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Droplet_LTORC
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Droplet Lagrangian Transient One-dimensional Reacting Code Implementation of both liquid and gas phase governing equations.
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Droplet_LTORC/residue.cpp

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  1. #ifndef GSL_DEF

  2. #define GSL_DEF

  3. #include <gsl/gsl_math.h>

  4. #include <gsl/gsl_spline.h>

  5. #endif

  6. #include "residue.h"

  7. #include "macros.h"

  8. #include <cmath>

  9. #include <stdio.h>

  10. #include "timing.hpp"

  11. 

  12. double maxGradPosition(const double* y, const size_t nt, 

  13. 	               const size_t nvar, const double* x, size_t nPts){

  14. 	double maxGradT=0.0e0;

  15. 	double gradT=0.0e0;

  16. 	double pos=0.0e0;

  17. 	size_t j,jm;

  18. 	for (size_t i = 1; i <nPts; i++) {

  19. 		j=i*nvar+nt;

  20. 		jm=(i-1)*nvar+nt;

  21. 		gradT=fabs((y[j]-y[jm])/(x[i]-x[i-1]));

  22. 		if (gradT>=maxGradT) {

  23. 			maxGradT=gradT;

  24. 			pos=x[i];

  25. 		}

  26. 	}

  27. 	return(pos);

  28. }

  29. 

  30. int maxGradIndex(const double* y, const size_t nt, 

  31. 	         const size_t nvar, const double* x, size_t nPts){

  32. 	double maxGradT=0.0e0;

  33. 	double gradT=0.0e0;

  34. 	int pos=0.0e0;

  35. 	size_t j,jm;

  36. 	for (size_t i = 1; i <nPts; i++) {

  37. 		j=i*nvar+nt;

  38. 		jm=(i-1)*nvar+nt;

  39. 		gradT=fabs((y[j]-y[jm])/(x[i]-x[i-1]));

  40. 		if (gradT>=maxGradT) {

  41. 			maxGradT=gradT;

  42. 			pos=i;

  43. 		}

  44. 	}

  45. 	return(pos);

  46. }

  47. 

  48. double maxCurvPosition(const double* y, const size_t nt, 

  49. 	               const size_t nvar, const double* x, size_t nPts){

  50. 	double maxCurvT=0.0e0;

  51. 	double gradTp=0.0e0;

  52. 	double gradTm=0.0e0;

  53. 	double curvT=0.0e0;

  54. 	double dx=0.0e0;

  55. 	double pos=0.0e0;

  56. 	size_t j,jm,jp;

  57. 	for (size_t i = 1; i <nPts-1; i++) {

  58. 		j=i*nvar+nt;

  59. 		jm=(i-1)*nvar+nt;

  60. 		jp=(i+1)*nvar+nt;

  61. 		gradTp=fabs((y[jp]-y[j])/(x[i+1]-x[i]));

  62. 		gradTm=fabs((y[j]-y[jm])/(x[i]-x[i-1]));

  63. 		dx=0.5e0*((x[i]+x[i+1])-(x[i-1]+x[i]));

  64. 		curvT=(gradTp-gradTm)/dx;

  65. 		if (curvT>=maxCurvT) {

  66. 			maxCurvT=curvT;

  67. 			pos=x[i];

  68. 		}

  69. 	}

  70. 	return(pos);

  71. }

  72. 

  73. int maxCurvIndex(const double* y, const size_t nt, 

  74. 	               const size_t nvar, const double* x, size_t nPts){

  75. 	double maxCurvT=0.0e0;

  76. 	double gradTp=0.0e0;

  77. 	double gradTm=0.0e0;

  78. 	double curvT=0.0e0;

  79. 	double dx=0.0e0;

  80. 	int pos=0;

  81. 	size_t j,jm,jp;

  82. 	for (size_t i = 1; i <nPts-1; i++) {

  83. 		j=i*nvar+nt;

  84. 		jm=(i-1)*nvar+nt;

  85. 		jp=(i+1)*nvar+nt;

  86. 		gradTp=fabs((y[jp]-y[j])/(x[i+1]-x[i]));

  87. 		gradTm=fabs((y[j]-y[jm])/(x[i]-x[i-1]));

  88. 		dx=0.5e0*((x[i]+x[i+1])-(x[i-1]+x[i]));

  89. 		curvT=(gradTp-gradTm)/dx;

  90. 		if (curvT>=maxCurvT) {

  91. 			maxCurvT=curvT;

  92. 			pos=i;

  93. 		}

  94. 	}

  95. 	return(pos);

  96. }

  97. 

  98. double isothermPosition(const double* y, const double T, const size_t nt, 

  99. 	                const size_t nvar, const double* x, const size_t nPts){

  100. 	double pos=x[nPts-1];

  101. 	size_t j;

  102. 	for (size_t i = 1; i <nPts; i++) {

  103. 		j=i*nvar+nt;

  104. 		if (y[j]<=T) {

  105. 			pos=x[i];

  106. 			break;

  107. 		}

  108. 	}

  109. 	return(pos);

  110. }

  111. 

  112. void updateSolution(double* y, double* ydot, const size_t nvar,

  113. 		    const double xOld[],const double xNew[],const size_t nPts){

  114. 

  115. 	double ytemp[nPts],ydottemp[nPts];

  116. 

  117. 	gsl_interp_accel* acc;

  118. 	gsl_spline* spline;

  119. 	acc = gsl_interp_accel_alloc();

  120. 	spline = gsl_spline_alloc(gsl_interp_steffen, nPts);

  121. 

  122. 	gsl_interp_accel* accdot;

  123. 	gsl_spline* splinedot;

  124. 	accdot    = gsl_interp_accel_alloc();

  125. 	splinedot = gsl_spline_alloc(gsl_interp_steffen, nPts);

  126. 

  127. 	for (size_t j = 0; j < nvar; j++) {

  128. 

  129. 		for (size_t i = 0; i < nPts; i++) {

  130. 			ytemp[i]=y[j+i*nvar];

  131. 			ydottemp[i]=ydot[j+i*nvar];

  132. 		}

  133. 

  134. 		gsl_spline_init(spline,xOld,ytemp,nPts);

  135. 		gsl_spline_init(splinedot,xOld,ydottemp,nPts);

  136. 

  137. 		for (size_t i = 0; i < nPts; i++) {

  138. 

  139. 		      	y[j+i*nvar]=gsl_spline_eval(spline,xNew[i],acc);

  140. 		      	ydot[j+i*nvar]=gsl_spline_eval(splinedot,xNew[i],accdot);

  141. 		}

  142. 	}

  143. 

  144. 	//Exploring "fixing" boundary conditions:

  145. 	//for (size_t j = 1; j < nvar; j++) {

  146. 	//	//printf("%15.6e\t%15.6e\n", y[j],y[j+nvar]);

  147. 	//	y[j]=y[j+nvar];

  148. 	//	//y[j+(nPts-1)*nvar]=y[j+(nPts-2)*nvar];

  149. 	//	//ydot[j+nvar]=ydot[j];

  150. 	//}

  151. 	//y[0]=0.0e0;

  152. 	

  153. 	gsl_interp_accel_free(acc);

  154. 	gsl_spline_free(spline);

  155. 

  156. 	gsl_interp_accel_free(accdot);

  157. 	gsl_spline_free(splinedot);

  158. }

  159. 

  160. //Locate bath gas:

  161. size_t BathGasIndex(UserData data){

  162. 	size_t index=0;

  163. 	double max1;

  164. 	double max=data->gas->massFraction(0);

  165. 	for(size_t k=1;k<data->nsp;k++){

  166. 		max1=data->gas->massFraction(k);

  167. 		if(max1>=max){

  168. 			max=max1;

  169. 			index=k;

  170. 		}

  171. 	}

  172. 	return(index+1);

  173. }

  174. 

  175. //Locate Oxidizer:

  176. size_t oxidizerIndex(UserData data){

  177. 	size_t index=0;

  178. 	for(size_t k=1;k<data->nsp;k++){

  179. 		if(data->gas->speciesName(k-1)=="O2"){

  180. 			index=k;

  181. 		}

  182. 	}

  183. 	return(index);

  184. }

  185. 

  186. //Locate OH:

  187. size_t OHIndex(UserData data){

  188. 	size_t index=0;

  189. 	for(size_t k=1;k<data->nsp;k++){

  190. 		if(data->gas->speciesName(k-1)=="OH"){

  191. 			index=k;

  192. 		}

  193. 	}

  194. 	return(index);

  195. }

  196. 

  197. //Locate HO2:

  198. size_t HO2Index(UserData data){

  199. 	size_t index=0;

  200. 	for(size_t k=1;k<data->nsp;k++){

  201. 		if(data->gas->speciesName(k-1)=="HO2"){

  202. 			index=k;

  203. 		}

  204. 	}

  205. 	return(index);

  206. }

  207. 

  208. //Locate species index:

  209. size_t specIndex(UserData data,char *specName){

  210. 	size_t index=0;

  211. 	for(size_t k=1;k<data->nsp;k++){

  212. 		if(data->gas->speciesName(k-1)==specName){

  213. 			index=k;

  214. 		}

  215. 	}

  216. 	return(index);

  217. }

  218. 

