Actual source code: ex10.c
petsc-3.7.5 2017-01-01
1: static const char help[] = "1D nonequilibrium radiation diffusion with Saha ionization model.\n\n";
3: /*
4: This example implements the model described in
6: Rauenzahn, Mousseau, Knoll. "Temporal accuracy of the nonequilibrium radiation diffusion
7: equations employing a Saha ionization model" 2005.
9: The paper discusses three examples, the first two are nondimensional with a simple
10: ionization model. The third example is fully dimensional and uses the Saha ionization
11: model with realistic parameters.
12: */
14: #include <petscts.h>
15: #include <petscdm.h>
16: #include <petscdmda.h>
18: typedef enum {BC_DIRICHLET,BC_NEUMANN,BC_ROBIN} BCType;
19: static const char *const BCTypes[] = {"DIRICHLET","NEUMANN","ROBIN","BCType","BC_",0};
20: typedef enum {JACOBIAN_ANALYTIC,JACOBIAN_MATRIXFREE,JACOBIAN_FD_COLORING,JACOBIAN_FD_FULL} JacobianType;
21: static const char *const JacobianTypes[] = {"ANALYTIC","MATRIXFREE","FD_COLORING","FD_FULL","JacobianType","FD_",0};
22: typedef enum {DISCRETIZATION_FD,DISCRETIZATION_FE} DiscretizationType;
23: static const char *const DiscretizationTypes[] = {"FD","FE","DiscretizationType","DISCRETIZATION_",0};
24: typedef enum {QUADRATURE_GAUSS1,QUADRATURE_GAUSS2,QUADRATURE_GAUSS3,QUADRATURE_GAUSS4,QUADRATURE_LOBATTO2,QUADRATURE_LOBATTO3} QuadratureType;
25: static const char *const QuadratureTypes[] = {"GAUSS1","GAUSS2","GAUSS3","GAUSS4","LOBATTO2","LOBATTO3","QuadratureType","QUADRATURE_",0};
27: typedef struct {
28: PetscScalar E; /* radiation energy */
29: PetscScalar T; /* material temperature */
30: } RDNode;
32: typedef struct {
33: PetscReal meter,kilogram,second,Kelvin; /* Fundamental units */
34: PetscReal Joule,Watt; /* Derived units */
35: } RDUnit;
37: typedef struct _n_RD *RD;
39: struct _n_RD {
40: void (*MaterialEnergy)(RD,const RDNode*,PetscScalar*,RDNode*);
41: DM da;
42: PetscBool monitor_residual;
43: DiscretizationType discretization;
44: QuadratureType quadrature;
45: JacobianType jacobian;
46: PetscInt initial;
47: BCType leftbc;
48: PetscBool view_draw;
49: char view_binary[PETSC_MAX_PATH_LEN];
50: PetscBool test_diff;
51: PetscBool endpoint;
52: PetscBool bclimit;
53: PetscBool bcmidpoint;
54: RDUnit unit;
56: /* model constants, see Table 2 and RDCreate() */
57: PetscReal rho,K_R,K_p,I_H,m_p,m_e,h,k,c,sigma_b,beta,gamma;
59: /* Domain and boundary conditions */
60: PetscReal Eapplied; /* Radiation flux from the left */
61: PetscReal L; /* Length of domain */
62: PetscReal final_time;
63: };
67: static PetscErrorCode RDDestroy(RD *rd)
68: {
72: DMDestroy(&(*rd)->da);
73: PetscFree(*rd);
74: return(0);
75: }
77: /* The paper has a time derivative for material energy (Eq 2) which is a dependent variable (computable from temperature
78: * and density through an uninvertible relation). Computing this derivative is trivial for trapezoid rule (used in the
79: * paper), but does not generalize nicely to higher order integrators. Here we use the implicit form which provides
80: * time derivatives of the independent variables (radiation energy and temperature), so we must compute the time
81: * derivative of material energy ourselves (could be done using AD).
82: *
83: * There are multiple ionization models, this interface dispatches to the one currently in use.
84: */
85: static void RDMaterialEnergy(RD rd,const RDNode *n,PetscScalar *Em,RDNode *dEm) { rd->MaterialEnergy(rd,n,Em,dEm); }
87: /* Solves a quadratic equation while propagating tangents */
88: static void QuadraticSolve(PetscScalar a,PetscScalar a_t,PetscScalar b,PetscScalar b_t,PetscScalar c,PetscScalar c_t,PetscScalar *x,PetscScalar *x_t)
89: {
90: PetscScalar
91: disc = b*b - 4.*a*c,
92: disc_t = 2.*b*b_t - 4.*a_t*c - 4.*a*c_t,
93: num = -b + PetscSqrtScalar(disc), /* choose positive sign */
94: num_t = -b_t + 0.5/PetscSqrtScalar(disc)*disc_t,
95: den = 2.*a,
96: den_t = 2.*a_t;
97: *x = num/den;
98: *x_t = (num_t*den - num*den_t) / PetscSqr(den);
99: }
101: /* The primary model presented in the paper */
102: static void RDMaterialEnergy_Saha(RD rd,const RDNode *n,PetscScalar *inEm,RDNode *dEm)
103: {
104: PetscScalar Em,alpha,alpha_t,
105: T = n->T,
106: T_t = 1.,
107: chi = rd->I_H / (rd->k * T),
108: chi_t = -chi / T * T_t,
109: a = 1.,
110: a_t = 0,
111: b = 4. * rd->m_p / rd->rho * PetscPowScalarReal(2. * PETSC_PI * rd->m_e * rd->I_H / PetscSqr(rd->h),1.5) * PetscExpScalar(-chi) * PetscPowScalarReal(chi,1.5), /* Eq 7 */
112: b_t = -b*chi_t + 1.5*b/chi*chi_t,
113: c = -b,
114: c_t = -b_t;
115: QuadraticSolve(a,a_t,b,b_t,c,c_t,&alpha,&alpha_t); /* Solve Eq 7 for alpha */
116: Em = rd->k * T / rd->m_p * (1.5*(1.+alpha) + alpha*chi); /* Eq 6 */
117: if (inEm) *inEm = Em;
118: if (dEm) {
119: dEm->E = 0;
120: dEm->T = Em / T * T_t + rd->k * T / rd->m_p * (1.5*alpha_t + alpha_t*chi + alpha*chi_t);
121: }
122: }
123: /* Reduced ionization model, Eq 30 */
124: static void RDMaterialEnergy_Reduced(RD rd,const RDNode *n,PetscScalar *Em,RDNode *dEm)
125: {
126: PetscScalar alpha,alpha_t,
127: T = n->T,
128: T_t = 1.,
129: chi = -0.3 / T,
130: chi_t = -chi / T * T_t,
131: a = 1.,
132: a_t = 0.,
133: b = PetscExpScalar(chi),
134: b_t = b*chi_t,
135: c = -b,
136: c_t = -b_t;
