Actual source code: ex5.c

petsc-3.4.2 2013-07-02
  1: static char help[] = "Nonlinear, time-dependent. Developed from radiative_surface_balance.c \n";
  2: /*
  3:   Contributed by Steve Froehlich, Illinois Institute of Technology

  5:    Usage:
  6:     mpiexec -n <np> ./ex5 [options]
  7:     ./ex5 -help  [view petsc options]
  8:     ./ex5 -ts_type sundials -ts_view
  9:     ./ex5 -da_grid_x 20 -da_grid_y 20 -log_summary
 10:     ./ex5 -da_grid_x 20 -da_grid_y 20 -ts_type rosw -ts_atol 1.e-6 -ts_rtol 1.e-6
 11:     ./ex5 -drawcontours -draw_pause 0.1 -draw_fields 0,1,2,3,4
 12: */

 14: /*
 15:    -----------------------------------------------------------------------

 17:    Governing equations:

 19:         R      = s*(Ea*Ta^4 - Es*Ts^4)
 20:         SH     = p*Cp*Ch*wind*(Ta - Ts)
 21:         LH     = p*L*Ch*wind*B(q(Ta) - q(Ts))
 22:         G      = k*(Tgnd - Ts)/dz

 24:         Fnet   = R + SH + LH + G

 26:         du/dt  = -u*(du/dx) - v*(du/dy) - 2*omeg*sin(lat)*v - (1/p)*(dP/dx)
 27:         dv/dt  = -u*(dv/dx) - v*(dv/dy) + 2*omeg*sin(lat)*u - (1/p)*(dP/dy)
 28:         dTs/dt = Fnet/(Cp*dz) - Div([u*Ts, v*Ts]) + D*Lap(Ts)
 29:                = Fnet/(Cs*dz) - u*(dTs/dx) - v*(dTs/dy) + D*(Ts_xx + Ts_yy)
 30:         dp/dt  = -Div([u*p,v*p])
 31:                = - u*dp/dx - v*dp/dy
 32:         dTa/dt = Fnet/Cp

 34:    Equation of State:

 36:         P = p*R*Ts

 38:    -----------------------------------------------------------------------

 40:    Program considers the evolution of a two dimensional atmosphere from
 41:    sunset to sunrise. There are two components:
 42:                 1. Surface energy balance model to compute diabatic dT (Fnet)
 43:                 2. Dynamical model using simplified primitive equations

 45:    Program is to be initiated at sunset and run to sunrise.

 47:    Inputs are:
 48:                 Surface temperature
 49:                 Dew point temperature
 50:                 Air temperature
 51:                 Temperature at cloud base (if clouds are present)
 52:                 Fraction of sky covered by clouds
 53:                 Wind speed
 54:                 Precipitable water in centimeters
 55:                 Wind direction

 57:    Inputs are are read in from the text file ex5_control.txt. To change an
 58:    input value use ex5_control.txt.

 60:    Solvers:
 61:             Backward Euler = default solver
 62:             Sundials = fastest and most accurate, requires Sundials libraries

 64:    This model is under development and should be used only as an example
 65:    and not as a predictive weather model.
 66: */

 68: #include <petscts.h>
 69: #include <petscdmda.h>

 71: /* stefan-boltzmann constant */
 72: #define SIG 0.000000056703
 73: /* absorption-emission constant for surface */
 74: #define EMMSFC   1
 75: /* amount of time (seconds) that passes before new flux is calculated */
 76: #define TIMESTEP 1

 78: /* variables of interest to be solved at each grid point */
 79: typedef struct {
 80:   PetscScalar Ts,Ta; /* surface and air temperature */
 81:   PetscScalar u,v;   /* wind speed */
 82:   PetscScalar p;     /* density */
 83: } Field;

 85: /* User defined variables. Used in solving for variables of interest */
 86: typedef struct {
 87:   DM          da;        /* grid */
 88:   PetscScalar csoil;     /* heat constant for layer */
 89:   PetscScalar dzlay;     /* thickness of top soil layer */
 90:   PetscScalar emma;      /* emission parameter */
 91:   PetscScalar wind;      /* wind speed */
 92:   PetscScalar dewtemp;   /* dew point temperature (moisture in air) */
 93:   PetscScalar pressure1; /* sea level pressure */
 94:   PetscScalar airtemp;   /* temperature of air near boundary layer inversion */
 95:   PetscScalar Ts;        /* temperature at the surface */
 96:   PetscScalar fract;     /* fraction of sky covered by clouds */
 97:   PetscScalar Tc;        /* temperature at base of lowest cloud layer */
 98:   PetscScalar lat;       /* Latitude in degrees */
 99:   PetscScalar init;      /* initialization scenario */
100:   PetscScalar deep_grnd_temp; /* temperature of ground under top soil surface layer */
101: } AppCtx;

103: /* Struct for visualization */
104: typedef struct {
105:   PetscBool   drawcontours;   /* flag - 1 indicates drawing contours */
106:   PetscViewer drawviewer;
107: } MonitorCtx;