  219. int setAlgebraicVariables(N_Vector* id, UserData data){

  220. 	double *iddata;

  221.   	N_VConst(ONE, *id);

  222.   	iddata   = N_VGetArrayPointer_OpenMP(*id);

  223. 	data->k_bath=BathGasIndex(data);

  224. 	data->k_oxidizer=oxidizerIndex(data);

  225. 	data->k_OH=OHIndex(data);

  226. 	data->k_HO2=HO2Index(data);

  227. 	data->k_drop=specIndex(data,data->dropSpec);

  228. 	printf("Oxidizer index: %lu\n",data->k_oxidizer);

  229. 	printf("Bath gas index:%lu\n",data->k_bath);

  230. 	printf("Droplet species index:%lu\n",data->k_drop);

  231. 	for (size_t i = 1; i <=data->npts; i++) {

  232. 		/*Algebraic variables: indicated by ZERO.*/

  233. 		Rid(i)=ZERO;

  234. 		Pid(i)=ZERO;

  235. 		Yid(i,data->k_bath)=ZERO;

  236. 		Mdotid(i)=ZERO;

  237. 	}	

  238. 	Mdotid(1)=ZERO;

  239. 	Rid(1)=ONE;

  240. 	Yid(1,data->k_drop)=ZERO;

  241. 	Tid(data->npts)=ZERO;

  242. 	if(data->constantPressure){

  243. 		Pid(data->npts)=ONE;

  244. 	}else{

  245. 		Pid(data->npts)=ZERO;

  246. 		Rid(data->npts)=ONE;

  247. 	}

  248. 	if(data->dirichletInner){

  249. 		Tid(1)=ZERO; 

  250. 	}else{

  251. 		Tid(1)=ONE;

  252. 	}

  253. 	if(data->dirichletOuter){

  254. 		for (size_t k = 1; k <=data->nsp; k++) {

  255. 			if(k!=data->k_bath){

  256. 				Yid(data->npts,k)=ONE;

  257. 			}

  258. 			Yid(1,k)=ZERO;

  259. 			Tid(data->npts)=ONE;

  260. 		}

  261. 	}else{

  262. 		for (size_t k = 1; k <=data->nsp; k++){

  263. 			Yid(1,k)=ZERO;

  264. 			Yid(data->npts,k)=ZERO;

  265. 			Tid(data->npts)=ZERO;

  266. 		}

  267. 	}

  268. 	return(0);

  269. }

  270. 

  271. inline double calc_area(double x,int* i){

  272. 	switch (*i) {

  273. 		case 0:

  274. 			return(ONE);

  275. 		case 1:

  276. 			return(x);

  277. 		case 2:

  278. 			return(x*x);

  279. 		default:

  280. 			return(ONE);

  281. 	}

  282. }

  283. 

  284. void readInitialCondition(FILE* input, double* ydata, const size_t nvar, const size_t nr, const size_t nPts, double Rg){

  285. 

  286. 	FILE* output;output=fopen("test.dat","w");

  287. 

  288. 	size_t bufLen=10000;

  289. 	size_t nRows=0;

  290. 	size_t nColumns=nvar;

  291. 

  292. 	char buf[bufLen];

  293. 	char buf1[bufLen];

  294. 	char comment[1];

  295. 	char *ret;

  296. 

  297. 	while (fgets(buf,bufLen, input)!=NULL){

  298. 		comment[0]=buf[0];

  299. 		if(strncmp(comment,"#",1)!=0){

  300. 			nRows++;

  301. 		}

  302. 	}

  303. 	rewind(input);

  304. 

  305. 	printf("nRows: %ld\n", nRows);

  306. 	double y[nRows*nColumns];

  307. 

  308. 	size_t i=0;

  309. 	while (fgets(buf,bufLen, input)!=NULL){

  310. 		comment[0]=buf[0];

  311. 		if(strncmp(comment,"#",1)==0){

  312. 		}

  313. 		else{

  314. 			ret=strtok(buf,"\t");

  315. 			size_t j=0;

  316. 			y[i*nColumns+j]=(double)(atof(ret));

  317. 			j++;

  318. 			while(ret!=NULL){

  319. 				ret=strtok(NULL,"\t");

  320. 				if(j<nColumns){

  321. 					y[i*nColumns+j]=(double)(atof(ret));

  322. 				}

  323. 				j++;

  324. 			}

  325. 			i++;

  326. 		}

  327. 	}

  328. 

  329. 	for (i = 0; i < nRows; i++) {

  330. 		for (size_t j = 0; j < nColumns; j++) {

  331. 			fprintf(output, "%15.6e\t",y[i*nColumns+j]);

  332. 		}

  333. 		fprintf(output, "\n");

  334. 	}

  335. 	fclose(output);

  336. 

  337. 	//double xOld[nRows],xNew[nPts],ytemp[nPts];

  338. 	double xOld[nRows],xNew[nPts],ytemp[nRows];

  339. 

  340. 	for (size_t j = 0; j < nRows; j++) {

  341. 		xOld[j]=y[j*nColumns+nr];

  342. 	}

  343. 

  344. 	//double dx=(xOld[nRows-1] - xOld[0])/((double)(nPts)-1.0e0);

  345. 	//for (size_t j = 0; j < nPts-1; j++) {

  346. 	//	xNew[j]=(double)j*dx + xOld[0];

  347. 	//}

  348. 	//xNew[nPts-1]=xOld[nRows-1];

  349. 	double dX0;

  350. 	int NN = nPts-2;

  351. 	

  352. 	dX0 = (xOld[nRows-1]-xOld[0])*(pow(Rg,1.0/NN) - 1.0)/(pow(Rg,(NN+1.0)/NN) - 1.0);

  353. 	xNew[0] = xOld[0];

  354. 	for (size_t i = 1; i < nPts-1; i++) {

  355. 		xNew[i]=xNew[i-1]+dX0*pow(Rg,(i-1.0)/NN);

  356. 	}

  357. 	xNew[nPts-1] = xOld[nRows-1];

  358. 

  359. 	gsl_interp_accel* acc;

  360. 	gsl_spline* spline;

  361. 	acc = gsl_interp_accel_alloc();

  362. 	spline = gsl_spline_alloc(gsl_interp_steffen, nRows);

  363. 

  364. 	for (size_t j = 0; j < nColumns; j++) {

  365. 

  366. 		for (size_t k = 0; k < nRows; k++) {

  367. 			ytemp[k]=y[j+k*nColumns];

  368. 		}

  369. 

  370. 		gsl_spline_init(spline,xOld,ytemp,nRows);

  371. 

  372. 		for (size_t k = 0; k < nPts; k++) {

  373. 		      	ydata[j+k*nColumns]=gsl_spline_eval(spline,xNew[k],acc);

  374. 		}

  375. 	}

  376. 	

  377. 	gsl_interp_accel_free(acc);

  378. 	gsl_spline_free(spline);

  379. 

  380. }

  381. 

  382. double systemMass(double* ydata,UserData data){

  383. 	double mass=0.0e0;

  384. 	double rho;

  385. 	for (size_t i = 2; i <=data->npts; i++) {

  386.   		data->gas->setState_TPY(T(i), P(i), &Y(i,1));   

  387. 		rho=data->gas->density();                                           

  388. 		//psi(i)=psi(i-1)+rho*(R(i)-R(i-1))*calc_area(HALF*(R(i)+R(i-1)),&m);

  389. 		mass+=rho*(R(i)-R(i-1))*calc_area(R(i),&data->metric);

  390. 	}

  391. 	return(mass);

  392. }

  393. 

  394. 

  395. int initializePsiGrid(double* ydata, double* psidata, UserData data){

  396. 

  397. 	double rho,rhom;

  398. 	/*Create a psi grid that corresponds CONSISTENTLY to the spatial grid

  399. 	 * "R" created above. Note that the Lagrangian variable psi has  units

  400. 	 * of kg. */

  401. 	psi(1)=ZERO;

  402. 	for (size_t i = 2; i <=data->npts; i++) {

  403.   		data->gas->setState_TPY(T(i), P(i), &Y(i,1));   

  404. 		rho=data->gas->density();                                           

  405.   		data->gas->setState_TPY(T(i-1), P(i-1), &Y(i-1,1));   

  406. 		rhom=data->gas->density();                                           

  407. 		//psi(i)=psi(i-1)+rho*(R(i)-R(i-1))*calc_area(HALF*(R(i)+R(i-1)),&data->metric);

  408. 		//psi(i)=psi(i-1)+rho*(R(i)-R(i-1))*calc_area(R(i),&data->metric);

  409. 		psi(i)=psi(i-1)+(R(i)-R(i-1))*(rho*calc_area(R(i),&data->metric)+rhom*calc_area(R(i-1),&data->metric))/TWO;

  410. 	}

  411. 