137: QuadraticSolve(a,a_t,b,b_t,c,c_t,&alpha,&alpha_t);
138: if (Em) *Em = (1.+alpha)*T + 0.3*alpha;
139: if (dEm) {
140: dEm->E = 0;
141: dEm->T = alpha_t*T + (1.+alpha)*T_t + 0.3*alpha_t;
142: }
143: }
145: /* Eq 5 */
146: static void RDSigma_R(RD rd,RDNode *n,PetscScalar *sigma_R,RDNode *dsigma_R)
147: {
148: *sigma_R = rd->K_R * rd->rho * PetscPowScalar(n->T,-rd->gamma);
149: dsigma_R->E = 0;
150: dsigma_R->T = -rd->gamma * (*sigma_R) / n->T;
151: }
153: /* Eq 4 */
154: static void RDDiffusionCoefficient(RD rd,PetscBool limit,RDNode *n,RDNode *nx,PetscScalar *D_R,RDNode *dD_R,RDNode *dxD_R)
155: {
156: PetscScalar sigma_R,denom;
157: RDNode dsigma_R,ddenom,dxdenom;
159: RDSigma_R(rd,n,&sigma_R,&dsigma_R);
160: denom = 3. * rd->rho * sigma_R + (int)limit * PetscAbsScalar(nx->E) / n->E;
161: ddenom.E = -(int)limit * PetscAbsScalar(nx->E) / PetscSqr(n->E);
162: ddenom.T = 3. * rd->rho * dsigma_R.T;
163: dxdenom.E = (int)limit * (PetscRealPart(nx->E)<0 ? -1. : 1.) / n->E;
164: dxdenom.T = 0;
165: *D_R = rd->c / denom;
166: if (dD_R) {
167: dD_R->E = -rd->c / PetscSqr(denom) * ddenom.E;
168: dD_R->T = -rd->c / PetscSqr(denom) * ddenom.T;
169: }
170: if (dxD_R) {
171: dxD_R->E = -rd->c / PetscSqr(denom) * dxdenom.E;
172: dxD_R->T = -rd->c / PetscSqr(denom) * dxdenom.T;
173: }
174: }
178: static PetscErrorCode RDStateView(RD rd,Vec X,Vec Xdot,Vec F)
179: {
181: DMDALocalInfo info;
182: PetscInt i;
183: const RDNode *x,*xdot,*f;
184: MPI_Comm comm;
187: PetscObjectGetComm((PetscObject)rd->da,&comm);
188: DMDAGetLocalInfo(rd->da,&info);
189: DMDAVecGetArrayRead(rd->da,X,(void*)&x);
190: DMDAVecGetArrayRead(rd->da,Xdot,(void*)&xdot);
191: DMDAVecGetArrayRead(rd->da,F,(void*)&f);
192: for (i=info.xs; i<info.xs+info.xm; i++) {
193: PetscSynchronizedPrintf(comm,"x[%D] (%10.2G,%10.2G) (%10.2G,%10.2G) (%10.2G,%10.2G)\n",i,PetscRealPart(x[i].E),PetscRealPart(x[i].T),
194: PetscRealPart(xdot[i].E),PetscRealPart(xdot[i].T), PetscRealPart(f[i].E),PetscRealPart(f[i].T));
195: }
196: DMDAVecRestoreArrayRead(rd->da,X,(void*)&x);
197: DMDAVecRestoreArrayRead(rd->da,Xdot,(void*)&xdot);
198: DMDAVecRestoreArrayRead(rd->da,F,(void*)&f);
199: PetscSynchronizedFlush(comm,PETSC_STDOUT);
200: return(0);
201: }
203: static PetscScalar RDRadiation(RD rd,const RDNode *n,RDNode *dn)
204: {
205: PetscScalar sigma_p = rd->K_p * rd->rho * PetscPowScalar(n->T,-rd->beta),
206: sigma_p_T = -rd->beta * sigma_p / n->T,
207: tmp = 4.* rd->sigma_b*PetscSqr(PetscSqr(n->T)) / rd->c - n->E,
208: tmp_E = -1.,
209: tmp_T = 4. * rd->sigma_b * 4 * n->T*(PetscSqr(n->T)) / rd->c,
210: rad = sigma_p * rd->c * rd->rho * tmp,
211: rad_E = sigma_p * rd->c * rd->rho * tmp_E,
212: rad_T = rd->c * rd->rho * (sigma_p_T * tmp + sigma_p * tmp_T);
213: if (dn) {
214: dn->E = rad_E;
215: dn->T = rad_T;
216: }
217: return rad;
218: }
220: static PetscScalar RDDiffusion(RD rd,PetscReal hx,const RDNode x[],PetscInt i,RDNode d[])
221: {
222: PetscReal ihx = 1./hx;
223: RDNode n_L,nx_L,n_R,nx_R,dD_L,dxD_L,dD_R,dxD_R,dfluxL[2],dfluxR[2];
224: PetscScalar D_L,D_R,fluxL,fluxR;
226: n_L.E = 0.5*(x[i-1].E + x[i].E);
227: n_L.T = 0.5*(x[i-1].T + x[i].T);
228: nx_L.E = (x[i].E - x[i-1].E)/hx;
229: nx_L.T = (x[i].T - x[i-1].T)/hx;
230: RDDiffusionCoefficient(rd,PETSC_TRUE,&n_L,&nx_L,&D_L,&dD_L,&dxD_L);
231: fluxL = D_L*nx_L.E;
232: dfluxL[0].E = -ihx*D_L + (0.5*dD_L.E - ihx*dxD_L.E)*nx_L.E;
233: dfluxL[1].E = +ihx*D_L + (0.5*dD_L.E + ihx*dxD_L.E)*nx_L.E;
234: dfluxL[0].T = (0.5*dD_L.T - ihx*dxD_L.T)*nx_L.E;
235: dfluxL[1].T = (0.5*dD_L.T + ihx*dxD_L.T)*nx_L.E;
237: n_R.E = 0.5*(x[i].E + x[i+1].E);
238: n_R.T = 0.5*(x[i].T + x[i+1].T);
239: nx_R.E = (x[i+1].E - x[i].E)/hx;
240: nx_R.T = (x[i+1].T - x[i].T)/hx;
241: RDDiffusionCoefficient(rd,PETSC_TRUE,&n_R,&nx_R,&D_R,&dD_R,&dxD_R);
242: fluxR = D_R*nx_R.E;
243: dfluxR[0].E = -ihx*D_R + (0.5*dD_R.E - ihx*dxD_R.E)*nx_R.E;
244: dfluxR[1].E = +ihx*D_R + (0.5*dD_R.E + ihx*dxD_R.E)*nx_R.E;
245: dfluxR[0].T = (0.5*dD_R.T - ihx*dxD_R.T)*nx_R.E;
246: dfluxR[1].T = (0.5*dD_R.T + ihx*dxD_R.T)*nx_R.E;
248: if (d) {
249: d[0].E = -ihx*dfluxL[0].E;
250: d[0].T = -ihx*dfluxL[0].T;
251: d[1].E = ihx*(dfluxR[0].E - dfluxL[1].E);
252: d[1].T = ihx*(dfluxR[0].T - dfluxL[1].T);
253: d[2].E = ihx*dfluxR[1].E;
254: d[2].T = ihx*dfluxR[1].T;
255: }
256: return ihx*(fluxR - fluxL);
257: }
261: static PetscErrorCode RDGetLocalArrays(RD rd,TS ts,Vec X,Vec Xdot,PetscReal *Theta,PetscReal *dt,Vec *X0loc,RDNode **x0,Vec *Xloc,RDNode **x,Vec *Xloc_t,RDNode **xdot)
262: {
264: PetscBool istheta;
267: DMGetLocalVector(rd->da,X0loc);
268: DMGetLocalVector(rd->da,Xloc);
269: DMGetLocalVector(rd->da,Xloc_t);
271: DMGlobalToLocalBegin(rd->da,X,INSERT_VALUES,*Xloc);
272: DMGlobalToLocalEnd(rd->da,X,INSERT_VALUES,*Xloc);
273: DMGlobalToLocalBegin(rd->da,Xdot,INSERT_VALUES,*Xloc_t);
274: DMGlobalToLocalEnd(rd->da,Xdot,INSERT_VALUES,*Xloc_t);
276: /*
277: The following is a hack to subvert TSTHETA which is like an implicit midpoint method to behave more like a trapezoid
278: rule. These methods have equivalent linear stability, but the nonlinear stability is somewhat different. The
279: radiation system is inconvenient to write in explicit form because the ionization model is "on the left".
