{-1} */
1228: (*ctx->physics.characteristic)(ctx->physics.user,dof,&x[i*dof],ctx->R,ctx->Rinv,ctx->speeds);
1229: /* Evaluate jumps across interfaces (i-1, i) and (i, i+1), put in characteristic basis */
1230: PetscMemzero(ctx->cjmpLR,2*dof*sizeof(ctx->cjmpLR[0]));
1231: cjmpL = &ctx->cjmpLR[0];
1232: cjmpR = &ctx->cjmpLR[dof];
1233: for (j=0; j<dof; j++) {
1234: PetscScalar jmpL,jmpR;
1235: jmpL = x[(i+0)*dof+j] - x[(i-1)*dof+j];
1236: jmpR = x[(i+1)*dof+j] - x[(i+0)*dof+j];
1237: for (k=0; k<dof; k++) {
1238: cjmpL[k] += ctx->Rinv[k+j*dof] * jmpL;
1239: cjmpR[k] += ctx->Rinv[k+j*dof] * jmpR;
1240: }
1241: }
1242: /* Apply limiter to the left and right characteristic jumps */
1243: info.m = dof;
1244: info.hx = hx;
1245: (*ctx->limit)(&info,cjmpL,cjmpR,ctx->cslope);
1246: for (j=0; j<dof; j++) ctx->cslope[j] /= hx; /* rescale to a slope */
1247: for (j=0; j<dof; j++) {
1248: PetscScalar tmp = 0;
1249: for (k=0; k<dof; k++) tmp += ctx->R[j+k*dof] * ctx->cslope[k];
1250: slope[i*dof+j] = tmp;
1251: }
1252: }
1254: for (i=xs; i<xs+xm+1; i++) {
1255: PetscReal maxspeed;
1256: PetscScalar *uL,*uR;
1257: uL = &ctx->uLR[0];
1258: uR = &ctx->uLR[dof];
1259: for (j=0; j<dof; j++) {
1260: uL[j] = x[(i-1)*dof+j] + slope[(i-1)*dof+j]*hx/2;
1261: uR[j] = x[(i-0)*dof+j] - slope[(i-0)*dof+j]*hx/2;
1262: }
1263: (*ctx->physics.riemann)(ctx->physics.user,dof,uL,uR,ctx->flux,&maxspeed);
1264: cfl_idt = PetscMax(cfl_idt,PetscAbsScalar(maxspeed/hx)); /* Max allowable value of 1/Delta t */
1266: if (i > xs) {
1267: for (j=0; j<dof; j++) f[(i-1)*dof+j] -= ctx->flux[j]/hx;
1268: }
1269: if (i < xs+xm) {
1270: for (j=0; j<dof; j++) f[i*dof+j] += ctx->flux[j]/hx;
1271: }
1272: }
1274: DMDAVecRestoreArray(da,Xloc,&x);
1275: DMDAVecRestoreArray(da,F,&f);
1276: DMDARestoreArray(da,PETSC_TRUE,&slope);
1277: DMRestoreLocalVector(da,&Xloc);
1279: MPI_Allreduce(&cfl_idt,&ctx->cfl_idt,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
1280: if (0) {
1281: /* We need to a way to inform the TS of a CFL constraint, this is a debugging fragment */
1282: PetscReal dt,tnow;
1283: TSGetTimeStep(ts,&dt);
1284: TSGetTime(ts,&tnow);
1285: if (dt > 0.5/ctx->cfl_idt) {
1286: if (1) {
1287: PetscPrintf(ctx->comm,"Stability constraint exceeded at t=%g, dt %g > %g\n",(double)tnow,(double)dt,(double)(0.5/ctx->cfl_idt));
1288: } else SETERRQ2(PETSC_COMM_SELF,1,"Stability constraint exceeded, %g > %g",(double)dt,(double)(ctx->cfl/ctx->cfl_idt));
1289: }
1290: }
1291: return(0);
1292: }
1296: static PetscErrorCode SmallMatMultADB(PetscScalar *C,PetscInt bs,const PetscScalar *A,const PetscReal *D,const PetscScalar *B)
1297: {
1298: PetscInt i,j,k;
1301: for (i=0; i<bs; i++) {
1302: for (j=0; j<bs; j++) {
1303: PetscScalar tmp = 0;
1304: for (k=0; k<bs; k++) tmp += A[i*bs+k] * D[k] * B[k*bs+j];
1305: C[i*bs+j] = tmp;
1306: }
1307: }
1308: return(0);
1309: }
1314: static PetscErrorCode FVIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat A,Mat B,void *vctx)