110: /* Inputs read in from text file */
111: struct in {
112:   PetscScalar Ts;     /* surface temperature  */
113:   PetscScalar Td;     /* dewpoint temperature */
114:   PetscScalar Tc;     /* temperature of cloud base */
115:   PetscScalar fr;     /* fraction of sky covered by clouds */
116:   PetscScalar wnd;    /* wind speed */
117:   PetscScalar Ta;     /* air temperature */
118:   PetscScalar pwt;    /* precipitable water */
119:   PetscScalar wndDir; /* wind direction */
120:   PetscScalar lat;    /* latitude */
121:   PetscReal   time;   /* time in hours */
122:   PetscScalar init;
123: };

125: /* functions */
126: extern PetscScalar emission(PetscScalar);                           /* sets emission/absorption constant depending on water vapor content */
127: extern PetscScalar calc_q(PetscScalar);                             /* calculates specific humidity */
128: extern PetscScalar mph2mpers(PetscScalar);                          /* converts miles per hour to meters per second */
129: extern PetscScalar Lconst(PetscScalar);                             /* calculates latent heat constant taken from Satellite estimates of wind speed and latent heat flux over the global oceans., Bentamy et al. */
130: extern PetscScalar fahr_to_cel(PetscScalar);                        /* converts Fahrenheit to Celsius */
131: extern PetscScalar cel_to_fahr(PetscScalar);                        /* converts Celsius to Fahrenheit */
132: extern PetscScalar calcmixingr(PetscScalar, PetscScalar);           /* calculates mixing ratio */
133: extern PetscScalar cloud(PetscScalar);                              /* cloud radiative parameterization */
134: extern PetscErrorCode FormInitialSolution(DM,Vec,void*);            /* Specifies initial conditions for the system of equations (PETSc defined function) */
135: extern PetscErrorCode RhsFunc(TS,PetscReal,Vec,Vec,void*);          /* Specifies the user defined functions                     (PETSc defined function) */
136: extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);     /* Specifies output and visualization tools                 (PETSc defined function) */
137: extern void readinput(struct in *put);                              /* reads input from text file */
138: extern PetscErrorCode calcfluxs(PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar*); /* calculates upward IR from surface */
139: extern PetscErrorCode calcfluxa(PetscScalar, PetscScalar, PetscScalar, PetscScalar*);                           /* calculates downward IR from atmosphere */
140: extern PetscErrorCode sensibleflux(PetscScalar, PetscScalar, PetscScalar, PetscScalar*);                        /* calculates sensible heat flux */
141: extern PetscErrorCode potential_temperature(PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar*);  /* calculates potential temperature */
142: extern PetscErrorCode latentflux(PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar*);             /* calculates latent heat flux */
143: extern PetscErrorCode calc_gflux(PetscScalar, PetscScalar, PetscScalar*);                                       /* calculates flux between top soil layer and underlying earth */

147: int main(int argc,char **argv)
148: {
150:   int            time;           /* amount of loops */
151:   struct in      put;
152:   PetscScalar    rh;             /* relative humidity */
153:   PetscScalar    x;              /* memory varialbe for relative humidity calculation */
154:   PetscScalar    deep_grnd_temp; /* temperature of ground under top soil surface layer */
155:   PetscScalar    emma;           /* absorption-emission constant for air */
156:   PetscScalar    pressure1 = 101300; /* surface pressure */
157:   PetscScalar    mixratio;       /* mixing ratio */
158:   PetscScalar    airtemp;        /* temperature of air near boundary layer inversion */
159:   PetscScalar    dewtemp;        /* dew point temperature */
160:   PetscScalar    sfctemp;        /* temperature at surface */
161:   PetscScalar    pwat;           /* total column precipitable water */
162:   PetscScalar    cloudTemp;      /* temperature at base of cloud */
163:   AppCtx         user;           /*  user-defined work context */
164:   MonitorCtx     usermonitor;    /* user-defined monitor context */
165:   PetscMPIInt    rank,size;
166:   TS             ts;
167:   SNES           snes;
168:   DM             da;
169:   Vec            T,rhs;          /* solution vector */
170:   Mat            J;              /* Jacobian matrix */
171:   PetscReal      ftime,dt;
172:   PetscInt       steps,dof = 5;

174:   PetscInitialize(&argc,&argv,(char*)0,help);
175:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
176:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

178:   /* Inputs */
179:   readinput(&put);

181:   sfctemp   = put.Ts;
182:   dewtemp   = put.Td;
183:   cloudTemp = put.Tc;
184:   airtemp   = put.Ta;
185:   pwat      = put.pwt;

187:   if (!rank) PetscPrintf(PETSC_COMM_SELF,"Initial Temperature = %g\n",sfctemp); /* input surface temperature */

189:   deep_grnd_temp = sfctemp - 10;   /* set underlying ground layer temperature */
190:   emma           = emission(pwat); /* accounts for radiative effects of water vapor */