280: */
281: PetscObjectTypeCompare((PetscObject)ts,TSTHETA,&istheta);
282: if (istheta && rd->endpoint) {
283: TSThetaGetTheta(ts,Theta);
284: } else *Theta = 1.;
286: TSGetTimeStep(ts,dt);
287: VecWAXPY(*X0loc,-(*Theta)*(*dt),*Xloc_t,*Xloc); /* back out the value at the start of this step */
288: if (rd->endpoint) {
289: VecWAXPY(*Xloc,*dt,*Xloc_t,*X0loc); /* move the abscissa to the end of the step */
290: }
292: DMDAVecGetArray(rd->da,*X0loc,x0);
293: DMDAVecGetArray(rd->da,*Xloc,x);
294: DMDAVecGetArray(rd->da,*Xloc_t,xdot);
295: return(0);
296: }
300: static PetscErrorCode RDRestoreLocalArrays(RD rd,Vec *X0loc,RDNode **x0,Vec *Xloc,RDNode **x,Vec *Xloc_t,RDNode **xdot)
301: {
305: DMDAVecRestoreArray(rd->da,*X0loc,x0);
306: DMDAVecRestoreArray(rd->da,*Xloc,x);
307: DMDAVecRestoreArray(rd->da,*Xloc_t,xdot);
308: DMRestoreLocalVector(rd->da,X0loc);
309: DMRestoreLocalVector(rd->da,Xloc);
310: DMRestoreLocalVector(rd->da,Xloc_t);
311: return(0);
312: }
316: static PetscErrorCode RDCheckDomain_Private(RD rd,TS ts,Vec X,PetscBool *in)
317: {
319: PetscInt minloc;
320: PetscReal min;
323: VecMin(X,&minloc,&min);
324: if (min < 0) {
325: SNES snes;
326: *in = PETSC_FALSE;
327: TSGetSNES(ts,&snes);
328: SNESSetFunctionDomainError(snes);
329: PetscInfo3(ts,"Domain violation at %D field %D value %g\n",minloc/2,minloc%2,(double)min);
330: } else *in = PETSC_TRUE;
331: return(0);
332: }
334: /* Energy and temperature must remain positive */
335: #define RDCheckDomain(rd,ts,X) do { \
336: PetscErrorCode _ierr; \
337: PetscBool _in; \
338: _RDCheckDomain_Private(rd,ts,X,&_in);CHKERRQ(_ierr); \
339: if (!_in) return(0); \
340: } while (0)
344: static PetscErrorCode RDIFunction_FD(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
345: {
347: RD rd = (RD)ctx;
348: RDNode *x,*x0,*xdot,*f;
349: Vec X0loc,Xloc,Xloc_t;
350: PetscReal hx,Theta,dt;
351: DMDALocalInfo info;
352: PetscInt i;
355: RDCheckDomain(rd,ts,X);
356: RDGetLocalArrays(rd,ts,X,Xdot,&Theta,&dt,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
357: DMDAVecGetArray(rd->da,F,&f);
358: DMDAGetLocalInfo(rd->da,&info);
359: VecZeroEntries(F);
361: hx = rd->L / (info.mx-1);
363: for (i=info.xs; i<info.xs+info.xm; i++) {
364: PetscReal rho = rd->rho;
365: PetscScalar Em_t,rad;
367: rad = (1.-Theta)*RDRadiation(rd,&x0[i],0) + Theta*RDRadiation(rd,&x[i],0);
368: if (rd->endpoint) {
369: PetscScalar Em0,Em1;
370: RDMaterialEnergy(rd,&x0[i],&Em0,NULL);
371: RDMaterialEnergy(rd,&x[i],&Em1,NULL);
372: Em_t = (Em1 - Em0) / dt;
373: } else {
374: RDNode dEm;
375: RDMaterialEnergy(rd,&x[i],NULL,&dEm);
376: Em_t = dEm.E * xdot[i].E + dEm.T * xdot[i].T;
377: }
378: /* Residuals are multiplied by the volume element (hx). */
379: /* The temperature equation does not have boundary conditions */
380: f[i].T = hx*(rho*Em_t + rad);
382: if (i == 0) { /* Left boundary condition */
383: PetscScalar D_R,bcTheta = rd->bcmidpoint ? Theta : 1.;
384: RDNode n, nx;
386: n.E = (1.-bcTheta)*x0[0].E + bcTheta*x[0].E;
387: n.T = (1.-bcTheta)*x0[0].T + bcTheta*x[0].T;
388: nx.E = ((1.-bcTheta)*(x0[1].E-x0[0].E) + bcTheta*(x[1].E-x[0].E))/hx;
389: nx.T = ((1.-bcTheta)*(x0[1].T-x0[0].T) + bcTheta*(x[1].T-x[0].T))/hx;
390: switch (rd->leftbc) {
391: case BC_ROBIN:
392: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D_R,0,0);
393: f[0].E = hx*(n.E - 2. * D_R * nx.E - rd->Eapplied);
394: break;
395: case BC_NEUMANN:
396: f[0].E = x[1].E - x[0].E;
397: break;
398: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %D",rd->initial);
399: }
400: } else if (i == info.mx-1) { /* Right boundary */
401: f[i].E = x[i].E - x[i-1].E; /* Homogeneous Neumann */
402: } else {
403: PetscScalar diff = (1.-Theta)*RDDiffusion(rd,hx,x0,i,0) + Theta*RDDiffusion(rd,hx,x,i,0);
404: f[i].E = hx*(xdot[i].E - diff - rad);
405: }
406: }
407: RDRestoreLocalArrays(rd,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
408: DMDAVecRestoreArray(rd->da,F,&f);
409: if (rd->monitor_residual) {RDStateView(rd,X,Xdot,F);}
410: return(0);
411: }
415: static PetscErrorCode RDIJacobian_FD(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
416: {
418: RD rd = (RD)ctx;
419: RDNode *x,*x0,*xdot;