1315: {
1316: FVCtx *ctx = (FVCtx*)vctx;
1317: PetscErrorCode ierr;
1318: PetscInt i,j,dof = ctx->physics.dof;
1319: PetscScalar *J;
1320: const PetscScalar *x;
1321: PetscReal hx;
1322: DM da;
1323: DMDALocalInfo dainfo;
1326: TSGetDM(ts,&da);
1327: DMDAVecGetArrayRead(da,X,(void*)&x);
1328: DMDAGetLocalInfo(da,&dainfo);
1329: hx = (ctx->xmax - ctx->xmin)/dainfo.mx;
1330: PetscMalloc1(dof*dof,&J);
1331: for (i=dainfo.xs; i<dainfo.xs+dainfo.xm; i++) {
1332: (*ctx->physics.characteristic)(ctx->physics.user,dof,&x[i*dof],ctx->R,ctx->Rinv,ctx->speeds);
1333: for (j=0; j<dof; j++) ctx->speeds[j] = PetscAbs(ctx->speeds[j]);
1334: SmallMatMultADB(J,dof,ctx->R,ctx->speeds,ctx->Rinv);
1335: for (j=0; j<dof*dof; j++) J[j] = J[j]/hx + shift*(j/dof == j%dof);
1336: MatSetValuesBlocked(B,1,&i,1,&i,J,INSERT_VALUES);
1337: }
1338: PetscFree(J);
1339: DMDAVecRestoreArrayRead(da,X,(void*)&x);
1341: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1342: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1343: if (A != B) {
1344: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1345: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1346: }
1347: return(0);
1348: }
1352: static PetscErrorCode FVSample(FVCtx *ctx,DM da,PetscReal time,Vec U)
1353: {
1355: PetscScalar *u,*uj;
1356: PetscInt i,j,k,dof,xs,xm,Mx;
1359: if (!ctx->physics.sample) SETERRQ(PETSC_COMM_SELF,1,"Physics has not provided a sampling function");
1360: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1361: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1362: DMDAVecGetArray(da,U,&u);
1363: PetscMalloc1(dof,&uj);
1364: for (i=xs; i<xs+xm; i++) {
1365: const PetscReal h = (ctx->xmax-ctx->xmin)/Mx,xi = ctx->xmin+h/2+i*h;
1366: const PetscInt N = 200;
1367: /* Integrate over cell i using trapezoid rule with N points. */
1368: for (k=0; k<dof; k++) u[i*dof+k] = 0;
1369: for (j=0; j<N+1; j++) {
1370: PetscScalar xj = xi+h*(j-N/2)/(PetscReal)N;
1371: (*ctx->physics.sample)(ctx->physics.user,ctx->initial,ctx->bctype,ctx->xmin,ctx->xmax,time,xj,uj);
1372: for (k=0; k<dof; k++) u[i*dof+k] += ((j==0 || j==N) ? 0.5 : 1.0)*uj[k]/N;
1373: }
1374: }
1375: DMDAVecRestoreArray(da,U,&u);
1376: PetscFree(uj);
1377: return(0);
1378: }
1382: static PetscErrorCode SolutionStatsView(DM da,Vec X,PetscViewer viewer)
1383: {
1384: PetscErrorCode ierr;
1385: PetscReal xmin,xmax;
1386: PetscScalar sum,tvsum,tvgsum;
1387: const PetscScalar *x;
1388: PetscInt imin,imax,Mx,i,j,xs,xm,dof;
1389: Vec Xloc;
1390: PetscBool iascii;
1393: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1394: if (iascii) {
1395: /* PETSc lacks a function to compute total variation norm (difficult in multiple dimensions), we do it here */
1396: DMGetLocalVector(da,&Xloc);
1397: DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
1398: DMGlobalToLocalEnd (da,X,INSERT_VALUES,Xloc);
1399: DMDAVecGetArrayRead(da,Xloc,(void*)&x);