  412. 	/*The mass of the entire system is the value of psi at the last grid

  413. 	 * point. Normalize psi by this mass so that it varies from zero to

  414. 	 * one. This makes psi dimensionless. So the mass needs to be

  415. 	 * multiplied back in the approporiate places in the governing

  416. 	 * equations so that units match.*/

  417. 	data->mass=psi(data->npts);

  418. 	for (size_t i = 1; i <=data->npts; i++) {

  419. 		psi(i)=psi(i)/data->mass;

  420. 	}

  421. 	return(0);

  422. }

  423. 

  424. 

  425. int setInitialCondition(N_Vector* y, 

  426. 	    		N_Vector* ydot, 

  427.             		UserData data){

  428. 

  429. 	double* ydata;

  430. 	double* ydotdata;

  431. 	double* psidata;

  432. 	double* innerMassFractionsData, Rd, massDrop;

  433. 	double rhomhalf, lambdamhalf, YVmhalf[data->nsp];

  434. 	double f=ZERO;

  435. 	double g=ZERO;

  436. 

  437. 	double perturb,rho;

  438. 	double epsilon=ZERO;

  439. 	int m,ier;

  440.   	ydata    = N_VGetArrayPointer_OpenMP(*y);

  441.   	ydotdata = N_VGetArrayPointer_OpenMP(*ydot);

  442. 	innerMassFractionsData =  data->innerMassFractions;

  443. 	Rd = data->Rd;

  444. 	massDrop = data->massDrop;

  445. 

  446. 	//Mass of droplet

  447. 	massDrop=1.0/3.0*Rd*Rd*Rd*997.0; //TODO: The density of the droplet should be a user input

  448. 

  449. 	if(data->adaptiveGrid){

  450.   		psidata  = data->grid->xOld;

  451. 	}

  452. 	else{

  453.   		psidata  = data->uniformGrid;

  454. 	}

  455. 

  456. 	m=data->metric;

  457. 

  458. 	data->innerTemperature=data->initialTemperature;

  459. 	for (size_t k = 1; k <=data->nsp; k++) {

  460.   		innerMassFractionsData[k-1]=data->gas->massFraction(k-1);

  461. 	}

  462. 

  463. 	//Define Grid:

  464. 	double dR=(data->domainLength)/((double)(data->npts)-1.0e0);

  465. 	double dv=(pow(data->domainLength,1+data->metric)-pow(data->firstRadius*data->domainLength,1+data->metric))/((double)(data->npts)-1.0e0);

  466. 	for (size_t i = 1; i <=data->npts; i++) {

  467. 		if(data->metric==0){

  468. 			R(i)=Rd+(double)((i-1)*dR);

  469. 		}else{

  470. 			if(i==1){

  471. 				R(i)=ZERO;

  472. 			}else if(i==2){

  473. 				R(i)=data->firstRadius*data->domainLength;

  474. 			}else{

  475. 				R(i)=pow(pow(R(i-1),1+data->metric)+dv,1.0/((double)(1+data->metric)));

  476. 			}

  477. 		}

  478. 		T(i)=data->initialTemperature;

  479. 		for (size_t k = 1; k <=data->nsp; k++) {

  480.   	        	Y(i,k)=data->gas->massFraction(k-1);	//Indexing different in Cantera

  481. 		}

  482.   	        P(i)=data->initialPressure*Cantera::OneAtm;

  483. 	}	

  484. 	R(data->npts)=data->domainLength+data->Rd;

  485. 

  486. 	double Tmax;

  487. 	double Tmin=data->initialTemperature;

  488. 	double w=data->mixingWidth;

  489. 	double YN2=ZERO;

  490. 	double YO2=ZERO;

  491. 	double YFuel,YOxidizer,sum;

  492. 

  493. 	//if(data->problemType==0){

  494. 	//	data->gas->equilibrate("HP");

  495. 	//	data->maxTemperature=data->gas->temperature();

  496. 	//}

  497. 	//else if(data->problemType==1){

  498. 	//	/*Premixed Combustion: Equilibrium products comprise ignition

  499. 	//	 * kernel at t=0. The width of the kernel is "mixingWidth"

  500. 	//	 * shifted by "shift" from the center.*/

  501. 	//	data->gas->equilibrate("HP");

  502. 	//	Tmax=data->gas->temperature();

  503. 	//	for (size_t i = 1; i <=data->npts; i++) {

  504. 	//		g=HALF*(tanh((R(i)-data->shift)/w)+ONE);	//increasing function of x

  505. 	//		f=ONE-g;					//decreasing function of x

  506. 	//		T(i)=(Tmax-Tmin)*f+Tmin;

  507. 	//		for (size_t k = 1; k <=data->nsp; k++) {

  508. 	//			Y(i,k)=(data->gas->massFraction(k-1)-Y(i,k))*f+Y(i,k);

  509. 	//		}

  510. 	//	}

  511. 	//	if(data->dirichletOuter){

  512. 	//		T(data->npts)=data->wallTemperature;

  513. 	//	}

  514. 	//}

  515. 	//else if(data->problemType==2){

  516. 	//	FILE* input;

  517. 	//	if(input=fopen("initialCondition.dat","r")){

  518. 	//		readInitialCondition(input, ydata, data->nvar, data->nr, data->npts);

  519. 	//		fclose(input);

  520. 	//	}

  521. 	//	else{

  522. 	//		printf("file initialCondition.dat not found!\n");

  523. 	//		return(-1);

  524. 	//	}

  525. 	//}

  526. 

  527. 	initializePsiGrid(ydata,psidata,data);

  528. 

  529. 	if(data->adaptiveGrid){

  530. 	//	if(data->problemType!=0){

  531. 	//		data->grid->position=maxGradPosition(ydata, data->nt, data->nvar,

  532. 	//						 data->grid->xOld, data->npts);

  533. 	//		//data->grid->position=maxCurvPosition(ydata, data->nt, data->nvar,

  534. 	//		//				 data->grid->xOld, data->npts);

  535. 	//	}

  536. 	//	else{

  537. 	//	}

  538. 		if(data->problemType!=3){

  539. 			data->grid->position=0.0e0;

  540. 			double x=data->grid->position+data->gridOffset*data->grid->leastMove;

  541. 			printf("New grid center:%15.6e\n",x);

  542. 			ier=reGrid(data->grid, x);

  543. 			if(ier==-1)return(-1);

  544. 			updateSolution(ydata, ydotdata, data->nvar,

  545. 			               data->grid->xOld,data->grid->x,data->npts);

  546. 			storeGrid(data->grid->x,data->grid->xOld,data->npts);

  547. 		}

  548. 	}

  549. 	else{

  550. 		double Rg = data->Rg, dpsi0;

  551. 		int NN = data->npts-2;

  552. 		double psiNew[data->npts];

  553. 		

  554. 		dpsi0 = (pow(Rg,1.0/NN) - 1.0)/(pow(Rg,(NN+1.0)/NN) - 1.0);

  555. 		psiNew[0] = 0;

  556. 		for (size_t i = 1; i < data->npts-1; i++) {

  557. 			psiNew[i]=psiNew[i-1]+dpsi0*pow(Rg,(i-1.0)/NN);

  558. 		}

  559. 		psiNew[data->npts-1] = 1.0;

  560. 		printf("Last point:%15.6e\n",psiNew[data->npts-1]);

  561. 		updateSolution(ydata, ydotdata, data->nvar,

  562. 		               data->uniformGrid,psiNew,data->npts);

  563. 		storeGrid(psiNew,data->uniformGrid,data->npts);

  564. 

  565. 		//double psiNew[data->npts];

  566. 		//double dpsi=1.0e0/((double)(data->npts)-1.0e0);

  567. 		//for (size_t i = 0; i < data->npts; i++) {

  568. 		//	psiNew[i]=(double)(i)*dpsi;

  569. 		//}

  570. 		//printf("Last point:%15.6e\n",psiNew[data->npts-1]);

  571. 		//updateSolution(ydata, ydotdata, data->nvar,

  572. 		//               data->uniformGrid,psiNew,data->npts);

  573. 		//storeGrid(psiNew,data->uniformGrid,data->npts);

  574. 	}

  575. 