420: Vec X0loc,Xloc,Xloc_t;
421: PetscReal hx,Theta,dt;
422: DMDALocalInfo info;
423: PetscInt i;
426: RDCheckDomain(rd,ts,X);
427: RDGetLocalArrays(rd,ts,X,Xdot,&Theta,&dt,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
428: DMDAGetLocalInfo(rd->da,&info);
429: hx = rd->L / (info.mx-1);
430: MatZeroEntries(B);
432: for (i=info.xs; i<info.xs+info.xm; i++) {
433: PetscInt col[3];
434: PetscReal rho = rd->rho;
435: PetscScalar /*Em_t,rad,*/ K[2][6];
436: RDNode dEm_t,drad;
438: /*rad = (1.-Theta)* */ RDRadiation(rd,&x0[i],0); /* + Theta* */ RDRadiation(rd,&x[i],&drad);
440: if (rd->endpoint) {
441: PetscScalar Em0,Em1;
442: RDNode dEm1;
443: RDMaterialEnergy(rd,&x0[i],&Em0,NULL);
444: RDMaterialEnergy(rd,&x[i],&Em1,&dEm1);
445: /*Em_t = (Em1 - Em0) / (Theta*dt);*/
446: dEm_t.E = dEm1.E / (Theta*dt);
447: dEm_t.T = dEm1.T / (Theta*dt);
448: } else {
449: const PetscScalar epsilon = x[i].T * PETSC_SQRT_MACHINE_EPSILON;
450: RDNode n1;
451: RDNode dEm,dEm1;
452: PetscScalar Em_TT;
454: n1.E = x[i].E;
455: n1.T = x[i].T+epsilon;
456: RDMaterialEnergy(rd,&x[i],NULL,&dEm);
457: RDMaterialEnergy(rd,&n1,NULL,&dEm1);
458: /* The Jacobian needs another derivative. We finite difference here instead of
459: * propagating second derivatives through the ionization model. */
460: Em_TT = (dEm1.T - dEm.T) / epsilon;
461: /*Em_t = dEm.E * xdot[i].E + dEm.T * xdot[i].T;*/
462: dEm_t.E = dEm.E * a;
463: dEm_t.T = dEm.T * a + Em_TT * xdot[i].T;
464: }
466: PetscMemzero(K,sizeof(K));
467: /* Residuals are multiplied by the volume element (hx). */
468: if (i == 0) {
469: PetscScalar D,bcTheta = rd->bcmidpoint ? Theta : 1.;
470: RDNode n, nx;
471: RDNode dD,dxD;
473: n.E = (1.-bcTheta)*x0[0].E + bcTheta*x[0].E;
474: n.T = (1.-bcTheta)*x0[0].T + bcTheta*x[0].T;
475: nx.E = ((1.-bcTheta)*(x0[1].E-x0[0].E) + bcTheta*(x[1].E-x[0].E))/hx;
476: nx.T = ((1.-bcTheta)*(x0[1].T-x0[0].T) + bcTheta*(x[1].T-x[0].T))/hx;
477: switch (rd->leftbc) {
478: case BC_ROBIN:
479: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D,&dD,&dxD);
480: K[0][1*2+0] = (bcTheta/Theta)*hx*(1. -2.*D*(-1./hx) - 2.*nx.E*dD.E + 2.*nx.E*dxD.E/hx);
481: K[0][1*2+1] = (bcTheta/Theta)*hx*(-2.*nx.E*dD.T);
482: K[0][2*2+0] = (bcTheta/Theta)*hx*(-2.*D*(1./hx) - 2.*nx.E*dD.E - 2.*nx.E*dxD.E/hx);
483: break;
484: case BC_NEUMANN:
485: K[0][1*2+0] = -1./Theta;
486: K[0][2*2+0] = 1./Theta;
487: break;
488: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %D",rd->initial);
489: }
490: } else if (i == info.mx-1) {
491: K[0][0*2+0] = -1./Theta;
492: K[0][1*2+0] = 1./Theta;
493: } else {
494: /*PetscScalar diff;*/
495: RDNode ddiff[3];
496: /*diff = (1.-Theta)*RDDiffusion(rd,hx,x0,i,0) + Theta* */ RDDiffusion(rd,hx,x,i,ddiff);
497: K[0][0*2+0] = -hx*ddiff[0].E;
498: K[0][0*2+1] = -hx*ddiff[0].T;
499: K[0][1*2+0] = hx*(a - ddiff[1].E - drad.E);
500: K[0][1*2+1] = hx*(-ddiff[1].T - drad.T);
501: K[0][2*2+0] = -hx*ddiff[2].E;
502: K[0][2*2+1] = -hx*ddiff[2].T;
503: }
505: K[1][1*2+0] = hx*(rho*dEm_t.E + drad.E);
506: K[1][1*2+1] = hx*(rho*dEm_t.T + drad.T);
508: col[0] = i-1;
509: col[1] = i;
510: col[2] = i+1<info.mx ? i+1 : -1;
511: MatSetValuesBlocked(B,1,&i,3,col,&K[0][0],INSERT_VALUES);
512: }
513: RDRestoreLocalArrays(rd,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
514: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
515: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
516: if (A != B) {
517: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
518: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
519: }
520: return(0);
521: }
523: /* Evaluate interpolants and derivatives at a select quadrature point */
524: static void RDEvaluate(PetscReal interp[][2],PetscReal deriv[][2],PetscInt q,const RDNode x[],PetscInt i,RDNode *n,RDNode *nx)
525: {
526: PetscInt j;
527: n->E = 0; n->T = 0; nx->E = 0; nx->T = 0;
528: for (j=0; j<2; j++) {
529: n->E += interp[q][j] * x[i+j].E;
530: n->T += interp[q][j] * x[i+j].T;
531: nx->E += deriv[q][j] * x[i+j].E;
532: nx->T += deriv[q][j] * x[i+j].T;
533: }
534: }
538: /*
539: Various quadrature rules. The nonlinear terms are non-polynomial so no standard quadrature will be exact.