1400: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1401: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1402: tvsum = 0;
1403: for (i=xs; i<xs+xm; i++) {
1404: for (j=0; j<dof; j++) tvsum += PetscAbsScalar(x[i*dof+j] - x[(i-1)*dof+j]);
1405: }
1406: MPI_Allreduce(&tvsum,&tvgsum,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
1407: DMDAVecRestoreArrayRead(da,Xloc,(void*)&x);
1408: DMRestoreLocalVector(da,&Xloc);
1410: VecMin(X,&imin,&xmin);
1411: VecMax(X,&imax,&xmax);
1412: VecSum(X,&sum);
1413: 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));
1414: } else SETERRQ(PETSC_COMM_SELF,1,"Viewer type not supported");
1415: return(0);
1416: }
1420: static PetscErrorCode SolutionErrorNorms(FVCtx *ctx,DM da,PetscReal t,Vec X,PetscReal *nrm1,PetscReal *nrmsup)
1421: {
1423: Vec Y;
1424: PetscInt Mx;
1427: VecGetSize(X,&Mx);
1428: VecDuplicate(X,&Y);
1429: FVSample(ctx,da,t,Y);
1430: VecAYPX(Y,-1,X);
1431: VecNorm(Y,NORM_1,nrm1);
1432: VecNorm(Y,NORM_INFINITY,nrmsup);
1433: *nrm1 /= Mx;
1434: VecDestroy(&Y);
1435: return(0);
1436: }
1440: int main(int argc,char *argv[])
1441: {
1442: char lname[256] = "mc",physname[256] = "advect",final_fname[256] = "solution.m";
1443: PetscFunctionList limiters = 0,physics = 0;
1444: MPI_Comm comm;
1445: TS ts;
1446: DM da;
1447: Vec X,X0,R;
1448: Mat B;
1449: FVCtx ctx;
1450: PetscInt i,dof,xs,xm,Mx,draw = 0;
1451: PetscBool view_final = PETSC_FALSE;
1452: PetscReal ptime;
1453: PetscErrorCode ierr;
1455: PetscInitialize(&argc,&argv,0,help);
1456: comm = PETSC_COMM_WORLD;
1457: PetscMemzero(&ctx,sizeof(ctx));
1459: /* Register limiters to be available on the command line */
1460: PetscFunctionListAdd(&limiters,"upwind" ,Limit_Upwind);
1461: PetscFunctionListAdd(&limiters,"lax-wendroff" ,Limit_LaxWendroff);
1462: PetscFunctionListAdd(&limiters,"beam-warming" ,Limit_BeamWarming);
1463: PetscFunctionListAdd(&limiters,"fromm" ,Limit_Fromm);
1464: PetscFunctionListAdd(&limiters,"minmod" ,Limit_Minmod);
1465: PetscFunctionListAdd(&limiters,"superbee" ,Limit_Superbee);
1466: PetscFunctionListAdd(&limiters,"mc" ,Limit_MC);
1467: PetscFunctionListAdd(&limiters,"vanleer" ,Limit_VanLeer);
1468: PetscFunctionListAdd(&limiters,"vanalbada" ,Limit_VanAlbada);
1469: PetscFunctionListAdd(&limiters,"vanalbadatvd" ,Limit_VanAlbadaTVD);
1470: PetscFunctionListAdd(&limiters,"koren" ,Limit_Koren);
1471: PetscFunctionListAdd(&limiters,"korensym" ,Limit_KorenSym);
1472: PetscFunctionListAdd(&limiters,"koren3" ,Limit_Koren3);
1473: PetscFunctionListAdd(&limiters,"cada-torrilhon2" ,Limit_CadaTorrilhon2);
1474: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r0p1",Limit_CadaTorrilhon3R0p1);
1475: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r1" ,Limit_CadaTorrilhon3R1);
1476: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r10" ,Limit_CadaTorrilhon3R10);
1477: PetscFunctionListAdd(&limiters,"cada-torrilhon3-r100",Limit_CadaTorrilhon3R100);