  576. 	if(data->problemType==0){

  577. 		data->gas->equilibrate("HP");

  578. 		data->maxTemperature=data->gas->temperature();

  579. 	}

  580. 	else if(data->problemType==1){

  581. 		/*Premixed Combustion: Equilibrium products comprise ignition

  582. 		 * kernel at t=0. The width of the kernel is "mixingWidth"

  583. 		 * shifted by "shift" from the center.*/

  584. 		data->gas->equilibrate("HP");

  585. 		Tmax=data->gas->temperature();

  586. 		for (size_t i = 1; i <=data->npts; i++) {

  587. 			g=HALF*(tanh((R(i)-data->shift)/w)+ONE);	//increasing function of x

  588. 			f=ONE-g;					//decreasing function of x

  589. 			T(i)=(Tmax-Tmin)*f+Tmin;

  590. 			for (size_t k = 1; k <=data->nsp; k++) {

  591. 				Y(i,k)=(data->gas->massFraction(k-1)-Y(i,k))*f+Y(i,k);

  592. 			}

  593. 		}

  594. 		if(data->dirichletOuter){

  595. 			T(data->npts)=data->wallTemperature;

  596. 		}

  597. 	}

  598. 	else if(data->problemType==2){

  599. 		FILE* input;

  600. 		if(input=fopen("initialCondition.dat","r")){

  601. 			readInitialCondition(input, ydata, data->nvar, data->nr, data->npts, data->Rg);

  602. 			fclose(input);

  603. 		}

  604. 		else{

  605. 			printf("file initialCondition.dat not found!\n");

  606. 			return(-1);

  607. 		}

  608. 		initializePsiGrid(ydata,psidata,data);

  609. 	}

  610. 	else if(data->problemType==3){

  611. 		FILE* input;

  612. 		if(input=fopen("restart.bin","r")){

  613. 			readRestart(y, ydot, input, data);

  614. 			fclose(input);

  615. 			printf("Restart solution loaded!\n");

  616. 			printf("Problem starting at t=%15.6e\n",data->tNow);

  617. 			return(0);

  618. 		}

  619. 		else{

  620. 			printf("file restart.bin not found!\n");

  621. 			return(-1);

  622. 		}

  623. 	}

  624. 

  625. 	if(data->reflectProblem){

  626. 		double temp;

  627. 		int j=1;

  628. 		while (data->npts+1-2*j>=0) {

  629. 			temp=T(j);

  630. 			T(j)=T(data->npts+1-j);

  631. 			T(data->npts+1-j)=temp;

  632. 			for (size_t k = 1; k <=data->nsp; k++) {

  633. 				temp=Y(j,k);

  634. 				Y(j,k)=Y(data->npts+1-j,k);

  635. 				Y(data->npts+1-j,k)=temp;

  636. 			}

  637. 			j=j+1;

  638. 		}

  639. 	}

  640. 

  641. 	/*Floor small values to zero*/

  642. 	for (size_t i = 1; i <=data->npts; i++) {

  643. 		for (size_t k = 1; k <=data->nsp; k++) {

  644. 			if(fabs(Y(i,k))<=data->massFractionTolerance){

  645. 				Y(i,k)=0.0e0;

  646. 			}

  647. 		}

  648. 	}

  649. 

  650. 	//Set grid to location of maximum curvature:

  651. 	if(data->adaptiveGrid){

  652. 		data->grid->position=maxCurvPosition(ydata, data->nt, data->nvar,

  653. 				  		data->grid->x, data->npts);

  654. 		ier=reGrid(data->grid, data->grid->position);

  655. 		updateSolution(ydata, ydotdata, data->nvar,

  656. 		               data->grid->xOld,data->grid->x,data->npts);

  657. 		storeGrid(data->grid->x,data->grid->xOld,data->npts);

  658. 	}

  659. 

  660. 	/*Ensure consistent boundary conditions*/	

  661. 	//T(1)=T(2);

  662. 	//for (size_t k = 1; k <=data->nsp; k++) {

  663. 	//	Y(1,k)=Y(2,k);

  664. 	//	Y(data->npts,k)=Y(data->npts-1,k);

  665. 	//}

  666. 

  667. 	return(0);

  668. }

  669. 

  670. inline double Qdot(double* t, 

  671. 	    	   double* x, 

  672. 	    	   double* ignTime, 

  673. 	    	   double* kernelSize, 

  674. 	    	   double* maxQdot){

  675. 	double qdot;

  676. 	if(*x<=*kernelSize){

  677. 		if((*t)<=(*ignTime)){

  678. 			qdot=(*maxQdot);

  679. 		}

  680. 		else{

  681. 			qdot=0.0e0;

  682. 		}

  683. 	}else{

  684. 		qdot=0.0e0;

  685. 	}

  686. 	return(qdot);

  687. }

  688. 

  689. inline void setGas(UserData data, 

  690. 	    double *ydata, 

  691. 	    size_t gridPoint){

  692.   	data->gas->setTemperature(T(gridPoint)); 	        

  693.   	data->gas->setMassFractions_NoNorm(&Y(gridPoint,1)); 	

  694.   	data->gas->setPressure(P(gridPoint));

  695. }

  696. 

  697. void getTransport(UserData data, 

  698. 		  double *ydata, 

  699. 		  size_t gridPoint,

  700. 		  double *rho,

  701. 		  double *lambda,

  702. 		  double YV[]){

  703. 

  704. 	double YAvg[data->nsp],

  705. 		 XLeft[data->nsp],

  706. 		 XRight[data->nsp],

  707. 		 gradX[data->nsp];

  708. 

  709. 	setGas(data,ydata,gridPoint);

  710. 	data->gas->getMoleFractions(XLeft);                                     

  711. 	setGas(data,ydata,gridPoint+1);

  712. 	data->gas->getMoleFractions(XRight);                                     

  713.                                                                              

  714. 	for (size_t k = 1; k <=data->nsp; k++) {                                          

  715. 		YAvg(k)=HALF*(Y(gridPoint,k)+

  716. 			      Y(gridPoint+1,k));                                 

  717. 		gradX(k)=(XRight(k)-XLeft(k))/

  718. 			 (R(gridPoint+1)-R(gridPoint));                       

  719. 	}                                                                    

  720. 	double TAvg = HALF*(T(gridPoint)+T(gridPoint+1));

  721. 	double gradT=(T(gridPoint+1)-T(gridPoint))/

  722. 		       (R(gridPoint+1)-R(gridPoint));                                  

  723. 

  724. 

  725.   	data->gas->setTemperature(TAvg); 	        

  726.   	data->gas->setMassFractions_NoNorm(YAvg); 	

  727.   	data->gas->setPressure(P(gridPoint));

  728. 

  729. 	*rho=data->gas->density();                                       

  730. 	*lambda=data->trmix->thermalConductivity();                      

  731. 	data->trmix->getSpeciesFluxes(1,&gradT,data->nsp,                     

  732. 				      gradX,data->nsp,YV);                

  733. 	//setGas(data,ydata,gridPoint);

  734. }

  735. 

  736. int residue(double t, N_Vector y, N_Vector ydot, N_Vector res, void *user_data){

  737. 

  738. 	/*Declare and fetch nvectors and user data:*/

  739. 

  740.   	double *ydata, *ydotdata, *resdata, *psidata, *innerMassFractionsData;

  741.   	

  742. 	UserData data;

  743. 	data = (UserData)user_data;

  744. 	size_t npts=data->npts;

  745. 	size_t nsp=data->nsp;

  746. 	size_t k_bath = data->k_bath;

  747. 	size_t k_drop = data->k_drop;

  748. 

  749. 	ydata 	= N_VGetArrayPointer_OpenMP(y); 

  750. 	ydotdata= N_VGetArrayPointer_OpenMP(ydot); 

  751. 	resdata = N_VGetArrayPointer_OpenMP(res);

  752. 	if(data->adaptiveGrid==1){

  753. 		psidata = data->grid->x;

  754. 	}else{

  755. 		psidata = data->uniformGrid;

  756. 	}

  757. 

  758. 	innerMassFractionsData =  data->innerMassFractions;

  759. 

  760. 	/* Grid stencil:*/

  761. 

  762. 	/*-------|---------*---------|---------*---------|-------*/

  763. 	/*-------|---------*---------|---------*---------|-------*/

  764. 	/*-------|---------*---------|---------*---------|-------*/

  765. 	/*-------m-------mhalf-------j-------phalf-------p-------*/

  766. 	/*-------|---------*---------|---------*---------|-------*/

  767. 	/*-------|---------*---------|---------*---------|-------*/

  768. 	/*-------|<=======dxm=======>|<=======dxp=======>|-------*/

  769. 	/*-------|---------*<======dxav=======>*---------|-------*/

  770. 	/*-------|<================dxpm=================>|-------*/

  771. 

  772. 	/* Various variables defined for book-keeping and storing previously

  773. 	 * calculated values:

  774. 	 * rho		: densities at points  m, mhalf, j, p, and phalf.

  775. 	 * area		: the matric at points m, mhalf, j, p, and phalf.

  776. 	 * m 		: exponent that determines geometry;

  777. 	 * lambda	: thermal conductivities at mhalf and phalf.

  778. 	 * mdot		: mass flow rate at m, j, and p.

  779. 	 * X		: mole fractions at j and p.

  780. 	 * YV		: diffusion fluxes at mhalf and phalf.

  781. 	 * Tgrad	: temperature gradient at mhalf and phalf.

  782. 	 * Tav		: average temperature between two points.

  783. 	 * Pav		: average pressure between two points.

  784. 	 * Yav		: average mass fractions between two points.

  785. 	 * Xgradhalf	: mole fraction gradient at j.

  786. 	 * Cpb		: mass based bulk specific heat.

  787. 	 * tranTerm	: transient terms.

  788. 	 * advTerm	: advection terms.

  789. 	 * diffTerm	: diffusion terms.

  790. 	 * srcTerm	: source terms.

  791. 	 */

  792. 