540: */
541: static PetscErrorCode RDGetQuadrature(RD rd,PetscReal hx,PetscInt *nq,PetscReal weight[],PetscReal interp[][2],PetscReal deriv[][2])
542: {
543: PetscInt q,j;
544: const PetscReal *refweight,(*refinterp)[2],(*refderiv)[2];
547: switch (rd->quadrature) {
548: case QUADRATURE_GAUSS1: {
549: static const PetscReal ww[1] = {1.},ii[1][2] = {{0.5,0.5}},dd[1][2] = {{-1.,1.}};
550: *nq = 1; refweight = ww; refinterp = ii; refderiv = dd;
551: } break;
552: case QUADRATURE_GAUSS2: {
553: static const PetscReal ii[2][2] = {{0.78867513459481287,0.21132486540518713},{0.21132486540518713,0.78867513459481287}},dd[2][2] = {{-1.,1.},{-1.,1.}},ww[2] = {0.5,0.5};
554: *nq = 2; refweight = ww; refinterp = ii; refderiv = dd;
555: } break;
556: case QUADRATURE_GAUSS3: {
557: static const PetscReal ii[3][2] = {{0.8872983346207417,0.1127016653792583},{0.5,0.5},{0.1127016653792583,0.8872983346207417}},
558: dd[3][2] = {{-1,1},{-1,1},{-1,1}},ww[3] = {5./18,8./18,5./18};
559: *nq = 3; refweight = ww; refinterp = ii; refderiv = dd;
560: } break;
561: case QUADRATURE_GAUSS4: {
562: static const PetscReal ii[][2] = {{0.93056815579702623,0.069431844202973658},
563: {0.66999052179242813,0.33000947820757187},
564: {0.33000947820757187,0.66999052179242813},
565: {0.069431844202973658,0.93056815579702623}},
566: dd[][2] = {{-1,1},{-1,1},{-1,1},{-1,1}},ww[] = {0.17392742256872692,0.3260725774312731,0.3260725774312731,0.17392742256872692};
568: *nq = 4; refweight = ww; refinterp = ii; refderiv = dd;
569: } break;
570: case QUADRATURE_LOBATTO2: {
571: static const PetscReal ii[2][2] = {{1.,0.},{0.,1.}},dd[2][2] = {{-1.,1.},{-1.,1.}},ww[2] = {0.5,0.5};
572: *nq = 2; refweight = ww; refinterp = ii; refderiv = dd;
573: } break;
574: case QUADRATURE_LOBATTO3: {
575: static const PetscReal ii[3][2] = {{1,0},{0.5,0.5},{0,1}},dd[3][2] = {{-1,1},{-1,1},{-1,1}},ww[3] = {1./6,4./6,1./6};
576: *nq = 3; refweight = ww; refinterp = ii; refderiv = dd;
577: } break;
578: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unknown quadrature %d",(int)rd->quadrature);
579: }
581: for (q=0; q<*nq; q++) {
582: weight[q] = refweight[q] * hx;
583: for (j=0; j<2; j++) {
584: interp[q][j] = refinterp[q][j];
585: deriv[q][j] = refderiv[q][j] / hx;
586: }
587: }
588: return(0);
589: }
593: /*
594: Finite element version
595: */
596: static PetscErrorCode RDIFunction_FE(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
597: {
599: RD rd = (RD)ctx;
600: RDNode *x,*x0,*xdot,*f;
601: Vec X0loc,Xloc,Xloc_t,Floc;
602: PetscReal hx,Theta,dt,weight[5],interp[5][2],deriv[5][2];
603: DMDALocalInfo info;
604: PetscInt i,j,q,nq;
607: RDCheckDomain(rd,ts,X);
608: RDGetLocalArrays(rd,ts,X,Xdot,&Theta,&dt,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
610: DMGetLocalVector(rd->da,&Floc);
611: VecZeroEntries(Floc);
612: DMDAVecGetArray(rd->da,Floc,&f);
613: DMDAGetLocalInfo(rd->da,&info);
615: /* Set up shape functions and quadrature for elements (assumes a uniform grid) */
616: hx = rd->L / (info.mx-1);
617: RDGetQuadrature(rd,hx,&nq,weight,interp,deriv);
619: for (i=info.xs; i<PetscMin(info.xs+info.xm,info.mx-1); i++) {
620: for (q=0; q<nq; q++) {
621: PetscReal rho = rd->rho;
622: PetscScalar Em_t,rad,D_R,D0_R;
623: RDNode n,n0,nx,n0x,nt,ntx;
624: RDEvaluate(interp,deriv,q,x,i,&n,&nx);
625: RDEvaluate(interp,deriv,q,x0,i,&n0,&n0x);
626: RDEvaluate(interp,deriv,q,xdot,i,&nt,&ntx);
628: rad = (1.-Theta)*RDRadiation(rd,&n0,0) + Theta*RDRadiation(rd,&n,0);
629: if (rd->endpoint) {
630: PetscScalar Em0,Em1;
631: RDMaterialEnergy(rd,&n0,&Em0,NULL);
632: RDMaterialEnergy(rd,&n,&Em1,NULL);
633: Em_t = (Em1 - Em0) / dt;
634: } else {
635: RDNode dEm;
636: RDMaterialEnergy(rd,&n,NULL,&dEm);
637: Em_t = dEm.E * nt.E + dEm.T * nt.T;
638: }
639: RDDiffusionCoefficient(rd,PETSC_TRUE,&n0,&n0x,&D0_R,0,0);
640: RDDiffusionCoefficient(rd,PETSC_TRUE,&n,&nx,&D_R,0,0);
641: for (j=0; j<2; j++) {
642: f[i+j].E += (deriv[q][j] * weight[q] * ((1.-Theta)*D0_R*n0x.E + Theta*D_R*nx.E)
643: + interp[q][j] * weight[q] * (nt.E - rad));
644: f[i+j].T += interp[q][j] * weight[q] * (rho * Em_t + rad);
645: }
646: }
647: }
648: if (info.xs == 0) {
649: switch (rd->leftbc) {
650: case BC_ROBIN: {
651: PetscScalar D_R,D_R_bc;
652: PetscReal ratio,bcTheta = rd->bcmidpoint ? Theta : 1.;
653: RDNode n, nx;
655: n.E = (1-bcTheta)*x0[0].E + bcTheta*x[0].E;
656: n.T = (1-bcTheta)*x0[0].T + bcTheta*x[0].T;
657: nx.E = (x[1].E-x[0].E)/hx;
658: nx.T = (x[1].T-x[0].T)/hx;
659: RDDiffusionCoefficient(rd,PETSC_TRUE,&n,&nx,&D_R,0,0);
660: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D_R_bc,0,0);
661: ratio = PetscRealPart(D_R/D_R_bc);
662: if (ratio > 1.) SETERRQ(PETSC_COMM_SELF,1,"Limited diffusivity is greater than unlimited");
663: if (ratio < 1e-3) SETERRQ(PETSC_COMM_SELF,1,"Heavily limited diffusivity");
664: f[0].E += -ratio*0.5*(rd->Eapplied - n.E);
665: } break;
666: case BC_NEUMANN:
667: /* homogeneous Neumann is the natural condition */
668: break;
669: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %D",rd->initial);
670: }
671: }
673: RDRestoreLocalArrays(rd,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
674: DMDAVecRestoreArray(rd->da,Floc,&f);
675: VecZeroEntries(F);
676: DMLocalToGlobalBegin(rd->da,Floc,ADD_VALUES,F);
677: DMLocalToGlobalEnd(rd->da,Floc,ADD_VALUES,F);
678: DMRestoreLocalVector(rd->da,&Floc);
680: if (rd->monitor_residual) {RDStateView(rd,X,Xdot,F);}
681: return(0);
682: }
686: static PetscErrorCode RDIJacobian_FE(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
687: {
689: RD rd = (RD)ctx;