1479: /* Register physical models to be available on the command line */
1480: PetscFunctionListAdd(&physics,"advect" ,PhysicsCreate_Advect);
1481: PetscFunctionListAdd(&physics,"burgers" ,PhysicsCreate_Burgers);
1482: PetscFunctionListAdd(&physics,"traffic" ,PhysicsCreate_Traffic);
1483: PetscFunctionListAdd(&physics,"acoustics" ,PhysicsCreate_Acoustics);
1484: PetscFunctionListAdd(&physics,"isogas" ,PhysicsCreate_IsoGas);
1485: PetscFunctionListAdd(&physics,"shallow" ,PhysicsCreate_Shallow);
1487: ctx.comm = comm;
1488: ctx.cfl = 0.9; ctx.bctype = FVBC_PERIODIC;
1489: ctx.xmin = -1; ctx.xmax = 1;
1490: PetscOptionsBegin(comm,NULL,"Finite Volume solver options","");
1491: PetscOptionsReal("-xmin","X min","",ctx.xmin,&ctx.xmin,NULL);
1492: PetscOptionsReal("-xmax","X max","",ctx.xmax,&ctx.xmax,NULL);
1493: PetscOptionsFList("-limit","Name of flux limiter to use","",limiters,lname,lname,sizeof(lname),NULL);
1494: PetscOptionsFList("-physics","Name of physics (Riemann solver and characteristics) to use","",physics,physname,physname,sizeof(physname),NULL);
1495: PetscOptionsInt("-draw","Draw solution vector, bitwise OR of (1=initial,2=final,4=final error)","",draw,&draw,NULL);
1496: PetscOptionsString("-view_final","Write final solution in ASCII MATLAB format to given file name","",final_fname,final_fname,sizeof(final_fname),&view_final);
1497: PetscOptionsInt("-initial","Initial condition (depends on the physics)","",ctx.initial,&ctx.initial,NULL);
1498: PetscOptionsBool("-exact","Compare errors with exact solution","",ctx.exact,&ctx.exact,NULL);
1499: PetscOptionsReal("-cfl","CFL number to time step at","",ctx.cfl,&ctx.cfl,NULL);
1500: PetscOptionsEnum("-bc_type","Boundary condition","",FVBCTypes,(PetscEnum)ctx.bctype,(PetscEnum*)&ctx.bctype,NULL);
1501: PetscOptionsEnd();
1503: /* Choose the limiter from the list of registered limiters */
1504: PetscFunctionListFind(limiters,lname,&ctx.limit);
1505: if (!ctx.limit) SETERRQ1(PETSC_COMM_SELF,1,"Limiter '%s' not found",lname);
1507: /* Choose the physics from the list of registered models */
1508: {
1509: PetscErrorCode (*r)(FVCtx*);
1510: PetscFunctionListFind(physics,physname,&r);
1511: if (!r) SETERRQ1(PETSC_COMM_SELF,1,"Physics '%s' not found",physname);
1512: /* Create the physics, will set the number of fields and their names */
1513: (*r)(&ctx);
1514: }
1516: /* Create a DMDA to manage the parallel grid */
1517: DMDACreate1d(comm,DM_BOUNDARY_PERIODIC,-50,ctx.physics.dof,2,NULL,&da);
1518: /* Inform the DMDA of the field names provided by the physics. */
1519: /* The names will be shown in the title bars when run with -ts_monitor_draw_solution */
1520: for (i=0; i<ctx.physics.dof; i++) {
1521: DMDASetFieldName(da,i,ctx.physics.fieldname[i]);
1522: }
1523: DMDAGetInfo(da,0, &Mx,0,0, 0,0,0, &dof,0,0,0,0,0);
1524: DMDAGetCorners(da,&xs,0,0,&xm,0,0);
1526: /* Set coordinates of cell centers */