  793. 	double rhomhalf,  rhom, lambdamhalf, YVmhalf[nsp], 

  794. 		 rho, 

  795. 		 rhophalf, lambdaphalf, YVphalf[nsp],

  796. 		 Cpb, Cvb,  Cp[nsp], Cpl, dHvl, rhol,  wdot[nsp],   enthalpy[nsp], energy[nsp],

  797. 		 tranTerm, diffTerm,    srcTerm, advTerm,

  798. 		 area,areamhalf,areaphalf,aream,areamhalfsq,areaphalfsq;

  799. 	

  800. 	/*Aliases for difference coefficients:*/

  801. 	double cendfm, cendfc, cendfp;

  802. 	/*Aliases for various grid spacings:*/

  803. 	double dpsip, dpsiav, dpsipm, dpsim, dpsimm;

  804. 	dpsip=dpsiav=dpsipm=dpsim=dpsimm=ONE;

  805. 	//double mass, mdotIn;

  806. 	double mass, massDrop;

  807. 	double sum, sum1, sum2, sum3;

  808. 

  809. 	size_t j,k;

  810. 	int m;

  811. 	m=data->metric;					//Unitless

  812. 	mass=data->mass;				//Units: kg

  813. 	//massDrop=data->massDrop;		//Units: kg

  814. 	//mdotIn=data->mdot*calc_area(R(npts),&m);	//Units: kg/s

  815. 

  816. //	/*evaluate properties at j=1*************************/

  817. 	setGas(data,ydata,1);

  818. 	rhom=data->gas->density();                                       

  819.     Cpb=data->gas->cp_mass();       	//J/kg/K

  820.     Cvb=data->gas->cv_mass();       	//J/kg/K

  821. 	//TODO: Create user input model for these. They should not be constant

  822. 	//Cpl=4.182e03;						//J/kg/K for liquid water

  823. 	Cpl=  5.67508633e-07*pow(T(1),4) - 7.78060597e-04*pow(T(1),3) + 4.08310544e-01*pow(T(1),2)  //J/kg/K for liquid water

  824. 		- 9.62429538e+01*T(1)        + 1.27131046e+04;

  825. 	

  826. 	//dHvl=2.260e6;						//J/kg	heat of vaporization of water

  827. 	double Tr = T(1)/647.1;				//Reduced Temperature: Droplet Temperature divided by critical temperature of water

  828. 	dHvl= 5.2053e07*pow(1-Tr,0.3199 - 0.212*Tr + 0.25795*Tr*Tr)/18.01;	//J/kg	latent heat of vaporization of water

  829. 	rhol = 997.0;	

  830. 	massDrop=1.0/3.0*R(1)*R(1)*R(1)*997.0; //TODO: The density of the droplet should be a user input

  831. 	aream= calc_area(R(1),&m);	    

  832. 

  833. 	/*******************************************************************/

  834. 	/*Calculate values at j=2's m and mhalf*****************************/

  835. 

  836. 	getTransport(data, ydata, 1, &rhomhalf,&lambdamhalf,YVmhalf);

  837. 	areamhalf= calc_area(HALF*(R(1)+R(2)),&m);                                 

  838. 	aream = calc_area(R(1),&m);                                 

  839. 	areamhalfsq= areamhalf*areamhalf;                                   

  840.                                                                              

  841. 	/*******************************************************************/

  842. 

  843. 	/*Fill up res with left side (center) boundary conditions:**********/

  844. 	/*We impose zero fluxes at the center:*/                        

  845. 

  846. 

  847. 	/*Mass:*/                                                            

  848. 	if(data->quasiSteady){

  849. 		Rres(1)=Rdot(1); // Should remain satisfied for quasi-steady droplet

  850. 	}else{

  851. 		Rres(1)=Rdot(1) + Mdot(1)/rhol/aream; 

  852. 	}

  853.                                                                         

  854. 	/*Species:*/                                                    

  855. 	sum=ZERO;

  856. 	

  857. 	//TODO: Antoine Parameters should be part of user input, not hardcoded

  858. 	Yres(1,k_drop)=Y(1,k_drop) - 1.0e5*pow(10,4.6543-(1435.264/(T(1)-64.848)))*data->gas->molecularWeight(k_drop-1) 

  859. 				    / P(1) / data->gas->meanMolecularWeight();

  860. 	//Yres(1,k_drop)=Y(1,k_drop) - 1.0e3*pow(2.71828,16.7-(4060.0/(T(1)-37.0)))*data->gas->molecularWeight(k_drop-1) 

  861. 	//			    / P(1) / data->gas->meanMolecularWeight();

  862. 	//Yres(1,k_drop)=Y(1,k_drop)-2.566785e-02;

  863. 	sum=sum+Y(1,k_drop);

  864. 

  865. 	Mdotres(1)=Mdot(1) - (YVmhalf(k_drop)*areamhalf) / (1-Y(1,k_drop)); //Evaporating mass

  866. 

  867. 	for (k = 1; k <=nsp; k++) {                                        

  868. 		if(k!=k_bath && k!=k_drop){

  869. 			//TODO: May need to include chemical source term

  870. 			Yres(1,k)=Y(1,k)*Mdot(1) + YVmhalf(k)*areamhalf;

  871. 			//Yres(1,k)=YVmhalf(k)*areamhalf;

  872. 		    sum=sum+Y(1,k);

  873. 			//if(fabs(Mdot(1))>1e-14){

  874. 		      		///Yres(1,k)=innerMassFractionsData[k-1]-

  875. 					///  Y(1,k)-

  876. 					///  (YVmhalf(k)*areamhalf)/Mdot(1);

  877. 					//Yres(1,k)=Y(1,k)*Mdot(1) + YVmhalf(k)*areamhalf;

  878. 			//}

  879. 			//else{

  880. 		    //  		//Yres(1,k)=Y(1,k)-innerMassFractionsData[k-1];

  881. 		    //  		Yres(1,k)=Y(2,k)-Y(1,k);

  882. 			//	/*The below flux boundary condition makes the

  883. 			//	 * problem more prone to diverge. How does one

  884. 			//	 * fix this?*/

  885. 		    //  		//Yres(1,k)=YVmhalf(k);

  886. 			//}

  887. 		}

  888. 	}                                                                 

  889. 	Yres(1,k_bath)=ONE-sum-Y(1,k_bath);                                     

  890. 	

  891. 	/*Energy:*/                                                     

  892. 	if(data->dirichletInner){

  893. 		//Tres(1)=Tdot(1);

  894. 		//Tres(1)=T(1)-data->innerTemperature;

  895. 		Tres(1)=lambdamhalf*rhomhalf*areamhalfsq*(T(2)-T(1))/((psi(2)-psi(1))*mass)/dHvl - YVmhalf(k_drop)*areamhalf/(1-Y(1,k_drop));

  896. 	}else{

  897. 		//Tres(1)=Tdot(1) - 

  898. 		//	(rhomhalf*areamhalfsq*lambdamhalf*(T(2)-T(1))/((psi(2)-psi(1))*mass) - Mdot(1)*dHvl)

  899. 		//	/ (massDrop * Cpl);

  900. 		Tres(1)=Tdot(1) - 

  901. 			(areamhalf*lambdamhalf*(T(2)-T(1))/(R(2)-R(1)) - Mdot(1)*dHvl)

  902. 			/ (massDrop * Cpl);

  903. 

  904. 

  905. 

  906. 		//Tres(1)=T(2)-T(1);

  907. 		//Tres(1)=Tdot(1) - (Pdot(1)/(rhom*Cpb))

  908. 		//	+(double)(data->metric+1)*(rhomhalf*lambdamhalf*areamhalfsq*(T(2)-T(1))/psi(2)-psi(1));

  909. 	}

  910. 

  911. 	/*Pressure:*/                                                        

  912. 	Pres(1)=P(2)-P(1);

  913. 	/*Fill up res with governing equations at inner points:*************/

  914. 	for (j = 2; j < npts; j++) {                                         

  915.                                                                              

  916. 		/*evaluate various mesh differences*///                      

  917.         	dpsip =        (psi(j+1) - psi(j)  )*mass;                            

  918.         	dpsim =        (psi(j)   - psi(j-1))*mass;                            

  919.         	dpsiav =  HALF*(psi(j+1) - psi(j-1))*mass;                            

  920.         	dpsipm =       (psi(j+1) - psi(j-1))*mass;                            

  921. 		/***********************************///                      

  922.                                                                              

  923. 		/*evaluate various central difference coefficients*/       

  924.         	cendfm = - dpsip / (dpsim*dpsipm);                               

  925.         	cendfc =   (dpsip-dpsim) / (dpsip*dpsim);                         

  926.         	cendfp =   dpsim / (dpsip*dpsipm);                               

  927. 		/**************************************************/

  928.                                                                    

  929.                                                                   

  930. 		/*evaluate properties at j*************************/

  931. 		setGas(data,ydata,j);

  932. 		rho=data->gas->density();		//kg/m^3

  933.         	Cpb=data->gas->cp_mass();       	//J/kg/K

  934.         	Cvb=data->gas->cv_mass();       	//J/kg/K

  935. 		data->gas->getNetProductionRates(wdot); //kmol/m^3

  936. 		data->gas->getEnthalpy_RT(enthalpy);	//unitless

  937. 		data->gas->getCp_R(Cp);			//unitless

  938. 		area = calc_area(R(j),&m);	        //m^2

  939.                                                                            

  940. 		/*evaluate properties at p*************************/

  941. 		getTransport(data, ydata, j, &rhophalf,&lambdaphalf,YVphalf);

  942. 		areaphalf= calc_area(HALF*(R(j)+R(j+1)),&m);	    

  943. 		areaphalfsq= areaphalf*areaphalf;		    

  944. 		/**************************************************///     

  945. 