690: RDNode *x,*x0,*xdot;
691: Vec X0loc,Xloc,Xloc_t;
692: PetscReal hx,Theta,dt,weight[5],interp[5][2],deriv[5][2];
693: DMDALocalInfo info;
694: PetscInt i,j,k,q,nq;
695: PetscScalar K[4][4];
698: RDCheckDomain(rd,ts,X);
699: RDGetLocalArrays(rd,ts,X,Xdot,&Theta,&dt,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
700: DMDAGetLocalInfo(rd->da,&info);
701: hx = rd->L / (info.mx-1);
702: RDGetQuadrature(rd,hx,&nq,weight,interp,deriv);
703: MatZeroEntries(B);
704: for (i=info.xs; i<PetscMin(info.xs+info.xm,info.mx-1); i++) {
705: PetscInt rc[2];
707: rc[0] = i; rc[1] = i+1;
708: PetscMemzero(K,sizeof(K));
709: for (q=0; q<nq; q++) {
710: PetscScalar D_R;
711: PETSC_UNUSED PetscScalar rad;
712: RDNode n,nx,nt,ntx,drad,dD_R,dxD_R,dEm;
713: RDEvaluate(interp,deriv,q,x,i,&n,&nx);
714: RDEvaluate(interp,deriv,q,xdot,i,&nt,&ntx);
715: rad = RDRadiation(rd,&n,&drad);
716: RDDiffusionCoefficient(rd,PETSC_TRUE,&n,&nx,&D_R,&dD_R,&dxD_R);
717: RDMaterialEnergy(rd,&n,NULL,&dEm);
718: for (j=0; j<2; j++) {
719: for (k=0; k<2; k++) {
720: K[j*2+0][k*2+0] += (+interp[q][j] * weight[q] * (a - drad.E) * interp[q][k]
721: + deriv[q][j] * weight[q] * ((D_R + dxD_R.E * nx.E) * deriv[q][k] + dD_R.E * nx.E * interp[q][k]));
722: K[j*2+0][k*2+1] += (+interp[q][j] * weight[q] * (-drad.T * interp[q][k])
723: + deriv[q][j] * weight[q] * (dxD_R.T * deriv[q][k] + dD_R.T * interp[q][k]) * nx.E);
724: K[j*2+1][k*2+0] += interp[q][j] * weight[q] * drad.E * interp[q][k];
725: K[j*2+1][k*2+1] += interp[q][j] * weight[q] * (a * rd->rho * dEm.T + drad.T) * interp[q][k];
726: }
727: }
728: }
729: MatSetValuesBlocked(B,2,rc,2,rc,&K[0][0],ADD_VALUES);
730: }
731: if (info.xs == 0) {
732: switch (rd->leftbc) {
733: case BC_ROBIN: {
734: PetscScalar D_R,D_R_bc;
735: PetscReal ratio;
736: RDNode n, nx;
738: n.E = (1-Theta)*x0[0].E + Theta*x[0].E;
739: n.T = (1-Theta)*x0[0].T + Theta*x[0].T;
740: nx.E = (x[1].E-x[0].E)/hx;
741: nx.T = (x[1].T-x[0].T)/hx;
742: RDDiffusionCoefficient(rd,PETSC_TRUE,&n,&nx,&D_R,0,0);
743: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D_R_bc,0,0);
744: ratio = PetscRealPart(D_R/D_R_bc);
745: MatSetValue(B,0,0,ratio*0.5,ADD_VALUES);
746: } break;
747: case BC_NEUMANN:
748: /* homogeneous Neumann is the natural condition */
749: break;
750: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %D",rd->initial);
751: }
752: }
754: RDRestoreLocalArrays(rd,&X0loc,&x0,&Xloc,&x,&Xloc_t,&xdot);
755: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
756: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
757: if (A != B) {
758: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
759: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
760: }
761: return(0);
762: }
764: /* Temperature that is in equilibrium with the radiation density */
765: static PetscScalar RDRadiationTemperature(RD rd,PetscScalar E) { return PetscPowScalar(E*rd->c/(4.*rd->sigma_b),0.25); }
769: static PetscErrorCode RDInitialState(RD rd,Vec X)
770: {
771: DMDALocalInfo info;
772: PetscInt i;
773: RDNode *x;
777: DMDAGetLocalInfo(rd->da,&info);
778: DMDAVecGetArray(rd->da,X,&x);
779: for (i=info.xs; i<info.xs+info.xm; i++) {
780: PetscReal coord = i*rd->L/(info.mx-1);
781: switch (rd->initial) {
782: case 1:
783: x[i].E = 0.001;
784: x[i].T = RDRadiationTemperature(rd,x[i].E);
785: break;
786: case 2:
787: x[i].E = 0.001 + 100.*PetscExpReal(-PetscSqr(coord/0.1));
788: x[i].T = RDRadiationTemperature(rd,x[i].E);
789: break;
790: case 3:
791: x[i].E = 7.56e-2 * rd->unit.Joule / PetscPowScalarInt(rd->unit.meter,3);
792: x[i].T = RDRadiationTemperature(rd,x[i].E);
793: break;
794: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No initial state %D",rd->initial);
795: }
796: }
797: DMDAVecRestoreArray(rd->da,X,&x);
798: return(0);
799: }
803: static PetscErrorCode RDView(RD rd,Vec X,PetscViewer viewer)
804: {
806: Vec Y;
807: const RDNode *x;
808: PetscScalar *y;
809: PetscInt i,m,M;
810: const PetscInt *lx;
811: DM da;
812: MPI_Comm comm;
815: /*
816: Create a DMDA (one dof per node, zero stencil width, same layout) to hold Trad
817: (radiation temperature). It is not necessary to create a DMDA for this, but this way
818: output and visualization will have meaningful variable names and correct scales.
819: */
820: DMDAGetInfo(rd->da,0, &M,0,0, 0,0,0, 0,0,0,0,0,0);
821: DMDAGetOwnershipRanges(rd->da,&lx,0,0);
822: PetscObjectGetComm((PetscObject)rd->da,&comm);
823: DMDACreate1d(comm,DM_BOUNDARY_NONE,M,1,0,lx,&da);
824: DMDASetUniformCoordinates(da,0.,rd->L,0.,0.,0.,0.);
825: DMDASetFieldName(da,0,"T_rad");
826: DMCreateGlobalVector(da,&Y);
828: /* Compute the radiation temperature from the solution at each node */
829: VecGetLocalSize(Y,&m);
830: VecGetArrayRead(X,(const PetscScalar **)&x);
831: VecGetArray(Y,&y);
832: for (i=0; i<m; i++) y[i] = RDRadiationTemperature(rd,x[i].E);
833: VecRestoreArrayRead(X,(const PetscScalar**)&x);
834: VecRestoreArray(Y,&y);
836: VecView(Y,viewer);
837: VecDestroy(&Y);
838: DMDestroy(&da);
839: return(0);
840: }
844: static PetscErrorCode RDTestDifferentiation(RD rd)
845: {
846: MPI_Comm comm;
848: RDNode n,nx;
849: PetscScalar epsilon;
852: PetscObjectGetComm((PetscObject)rd->da,&comm);
853: epsilon = 1e-8;
854: {
855: RDNode dEm,fdEm;
856: PetscScalar T0 = 1000.,T1 = T0*(1.+epsilon),Em0,Em1;
857: n.E = 1.;
858: n.T = T0;
859: rd->MaterialEnergy(rd,&n,&Em0,&dEm);
860: n.E = 1.+epsilon;
861: n.T = T0;
862: rd->MaterialEnergy(rd,&n,&Em1,0);
863: fdEm.E = (Em1-Em0)/epsilon;
864: n.E = 1.;
865: n.T = T1;
866: rd->MaterialEnergy(rd,&n,&Em1,0);