1527: DMDASetUniformCoordinates(da,ctx.xmin+0.5*(ctx.xmax-ctx.xmin)/Mx,ctx.xmax+0.5*(ctx.xmax-ctx.xmin)/Mx,0,0,0,0);
1529: /* Allocate work space for the Finite Volume solver (so it doesn't have to be reallocated on each function evaluation) */
1530: PetscMalloc4(dof*dof,&ctx.R,dof*dof,&ctx.Rinv,2*dof,&ctx.cjmpLR,1*dof,&ctx.cslope);
1531: PetscMalloc3(2*dof,&ctx.uLR,dof,&ctx.flux,dof,&ctx.speeds);
1533: /* Create a vector to store the solution and to save the initial state */
1534: DMCreateGlobalVector(da,&X);
1535: VecDuplicate(X,&X0);
1536: VecDuplicate(X,&R);
1538: DMCreateMatrix(da,&B);
1540: /* Create a time-stepping object */
1541: TSCreate(comm,&ts);
1542: TSSetDM(ts,da);
1543: TSSetRHSFunction(ts,R,FVRHSFunction,&ctx);
1544: TSSetIJacobian(ts,B,B,FVIJacobian,&ctx);
1545: TSSetType(ts,TSSSP);
1546: TSSetDuration(ts,1000,10);
1547: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1548:
1549: /* Compute initial conditions and starting time step */
1550: FVSample(&ctx,da,0,X0);
1551: FVRHSFunction(ts,0,X0,X,(void*)&ctx); /* Initial function evaluation, only used to determine max speed */
1552: VecCopy(X0,X); /* The function value was not used so we set X=X0 again */
1553: TSSetInitialTimeStep(ts,0,ctx.cfl/ctx.cfl_idt);
1554: TSSetFromOptions(ts); /* Take runtime options */
1555: SolutionStatsView(da,X,PETSC_VIEWER_STDOUT_WORLD);
1556: {
1557: PetscReal nrm1,nrmsup;
1558: PetscInt steps;
1560: TSSolve(ts,X);
1561: TSGetSolveTime(ts,&ptime);
1562: TSGetTimeStepNumber(ts,&steps);
1564: PetscPrintf(comm,"Final time %8.5f, steps %D\n",(double)ptime,steps);
1565: if (ctx.exact) {
1566: SolutionErrorNorms(&ctx,da,ptime,X,&nrm1,&nrmsup);
1567: PetscPrintf(comm,"Error ||x-x_e||_1 %8.4e ||x-x_e||_sup %8.4e\n",(double)nrm1,(double)nrmsup);
1568: }
1569: }
1571: SolutionStatsView(da,X,PETSC_VIEWER_STDOUT_WORLD);
1572: if (draw & 0x1) {VecView(X0,PETSC_VIEWER_DRAW_WORLD);}
1573: if (draw & 0x2) {VecView(X,PETSC_VIEWER_DRAW_WORLD);}
1574: if (draw & 0x4) {
1575: Vec Y;
1576: VecDuplicate(X,&Y);
1577: FVSample(&ctx,da,ptime,Y);
1578: VecAYPX(Y,-1,X);
1579: VecView(Y,PETSC_VIEWER_DRAW_WORLD);
1580: VecDestroy(&Y);
1581: }
1583: if (view_final) {
1584: PetscViewer viewer;
1585: PetscViewerASCIIOpen(PETSC_COMM_WORLD,final_fname,&viewer);
1586: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
1587: VecView(X,viewer);
1588: PetscViewerPopFormat(viewer);
1589: PetscViewerDestroy(&viewer);
1590: }
1592: /* Clean up */
1593: (*ctx.physics.destroy)(ctx.physics.user);
1594: for (i=0; i<ctx.physics.dof; i++) {PetscFree(ctx.physics.fieldname[i]);}
1595: PetscFree4(ctx.R,ctx.Rinv,ctx.cjmpLR,ctx.cslope);
1596: PetscFree3(ctx.uLR,ctx.flux,ctx.speeds);
1597: VecDestroy(&X);
1598: VecDestroy(&X0);
1599: VecDestroy(&R);
1600: MatDestroy(&B);
1601: DMDestroy(&da);
1602: TSDestroy(&ts);
1603: PetscFunctionListDestroy(&limiters);
1604: PetscFunctionListDestroy(&physics);
1605: PetscFinalize();
1606: return 0;
1607: }