  946. 		/*Evaporating Mass*/

  947. 		Mdotres(j)=Mdot(j) - Mdot(j-1); 

  948. 

  949. 		/*Mass:*/

  950. 		/* ∂r/∂ψ = 1/ρA */

  951. 		Rres(j)=((R(j)-R(j-1))/dpsim)-(TWO/(rhom*aream+rho*area));

  952. 

  953. 		/*Energy:*/

  954. 		/* ∂T/∂t = - ṁ(∂T/∂ψ) 

  955. 		 * 	   + (∂/∂ψ)(λρA²∂T/∂ψ) 

  956. 		 * 	   - (A/cₚ) ∑ YᵢVᵢcₚᵢ(∂T/∂ψ) 

  957. 		 * 	   - (1/ρcₚ)∑ ώᵢhᵢ 

  958. 		 * 	   + (1/ρcₚ)(∂P/∂t) */

  959. 		/*Notes: 

  960. 		 * λ has units J/m/s/K.

  961. 		 * YᵢVᵢ has units kg/m^2/s.

  962. 		 * hᵢ has units J/kmol, so we must multiply the enthalpy

  963. 		 * defined above (getEnthalpy_RT) by T (K) and the gas constant

  964. 		 * (J/kmol/K) to get the right units.

  965. 		 * cₚᵢ has units J/kg/K, so we must multiply the specific heat

  966. 		 * defined above (getCp_R) by the gas constant (J/kmol/K) and

  967. 		 * divide by the molecular weight (kg/kmol) to get the right

  968. 		 * units.

  969. 		 * */

  970. 

  971. 		//enthalpy formulation:

  972. 		//tranTerm = Tdot(j) - (Pdot(j)/(rho*Cpb));

  973. 		tranTerm = Tdot(j);

  974. 		sum=ZERO;

  975. 		sum1=ZERO;

  976. 		for (k = 1; k <=nsp; k++) {

  977. 			sum=sum+wdot(k)*enthalpy(k);

  978. 			sum1=sum1+(Cp(k)/data->gas->molecularWeight(k-1))*rho

  979. 			     *HALF*(YVmhalf(k)+YVphalf(k));

  980. 		}

  981. 		sum=sum*Cantera::GasConstant*T(j);

  982. 		sum1=sum1*Cantera::GasConstant;

  983. 		diffTerm  =(( (rhophalf*areaphalfsq*lambdaphalf*(T(j+1)-T(j))/dpsip)

  984. 			      -(rhomhalf*areamhalfsq*lambdamhalf*(T(j)-T(j-1))/dpsim) )

  985. 			     /(dpsiav*Cpb) )

  986. 			  -(sum1*area*(cendfp*T(j+1)

  987. 			              +cendfc*T(j)

  988. 			              +cendfm*T(j-1))/Cpb);

  989. 		srcTerm   = (sum-Qdot(&t,&R(j),&data->ignTime,&data->kernelSize,&data->maxQDot))/(rho*Cpb); // Qdot is forced heating to cause ignition, sum is the conversion of chemical enthalpy to sensible enthalpy

  990. 		advTerm   = (Mdot(j)*(T(j)-T(j-1))/dpsim);

  991. 		Tres(j)= tranTerm - (Pdot(j)/(rho*Cpb))

  992. 			+advTerm 

  993. 			-diffTerm

  994. 			+srcTerm;

  995. 

  996. 	//	//energy formulation:

  997. 	//	tranTerm = Tdot(j);

  998. 	//	sum=ZERO;

  999. 	//	sum1=ZERO;

  1000. 	//	sum2=ZERO;

  1001. 	//	sum3=ZERO;

  1002. 	//	for (k = 1; k <=nsp; k++) {

  1003. 	//		energy(k)=enthalpy(k)-ONE;

  1004. 	//		sum=sum+wdot(k)*energy(k);

  1005. 	//		sum1=sum1+(Cp(k)/data->gas->molecularWeight(k-1))*rho

  1006. 	//		     *HALF*(YVmhalf(k)+YVphalf(k));

  1007. 	//		sum2=sum2+(YVmhalf(k)/data->gas->molecularWeight(k-1));

  1008. 	//		sum3=sum3+(YVphalf(k)/data->gas->molecularWeight(k-1));

  1009. 	//	}

  1010. 	//	sum=sum*Cantera::GasConstant*T(j);

  1011. 	//	sum1=sum1*Cantera::GasConstant;

  1012. 	//	diffTerm  =(( (rhophalf*areaphalfsq*lambdaphalf*(T(j+1)-T(j))/dpsip)

  1013. 	//		      -(rhomhalf*areamhalfsq*lambdamhalf*(T(j)-T(j-1))/dpsim) )

  1014. 	//		     /(dpsiav*Cvb) )

  1015. 	//		  -(sum1*area*(cendfp*T(j+1)

  1016. 	//		              +cendfc*T(j)

  1017. 	//		              +cendfm*T(j-1))/Cvb);

  1018. 	//	srcTerm   = (sum-Qdot(&t,&R(j),&data->ignTime,&data->kernelSize,&data->maxQDot))/(rho*Cvb);

  1019. 	//	advTerm   = (mdotIn*(T(j)-T(j-1))/dpsim);

  1020. 	//	advTerm = advTerm + (Cantera::GasConstant*T(j)*area/Cvb)*((sum3-sum2)/dpsiav);

  1021. 	//	Tres(j)= tranTerm

  1022. 	//		+advTerm 

  1023. 	//		-diffTerm

  1024. 	//		+srcTerm;

  1025. 

  1026. 		/*Species:*/

  1027. 		/* ∂Yᵢ/∂t = - ṁ(∂Yᵢ/∂ψ) 

  1028. 		 * 	    - (∂/∂ψ)(AYᵢVᵢ) 

  1029. 		 * 	    + (ώᵢWᵢ/ρ)  */

  1030. 

  1031. 		sum=ZERO;

  1032. 		for (k = 1; k <=nsp; k++) {

  1033. 			if(k!=k_bath){

  1034. 				tranTerm  = Ydot(j,k);

  1035. 				diffTerm  = (YVphalf(k)*areaphalf

  1036. 					    -YVmhalf(k)*areamhalf)/dpsiav;

  1037. 				srcTerm   = wdot(k)

  1038. 			     		    *(data->gas->molecularWeight(k-1))/rho;

  1039. 				advTerm   = (Mdot(j)*(Y(j,k)-Y(j-1,k))/dpsim);

  1040. 

  1041. 				Yres(j,k)= tranTerm 

  1042. 					  +advTerm

  1043. 					  +diffTerm

  1044. 					  -srcTerm;

  1045. 

  1046. 		      		sum=sum+Y(j,k);

  1047. 			}

  1048. 		}

  1049. 		Yres(j,k_bath)=ONE-sum-Y(j,k_bath);

  1050. 

  1051. 		/*Pressure:*/

  1052. 		Pres(j) = P(j+1)-P(j);

  1053. 

  1054. 		/*Assign values evaluated at p and phalf to m       

  1055. 		 * and mhalf to save some cpu cost:****************/

  1056. 		areamhalf=areaphalf;                                

  1057. 		areamhalfsq=areaphalfsq;                            

  1058. 		aream=area;

  1059. 		rhom=rho;

  1060. 		rhomhalf=rhophalf;                                  

  1061. 		lambdamhalf=lambdaphalf;                            

  1062. 		for (k = 1; k <=nsp; k++) {                         

  1063. 			YVmhalf(k)=YVphalf(k);                      

  1064. 		}                                                   

  1065. 		/**************************************************/

  1066. 		                                                    

  1067. 	}                                                           

  1068. 	/*******************************************************************///

  1069. 

  1070. 

  1071. 	/*Fill up res with right side (wall) boundary conditions:***********/

  1072. 	/*We impose zero fluxes at the wall:*/                               

  1073. 	setGas(data,ydata,npts);

  1074. 	rho=data->gas->density();                               

  1075. 	area = calc_area(R(npts),&m);				   

  1076. 

  1077. 	/*Mass:*/                                                          

  1078. 	dpsim=(psi(npts)-psi(npts-1))*mass;

  1079. 	Rres(npts)=((R(npts)-R(npts-1))/dpsim)-(TWO/(rhom*aream+rho*area));

  1080. 