867: fdEm.T = (Em1-Em0)/(T0*epsilon);
868: PetscPrintf(comm,"dEm {%g,%g}, fdEm {%g,%g}, diff {%g,%g}\n",(double)PetscRealPart(dEm.E),(double)PetscRealPart(dEm.T),
869: (double)PetscRealPart(fdEm.E),(double)PetscRealPart(fdEm.T),(double)PetscRealPart(dEm.E-fdEm.E),(double)PetscRealPart(dEm.T-fdEm.T));
870: }
871: {
872: PetscScalar D0,D;
873: RDNode dD,dxD,fdD,fdxD;
874: n.E = 1.; n.T = 1.; nx.E = 1.; n.T = 1.;
875: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D0,&dD,&dxD);
876: n.E = 1.+epsilon; n.T = 1.; nx.E = 1.; n.T = 1.;
877: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D,0,0); fdD.E = (D-D0)/epsilon;
878: n.E = 1; n.T = 1.+epsilon; nx.E = 1.; n.T = 1.;
879: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D,0,0); fdD.T = (D-D0)/epsilon;
880: n.E = 1; n.T = 1.; nx.E = 1.+epsilon; n.T = 1.;
881: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D,0,0); fdxD.E = (D-D0)/epsilon;
882: n.E = 1; n.T = 1.; nx.E = 1.; n.T = 1.+epsilon;
883: RDDiffusionCoefficient(rd,rd->bclimit,&n,&nx,&D,0,0); fdxD.T = (D-D0)/epsilon;
884: PetscPrintf(comm,"dD {%g,%g}, fdD {%g,%g}, diff {%g,%g}\n",(double)PetscRealPart(dD.E),(double)PetscRealPart(dD.T),
885: (double)PetscRealPart(fdD.E),(double)PetscRealPart(fdD.T),(double)PetscRealPart(dD.E-fdD.E),(double)PetscRealPart(dD.T-fdD.T));
886: PetscPrintf(comm,"dxD {%g,%g}, fdxD {%g,%g}, diffx {%g,%g}\n",(double)PetscRealPart(dxD.E),(double)PetscRealPart(dxD.T),
887: (double)PetscRealPart(fdxD.E),(double)PetscRealPart(fdxD.T),(double)PetscRealPart(dxD.E-fdxD.E),(double)PetscRealPart(dxD.T-fdxD.T));
888: }
889: {
890: PetscInt i;
891: PetscReal hx = 1.;
892: PetscScalar a0;
893: RDNode n0[3],n1[3],d[3],fd[3];
895: n0[0].E = 1.;
896: n0[0].T = 1.;
897: n0[1].E = 5.;
898: n0[1].T = 3.;
899: n0[2].E = 4.;
900: n0[2].T = 2.;
901: a0 = RDDiffusion(rd,hx,n0,1,d);
902: for (i=0; i<3; i++) {
903: PetscMemcpy(n1,n0,sizeof(n0)); n1[i].E += epsilon;
904: fd[i].E = (RDDiffusion(rd,hx,n1,1,0)-a0)/epsilon;
905: PetscMemcpy(n1,n0,sizeof(n0)); n1[i].T += epsilon;
906: fd[i].T = (RDDiffusion(rd,hx,n1,1,0)-a0)/epsilon;
907: PetscPrintf(comm,"ddiff[%D] {%g,%g}, fd {%g %g}, diff {%g,%g}\n",i,(double)PetscRealPart(d[i].E),(double)PetscRealPart(d[i].T),
908: (double)PetscRealPart(fd[i].E),(double)PetscRealPart(fd[i].T),(double)PetscRealPart(d[i].E-fd[i].E),(double)PetscRealPart(d[i].T-fd[i].T));
909: }
910: }
911: {
912: PetscScalar rad0,rad;
913: RDNode drad,fdrad;
914: n.E = 1.; n.T = 1.;
915: rad0 = RDRadiation(rd,&n,&drad);
916: n.E = 1.+epsilon; n.T = 1.;
917: rad = RDRadiation(rd,&n,0); fdrad.E = (rad-rad0)/epsilon;
918: n.E = 1.; n.T = 1.+epsilon;
919: rad = RDRadiation(rd,&n,0); fdrad.T = (rad-rad0)/epsilon;
920: PetscPrintf(comm,"drad {%g,%g}, fdrad {%g,%g}, diff {%g,%g}\n",(double)PetscRealPart(drad.E),(double)PetscRealPart(drad.T),
921: (double)PetscRealPart(fdrad.E),(double)PetscRealPart(fdrad.T),(double)PetscRealPart(drad.E-drad.E),(double)PetscRealPart(drad.T-fdrad.T));
922: }
923: return(0);
924: }
928: static PetscErrorCode RDCreate(MPI_Comm comm,RD *inrd)
929: {
931: RD rd;
932: PetscReal meter,kilogram,second,Kelvin,Joule,Watt;
935: *inrd = 0;
936: PetscNew(&rd);
938: PetscOptionsBegin(comm,NULL,"Options for nonequilibrium radiation-diffusion with RD ionization",NULL);
939: {
940: rd->initial = 1;
941: PetscOptionsInt("-rd_initial","Initial condition (1=Marshak, 2=Blast, 3=Marshak+)","",rd->initial,&rd->initial,0);
942: switch (rd->initial) {
943: case 1:
944: case 2:
945: rd->unit.kilogram = 1.;
946: rd->unit.meter = 1.;
947: rd->unit.second = 1.;
948: rd->unit.Kelvin = 1.;
949: break;
950: case 3:
951: rd->unit.kilogram = 1.e12;
952: rd->unit.meter = 1.;
953: rd->unit.second = 1.e9;
954: rd->unit.Kelvin = 1.;
955: break;
956: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unknown initial condition %d",rd->initial);
957: }
958: /* Fundamental units */
959: PetscOptionsReal("-rd_unit_meter","Length of 1 meter in nondimensional units","",rd->unit.meter,&rd->unit.meter,0);
960: PetscOptionsReal("-rd_unit_kilogram","Mass of 1 kilogram in nondimensional units","",rd->unit.kilogram,&rd->unit.kilogram,0);
961: PetscOptionsReal("-rd_unit_second","Time of a second in nondimensional units","",rd->unit.second,&rd->unit.second,0);
962: PetscOptionsReal("-rd_unit_Kelvin","Temperature of a Kelvin in nondimensional units","",rd->unit.Kelvin,&rd->unit.Kelvin,0);
963: /* Derived units */
964: rd->unit.Joule = rd->unit.kilogram*PetscSqr(rd->unit.meter/rd->unit.second);
965: rd->unit.Watt = rd->unit.Joule/rd->unit.second;
966: /* Local aliases */
967: meter = rd->unit.meter;
968: kilogram = rd->unit.kilogram;
969: second = rd->unit.second;
970: Kelvin = rd->unit.Kelvin;
971: Joule = rd->unit.Joule;
972: Watt = rd->unit.Watt;
974: PetscOptionsBool("-rd_monitor_residual","Display residuals every time they are evaluated","",rd->monitor_residual,&rd->monitor_residual,NULL);
975: PetscOptionsEnum("-rd_discretization","Discretization type","",DiscretizationTypes,(PetscEnum)rd->discretization,(PetscEnum*)&rd->discretization,NULL);
976: if (rd->discretization == DISCRETIZATION_FE) {
977: rd->quadrature = QUADRATURE_GAUSS2;
978: PetscOptionsEnum("-rd_quadrature","Finite element quadrature","",QuadratureTypes,(PetscEnum)rd->quadrature,(PetscEnum*)&rd->quadrature,NULL);
979: }
980: PetscOptionsEnum("-rd_jacobian","Type of finite difference Jacobian","",JacobianTypes,(PetscEnum)rd->jacobian,(PetscEnum*)&rd->jacobian,NULL);
981: switch (rd->initial) {
982: case 1:
983: rd->leftbc = BC_ROBIN;
984: rd->Eapplied = 4 * rd->unit.Joule / PetscPowRealInt(rd->unit.meter,3);