  1081. 	/*Energy:*/                                             

  1082. 	if(data->dirichletOuter){

  1083. 		//Tres(npts)=T(npts)-data->wallTemperature;

  1084. 		Tres(npts)=Tdot(npts);

  1085. 	}

  1086. 	else{

  1087. 		Tres(npts)=T(npts)-T(npts-1);

  1088. 	}

  1089.                                                                 

  1090. 	/*Species:*/                                            

  1091. 	sum=ZERO;

  1092. 	if(data->dirichletOuter){

  1093. 		for (k = 1; k <=nsp; k++) {                             

  1094. 			if(k!=k_bath){

  1095. 			    	Yres(npts,k)=Ydot(npts,k);

  1096. 			    	sum=sum+Y(npts,k);

  1097. 			}

  1098. 		}                                                       

  1099. 	}

  1100. 	else{

  1101. 		for (k = 1; k <=nsp; k++) {                             

  1102. 			if(k!=k_bath){

  1103. 			    	Yres(npts,k)=Y(npts,k)-Y(npts-1,k);

  1104. 			    	//Yres(npts,k)=YVmhalf(k);         

  1105. 			    	sum=sum+Y(npts,k);

  1106. 			}

  1107. 		}                                                       

  1108. 	}

  1109. 	Yres(npts,k_bath)=ONE-sum-Y(npts,k_bath);             

  1110.                                                                 

  1111. 	

  1112. 	/*Pressure:*/                                                      

  1113. 	if(data->constantPressure){

  1114. 		Pres(npts)=Pdot(npts)-data->dPdt;                                     

  1115. 	}

  1116. 	else{

  1117. 		Pres(npts)=R(npts)-data->domainLength;                     

  1118. 		//Pres(npts)=Rdot(npts);                     

  1119. 	}

  1120. 

  1121. 	/*Evaporating Mass*/

  1122. 	Mdotres(npts)=Mdot(npts) - Mdot(npts-1); 

  1123. 

  1124. 	//for (j = 1; j <=npts; j++) {

  1125. 	//	//for (k = 1; k <=nsp; k++) {

  1126. 	//	//	Yres(j,k)=Ydot(j,k);

  1127. 	//	//}

  1128. 	//	//Tres(j)=Tdot(j);

  1129. 	//}

  1130. 

  1131. 	return(0);

  1132. 

  1133. }

  1134. 

  1135. void printSpaceTimeHeader(UserData data)

  1136. {

  1137. 	fprintf((data->output), "%15s\t","#1");

  1138. 	for (size_t k = 1; k <=data->nvar+1; k++) {

  1139. 		fprintf((data->output), "%15lu\t",k+1);

  1140. 	}

  1141. 	fprintf((data->output), "%15lu\n",data->nvar+3);

  1142. 

  1143. 	fprintf((data->output), "%15s\t%15s\t%15s\t","#psi","time(s)","dpsi");

  1144. 	fprintf((data->output), "%15s\t%15s\t","radius(m)","Temp(K)");

  1145. 	for (size_t k = 1; k <=data->nsp; k++) {

  1146. 		fprintf((data->output), "%15s\t",data->gas->speciesName(k-1).c_str());

  1147. 	}

  1148. 	fprintf((data->output), "%15s\t","Pressure(Pa)");

  1149. 	fprintf((data->output), "%15s\n","Mdot (kg/s)");

  1150. }

  1151. 

  1152. void printSpaceTimeOutput(double t, N_Vector* y, FILE* output, UserData data)

  1153. {

  1154. 	double *ydata,*psidata;

  1155.   	ydata    = N_VGetArrayPointer_OpenMP(*y);

  1156. 

  1157. 	if(data->adaptiveGrid){

  1158.   		psidata  = data->grid->x;

  1159. 	}else{

  1160.   		psidata  = data->uniformGrid;

  1161. 	}

  1162. 

  1163. 	for (size_t i = 0; i < data->npts; i++) {

  1164. 		fprintf(output, "%15.9e\t%15.9e\t",psi(i+1),t);

  1165. 		if(i==0){

  1166. 			fprintf(output, "%15.9e\t",psi(2)-psi(1));

  1167. 		}

  1168. 		else{

  1169. 			fprintf(output, "%15.6e\t",psi(i+1)-psi(i));

  1170. 		}

  1171. 		for (size_t j = 0; j < data->nvar; j++) {

  1172. 			if(j!=data->nvar-1){

  1173. 				fprintf(output, "%15.9e\t",ydata[j+i*data->nvar]);

  1174. 			}else{

  1175. 				fprintf(output, "%15.9e",ydata[j+i*data->nvar]);

  1176. 			}

  1177. 		}

  1178. 		fprintf(output, "\n");

  1179. 	}

  1180. 	fprintf(output, "\n");

  1181. }

  1182. 

  1183. void writeRestart(double t, N_Vector* y, N_Vector* ydot, FILE* output, UserData data){

  1184. 	double *ydata,*psidata, *ydotdata;

  1185. 	ydata = N_VGetArrayPointer_OpenMP(*y);

  1186. 	ydotdata = N_VGetArrayPointer_OpenMP(*ydot);

  1187. 	if(data->adaptiveGrid){

  1188.   		psidata  = data->grid->x;

  1189. 	}else{

  1190.   		psidata  = data->uniformGrid;

  1191. 	}

  1192.  	fwrite(&t, sizeof(t), 1, output);		//write time

  1193.  	fwrite(psidata, data->npts*sizeof(psidata), 1, output);	//write grid

  1194.  	fwrite(ydata, data->neq*sizeof(ydata), 1, output);	//write solution

  1195.  	fwrite(ydotdata, data->neq*sizeof(ydotdata), 1, output);	//write solutiondot

  1196. }

  1197. 

  1198. void readRestart(N_Vector* y, N_Vector* ydot, FILE* input, UserData data){

  1199. 	double *ydata,*psidata, *ydotdata;

  1200. 	double t;

  1201. 	if(data->adaptiveGrid){

  1202.   		psidata  = data->grid->x;

  1203. 	}else{

  1204.   		psidata  = data->uniformGrid;

  1205. 	}

  1206. 	ydata = N_VGetArrayPointer_OpenMP(*y);

  1207. 	ydotdata = N_VGetArrayPointer_OpenMP(*ydot);

  1208.  	fread(&t, sizeof(t), 1, input);

  1209. 	data->tNow=t;

  1210.  	fread(psidata, data->npts*sizeof(psidata), 1, input);

  1211.  	fread(ydata, data->neq*sizeof(ydata), 1, input);

  1212.  	fread(ydotdata, data->neq*sizeof(ydotdata), 1, input);

  1213. 	if(data->adaptiveGrid){

  1214. 		storeGrid(data->grid->x,data->grid->xOld,data->npts);

  1215. 	}

  1216. }

  1217. 

  1218. void printGlobalHeader(UserData data)

  1219. {

  1220. 	fprintf((data->globalOutput), "%8s\t","#Time(s)");

  1221. 	//fprintf((data->globalOutput), "%15s","S_u(exp*)(m/s)");

  1222. 	fprintf((data->globalOutput), "%15s","bFlux(kg/m^2/s)");

  1223. 	fprintf((data->globalOutput), "%16s","  IsothermPos(m)");

  1224. 	fprintf((data->globalOutput), "%15s\t","Pressure(Pa)");

  1225. 	fprintf((data->globalOutput), "%15s\t","Pdot(Pa/s)");

  1226. 	fprintf((data->globalOutput), "%15s\t","gamma");

  1227. 	fprintf((data->globalOutput), "%15s\t","S_u(m/s)");

  1228. 	fprintf((data->globalOutput), "%15s\t","Tu(K)");

  1229. 	fprintf((data->globalOutput), "\n");

  1230. }

  1231. //

  1232. //void printSpaceTimeRates(double t, N_Vector ydot, UserData data)

  1233. //{

  1234. //	double *ydotdata,*psidata;

  1235. //  	ydotdata    = N_VGetArrayPointer_OpenMP(ydot);

  1236. //  	psidata    = N_VGetArrayPointer_OpenMP(data->grid);

  1237. //	for (int i = 0; i < data->npts; i++) {

  1238. //		fprintf((data->ratesOutput), "%15.6e\t%15.6e\t",psi(i+1),t);

  1239. //		for (int j = 0; j < data->nvar; j++) {

  1240. //			fprintf((data->ratesOutput), "%15.6e\t",ydotdata[j+i*data->nvar]);

  1241. //		}

  1242. //		fprintf((data->ratesOutput), "\n");

  1243. //	}

  1244. //	fprintf((data->ratesOutput), "\n\n");

  1245. //}

  1246. //

  1247. void printGlobalVariables(double t, N_Vector* y, N_Vector* ydot, UserData data)

  1248. {

  1249. 	double *ydata,*ydotdata, *innerMassFractionsData, *psidata;

  1250. 	innerMassFractionsData =  data->innerMassFractions;

  1251. 

  1252. 	if(data->adaptiveGrid){

  1253.   		psidata  = data->grid->x;

  1254. 	}else{

  1255.   		psidata  = data->uniformGrid;

  1256. 	}

  1257. 

  1258. 	double TAvg, RAvg, YAvg, psiAvg;

  1259.   	ydata    = N_VGetArrayPointer_OpenMP(*y);

  1260.   	ydotdata = N_VGetArrayPointer_OpenMP(*ydot);

  1261. 	TAvg=data->isotherm;

  1262. 	double sum=ZERO;

  1263. 	double dpsim,area,aream,drdt;

  1264. 	double Cpb,Cvb,gamma,rho,flameArea,Tu;

  1265. 

  1266. 

  1267. 	/*Find the isotherm chosen by the user*/

  1268. 	size_t j=1;

  1269. 	size_t jj=1;

  1270. 	size_t jjj=1;

  1271. 	double wdot[data->nsp];

  1272. 	double wdotMax=0.0e0;

  1273. 	double advTerm=0.0e0;

  1274. 	psiAvg=0.0e0;

  1275. 	if(T(data->npts)>T(1)){

  1276. 		while (T(j)<TAvg) {

  1277. 			j=j+1;

  1278. 		}

  1279. 		YAvg=innerMassFractionsData[data->k_oxidizer-1]-Y(data->npts,data->k_oxidizer);

  1280. 		while (fabs((T(jj+1)-T(jj))/T(jj))>1e-08) {

  1281. 			jj=jj+1;

  1282. 		}

  1283. 

  1284. 		setGas(data,ydata,jj);

  1285. 		Tu=T(jj);

  1286. 		rho=data->gas->density();

  1287.         	Cpb=data->gas->cp_mass();       	//J/kg/K

  1288.         	Cvb=data->gas->cv_mass();       	//J/kg/K

  1289. 		gamma=Cpb/Cvb;

  1290. 		

  1291. 	}

  1292. 	else{

  1293. 		while (T(j)>TAvg) {

  1294. 			j=j+1;

  1295. 		}

  1296. 		YAvg=innerMassFractionsData[data->k_oxidizer-1]-Y(1,data->k_oxidizer);

  1297. 		while (fabs((T(data->npts-jj-1)-T(data->npts-jj))/T(data->npts-jj))>1e-08) {

  1298. 			jj=jj+1;

  1299. 		}

  1300. 

  1301. 		setGas(data,ydata,data->npts-jj);

  1302. 		Tu=T(data->npts-jj);

  1303. 		rho=data->gas->density();

  1304.         	Cpb=data->gas->cp_mass();       	//J/kg/K

  1305.         	Cvb=data->gas->cv_mass();       	//J/kg/K

  1306. 		gamma=Cpb/Cvb;

  1307. 	}

  1308. 	if(T(j)<TAvg){

  1309. 		RAvg=((R(j+1)-R(j))/(T(j+1)-T(j)))*(TAvg-T(j))+R(j);

  1310. 	}

  1311. 	else{

  1312. 		RAvg=((R(j)-R(j-1))/(T(j)-T(j-1)))*(TAvg-T(j-1))+R(j-1);

  1313. 	}

  1314. 

  1315. 	////Experimental burning speed calculation:	

  1316. 	//int nMax=0;

  1317. 	////nMax=maxCurvIndex(ydata, data->nt, data->nvar,

  1318. 	////     	data->grid->x, data->npts);

  1319. 	//nMax=maxGradIndex(ydata, data->nt, data->nvar,

  1320. 	//     	data->grid->x, data->npts);

  1321. 	//advTerm=(T(nMax)-T(nMax-1))/(data->mass*(psi(nMax)-psi(nMax-1)));

  1322. 	//aream=calc_area(R(nMax),&data->metric);	    

  1323. 	////setGas(data,ydata,nMax);

  1324. 	////rho=data->gas->density();

  1325. 	//psiAvg=-Tdot(nMax)/(rho*aream*advTerm);

  1326. 	////if(t>data->ignTime){

  1327. 	////	for(size_t n=2;n<data->npts;n++){

  1328. 	////		setGas(data,ydata,n);

  1329. 	////		data->gas->getNetProductionRates(wdot); //kmol/m^3

  1330. 	////		advTerm=(T(n)-T(n-1))/(data->mass*(psi(n)-psi(n-1)));

  1331. 	////		if(fabs(wdot[data->k_oxidizer-1])>=wdotMax){

  1332. 	////			aream=calc_area(R(n),&data->metric);	    

  1333. 	////			psiAvg=-Tdot(n)/(rho*aream*advTerm);

  1334. 	////			wdotMax=fabs(wdot[data->k_oxidizer-1]);

  1335. 	////		}

  1336. 	////	}

  1337. 	////}

  1338. 	////else{

  1339. 	////	psiAvg=0.0e0;

  1340. 	////}

  1341. 

  1342. 

  1343. 	//drdt=(RAvg-data->flamePosition[1])/(t-data->flameTime[1]);

  1344. 	//data->flamePosition[0]=data->flamePosition[1];

  1345. 	//data->flamePosition[1]=RAvg;

  1346. 	//data->flameTime[0]=data->flameTime[1];

  1347. 	//data->flameTime[1]=t;

  1348. 	//flameArea=calc_area(RAvg,&data->metric);

  1349. 

  1350. 	/*Use the Trapezoidal rule to calculate the mass burning rate based on

  1351. 	 * the consumption of O2*/

  1352. 	aream= calc_area(R(1)+1e-03*data->domainLength,&data->metric);	    

  1353. 	for (j = 2; j <data->npts; j++) {

  1354.         	dpsim=(psi(j)-psi(j-1))*data->mass;                            

  1355. 		area= calc_area(R(j),&data->metric);	    

  1356. 		sum=sum+HALF*dpsim*((Ydot(j-1,data->k_oxidizer)/aream)

  1357. 				   +(Ydot(j,data->k_oxidizer)/area));

  1358. 		aream=area;

  1359. 	}

  1360. 

  1361. 	//double maxOH,maxHO2;

  1362. 	//maxOH=0.0e0;

  1363. 	//maxHO2=0.0e0;

  1364. 	//for(j=1;j<data->npts;j++){

  1365. 	//	if(Y(j,data->k_OH)>maxOH){

  1366. 	//		maxOH=Y(j,data->k_OH);

  1367. 	//	}

  1368. 	//}

  1369. 	//for(j=1;j<data->npts;j++){

  1370. 	//	if(Y(j,data->k_HO2)>maxHO2){

  1371. 	//		maxHO2=Y(j,data->k_HO2);

  1372. 	//	}

  1373. 	//}

  1374. 

  1375. 	fprintf((data->globalOutput), "%15.6e\t",t);

  1376. 	//fprintf((data->globalOutput), "%15.6e\t",psiAvg);

  1377. 	fprintf((data->globalOutput), "%15.6e\t",fabs(sum)/YAvg);

  1378. 	fprintf((data->globalOutput), "%15.6e\t",RAvg);

  1379. 	fprintf((data->globalOutput), "%15.6e\t",P(data->npts));

  1380. 	fprintf((data->globalOutput), "%15.6e\t",Pdot(data->npts));

  1381. 	fprintf((data->globalOutput), "%15.6e\t",gamma);

  1382. 	fprintf((data->globalOutput), "%15.6e\t",fabs(sum)/(YAvg*rho));

  1383. 	fprintf((data->globalOutput), "%15.6e\t",Tu);

  1384. 	fprintf((data->globalOutput), "\n");

  1385. }

  1386. 

  1387. //

  1388. //void printSpaceTimeOutputInterpolated(double t, N_Vector y, UserData data)

  1389. //{

  1390. //	double *ydata,*psidata;

  1391. //  	ydata    = N_VGetArrayPointer_OpenMP(y);

  1392. //  	psidata    = N_VGetArrayPointer_OpenMP(data->grid);

  1393. //	for (int i = 0; i < data->npts; i++) {

  1394. //		fprintf((data->gridOutput), "%15.6e\t%15.6e\t",psi(i+1),t);

  1395. //		for (int j = 0; j < data->nvar; j++) {

  1396. //			fprintf((data->gridOutput), "%15.6e\t",ydata[j+i*data->nvar]);

  1397. //		}

  1398. //		fprintf((data->gridOutput), "\n");

  1399. //	}

  1400. //	fprintf((data->gridOutput), "\n\n");

  1401. //}

  1402. //

  1403. //

  1404. ////void repairSolution(N_Vector y, N_Vector ydot, UserData data){

  1405. ////	int npts=data->npts;

  1406. ////  	double *ydata;

  1407. ////  	double *ydotdata;

  1408. ////	ydata    = N_VGetArrayPointer_OpenMP(y); 

  1409. ////	ydotdata    = N_VGetArrayPointer_OpenMP(ydot); 

  1410. ////

  1411. ////	T(2)=T(1);

  1412. ////	T(npts-1)=T(npts);

  1413. ////	Tdot(2)=Tdot(1);

  1414. ////	Tdot(npts-1)=Tdot(npts);

  1415. ////	for (int k = 1; k <=data->nsp; k++) {

  1416. ////		    Y(2,k)=Y(1,k);

  1417. ////		    Y(npts-1,k)=Y(npts,k);

  1418. ////

  1419. ////		    Ydot(2,k)=Ydot(1,k);

  1420. ////		    Ydot(npts-1,k)=Ydot(npts,k);

  1421. ////	}

  1422. ////}