985: rd->L = 1. * rd->unit.meter;
986: rd->beta = 3.0;
987: rd->gamma = 3.0;
988: rd->final_time = 3 * second;
989: break;
990: case 2:
991: rd->leftbc = BC_NEUMANN;
992: rd->Eapplied = 0.;
993: rd->L = 1. * rd->unit.meter;
994: rd->beta = 3.0;
995: rd->gamma = 3.0;
996: rd->final_time = 1 * second;
997: break;
998: case 3:
999: rd->leftbc = BC_ROBIN;
1000: rd->Eapplied = 7.503e6 * rd->unit.Joule / PetscPowRealInt(rd->unit.meter,3);
1001: rd->L = 5. * rd->unit.meter;
1002: rd->beta = 3.5;
1003: rd->gamma = 3.5;
1004: rd->final_time = 20e-9 * second;
1005: break;
1006: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Initial %D",rd->initial);
1007: }
1008: PetscOptionsEnum("-rd_leftbc","Left boundary condition","",BCTypes,(PetscEnum)rd->leftbc,(PetscEnum*)&rd->leftbc,NULL);
1009: PetscOptionsReal("-rd_E_applied","Radiation flux at left end of domain","",rd->Eapplied,&rd->Eapplied,NULL);
1010: PetscOptionsReal("-rd_beta","Thermal exponent for photon absorption","",rd->beta,&rd->beta,NULL);
1011: PetscOptionsReal("-rd_gamma","Thermal exponent for diffusion coefficient","",rd->gamma,&rd->gamma,NULL);
1012: PetscOptionsBool("-rd_view_draw","Draw final solution","",rd->view_draw,&rd->view_draw,NULL);
1013: PetscOptionsBool("-rd_endpoint","Discretize using endpoints (like trapezoid rule) instead of midpoint","",rd->endpoint,&rd->endpoint,NULL);
1014: PetscOptionsBool("-rd_bcmidpoint","Impose the boundary condition at the midpoint (Theta) of the interval","",rd->bcmidpoint,&rd->bcmidpoint,NULL);
1015: PetscOptionsBool("-rd_bclimit","Limit diffusion coefficient in definition of Robin boundary condition","",rd->bclimit,&rd->bclimit,NULL);
1016: PetscOptionsBool("-rd_test_diff","Test differentiation in constitutive relations","",rd->test_diff,&rd->test_diff,NULL);
1017: PetscOptionsString("-rd_view_binary","File name to hold final solution","",rd->view_binary,rd->view_binary,sizeof(rd->view_binary),NULL);
1018: }
1019: PetscOptionsEnd();
1021: switch (rd->initial) {
1022: case 1:
1023: case 2:
1024: rd->rho = 1.;
1025: rd->c = 1.;
1026: rd->K_R = 1.;
1027: rd->K_p = 1.;
1028: rd->sigma_b = 0.25;
1029: rd->MaterialEnergy = RDMaterialEnergy_Reduced;
1030: break;
1031: case 3:
1032: /* Table 2 */
1033: rd->rho = 1.17e-3 * kilogram / (meter*meter*meter); /* density */
1034: rd->K_R = 7.44e18 * PetscPowRealInt(meter,5) * PetscPowReal(Kelvin,3.5) * PetscPowRealInt(kilogram,-2); /* */
1035: rd->K_p = 2.33e20 * PetscPowRealInt(meter,5) * PetscPowReal(Kelvin,3.5) * PetscPowRealInt(kilogram,-2); /* */
1036: rd->I_H = 2.179e-18 * Joule; /* Hydrogen ionization potential */
1037: rd->m_p = 1.673e-27 * kilogram; /* proton mass */
1038: rd->m_e = 9.109e-31 * kilogram; /* electron mass */
1039: rd->h = 6.626e-34 * Joule * second; /* Planck's constant */
1040: rd->k = 1.381e-23 * Joule / Kelvin; /* Boltzman constant */
1041: rd->c = 3.00e8 * meter / second; /* speed of light */
1042: rd->sigma_b = 5.67e-8 * Watt * PetscPowRealInt(meter,-2) * PetscPowRealInt(Kelvin,-4); /* Stefan-Boltzman constant */
1043: rd->MaterialEnergy = RDMaterialEnergy_Saha;
1044: break;
1045: }
1047: DMDACreate1d(comm,DM_BOUNDARY_NONE,-20,sizeof(RDNode)/sizeof(PetscScalar),1,NULL,&rd->da);
1048: DMDASetFieldName(rd->da,0,"E");
1049: DMDASetFieldName(rd->da,1,"T");
1050: DMDASetUniformCoordinates(rd->da,0.,1.,0.,0.,0.,0.);
1052: *inrd = rd;
1053: return(0);
1054: }
1058: int main(int argc, char *argv[])
1059: {
1061: RD rd;
1062: TS ts;
1063: SNES snes;
1064: Vec X;
1065: Mat A,B;
1066: PetscInt steps;
1067: PetscReal ftime;
1069: PetscInitialize(&argc,&argv,0,help);
1070: RDCreate(PETSC_COMM_WORLD,&rd);
1071: DMCreateGlobalVector(rd->da,&X);
1072: DMSetMatType(rd->da,MATAIJ);
1073: DMCreateMatrix(rd->da,&B);
1074: RDInitialState(rd,X);
1076: TSCreate(PETSC_COMM_WORLD,&ts);
1077: TSSetProblemType(ts,TS_NONLINEAR);
1078: TSSetType(ts,TSTHETA);
1079: TSSetDM(ts,rd->da);
1080: switch (rd->discretization) {
1081: case DISCRETIZATION_FD:
1082: TSSetIFunction(ts,NULL,RDIFunction_FD,rd);
1083: if (rd->jacobian == JACOBIAN_ANALYTIC) TSSetIJacobian(ts,B,B,RDIJacobian_FD,rd);
1084: break;
1085: case DISCRETIZATION_FE:
1086: TSSetIFunction(ts,NULL,RDIFunction_FE,rd);
1087: if (rd->jacobian == JACOBIAN_ANALYTIC) TSSetIJacobian(ts,B,B,RDIJacobian_FE,rd);
1088: break;
1089: }
1090: TSSetDuration(ts,10000,rd->final_time);
1091: TSSetInitialTimeStep(ts,0.,1e-3);
1092: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1093: TSSetFromOptions(ts);
1095: A = B;
1096: TSGetSNES(ts,&snes);
1097: switch (rd->jacobian) {
1098: case JACOBIAN_ANALYTIC:
1099: break;
1100: case JACOBIAN_MATRIXFREE:
1101: break;
1102: case JACOBIAN_FD_COLORING: {
1103: SNESSetJacobian(snes,A,B,SNESComputeJacobianDefaultColor,0);
1104: } break;
1105: case JACOBIAN_FD_FULL:
1106: SNESSetJacobian(snes,A,B,SNESComputeJacobianDefault,ts);
1107: break;
1108: }
1110: if (rd->test_diff) {
1111: RDTestDifferentiation(rd);
1112: }
1113: TSSolve(ts,X);
1114: TSGetSolveTime(ts,&ftime);
1115: TSGetTimeStepNumber(ts,&steps);
1116: PetscPrintf(PETSC_COMM_WORLD,"Steps %D final time %g\n",steps,(double)ftime);
1117: if (rd->view_draw) {
1118: RDView(rd,X,PETSC_VIEWER_DRAW_WORLD);
1119: }
1120: if (rd->view_binary[0]) {
1121: PetscViewer viewer;
1122: PetscViewerBinaryOpen(PETSC_COMM_WORLD,rd->view_binary,FILE_MODE_WRITE,&viewer);
1123: RDView(rd,X,viewer);
1124: PetscViewerDestroy(&viewer);
1125: }
1126: VecDestroy(&X);
1127: MatDestroy(&B);
1128: RDDestroy(&rd);
1129: TSDestroy(&ts);
1130: PetscFinalize();
1131: return 0;
1132: }