192:   /* Converts from Fahrenheit to Celsuis */
193:   sfctemp        = fahr_to_cel(sfctemp);
194:   airtemp        = fahr_to_cel(airtemp);
195:   dewtemp        = fahr_to_cel(dewtemp);
196:   cloudTemp      = fahr_to_cel(cloudTemp);
197:   deep_grnd_temp = fahr_to_cel(deep_grnd_temp);

199:   /* Converts from Celsius to Kelvin */
200:   sfctemp        += 273;
201:   airtemp        += 273;
202:   dewtemp        += 273;
203:   cloudTemp      += 273;
204:   deep_grnd_temp += 273;

206:   /* Calculates initial relative humidity */
207:   x        = calcmixingr(dewtemp,pressure1);
208:   mixratio = calcmixingr(sfctemp,pressure1);
209:   rh       = (x/mixratio)*100;

211:   if (!rank) printf("Initial RH = %.1f percent\n\n",rh);   /* prints initial relative humidity */

213:   time = 3600*put.time;                         /* sets amount of timesteps to run model */

215:   /* Configure PETSc TS solver */
216:   /*------------------------------------------*/

218:   /* Create grid */
219:   DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,-20,-20,
220:                       PETSC_DECIDE,PETSC_DECIDE,dof,1,NULL,NULL,&da);
221:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);

223:   /* Define output window for each variable of interest */
224:   DMDASetFieldName(da,0,"Ts");
225:   DMDASetFieldName(da,1,"Ta");
226:   DMDASetFieldName(da,2,"u");
227:   DMDASetFieldName(da,3,"v");
228:   DMDASetFieldName(da,4,"p");

230:   /* set values for appctx */
231:   user.da             = da;
232:   user.Ts             = sfctemp;
233:   user.fract          = put.fr;          /* fraction of sky covered by clouds */
234:   user.dewtemp        = dewtemp;         /* dew point temperature (mositure in air) */
235:   user.csoil          = 2000000;         /* heat constant for layer */
236:   user.dzlay          = 0.08;            /* thickness of top soil layer */
237:   user.emma           = emma;            /* emission parameter */
238:   user.wind           = put.wnd;         /* wind spped */
239:   user.pressure1      = pressure1;       /* sea level pressure */
240:   user.airtemp        = airtemp;         /* temperature of air near boundar layer inversion */
241:   user.Tc             = cloudTemp;       /* temperature at base of lowest cloud layer */
242:   user.init           = put.init;        /* user chosen initiation scenario */
243:   user.lat            = 70*0.0174532;    /* converts latitude degrees to latitude in radians */
244:   user.deep_grnd_temp = deep_grnd_temp;  /* temp in lowest ground layer */

246:   /* set values for MonitorCtx */
247:   usermonitor.drawcontours = PETSC_FALSE;
248:   PetscOptionsHasName(NULL,"-drawcontours",&usermonitor.drawcontours);
249:   if (usermonitor.drawcontours) {
250:     PetscReal bounds[] = {1000.0,-1000.,  -1000.,-1000.,  1000.,-1000.,  1000.,-1000.,  1000,-1000, 100700,100800};
251:     PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer);
252:     PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds);
253:   }

255:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
256:      Extract global vectors from DA;
257:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
258:   DMCreateGlobalVector(da,&T);
259:   VecDuplicate(T,&rhs); /* r: vector to put the computed right hand side */

261:   TSCreate(PETSC_COMM_WORLD,&ts);
262:   TSSetProblemType(ts,TS_NONLINEAR);
263:   TSSetType(ts,TSBEULER);
264:   TSSetRHSFunction(ts,rhs,RhsFunc,&user);

266:   /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
267:   PetscBool     use_coloring  = PETSC_TRUE;
268:   MatFDColoring matfdcoloring = 0;
269:   DMCreateMatrix(da,MATAIJ,&J);
270:   TSGetSNES(ts,&snes);
271:   if (use_coloring) {
272:     ISColoring iscoloring;
273:     DMCreateColoring(da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);
274:     MatFDColoringCreate(J,iscoloring,&matfdcoloring);
275:     MatFDColoringSetFromOptions(matfdcoloring);
276:     ISColoringDestroy(&iscoloring);
277:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);
278:     SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
279:   } else {
280:     SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);
281:   }

283:   /* Define what to print for ts_monitor option */
284:   PetscBool monitor_off = PETSC_FALSE;
285:   PetscOptionsHasName(NULL,"-monitor_off",&monitor_off);
286:   if (!monitor_off) {
287:     TSMonitorSet(ts,Monitor,&usermonitor,NULL);
288:   }
289:   FormInitialSolution(da,T,&user);
290:   dt    = TIMESTEP; /* initial time step */
291:   ftime = TIMESTEP*time;
292:   if (!rank) printf("time %d, ftime %g hour, TIMESTEP %g\n",time,ftime/3600,dt);

294:   TSSetInitialTimeStep(ts,0.0,dt);
295:   TSSetDuration(ts,time,ftime);
296:   TSSetSolution(ts,T);
297:   TSSetDM(ts,da);

299:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
300:      Set runtime options
301:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
302:   TSSetFromOptions(ts);

304:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
305:      Solve nonlinear system
306:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
307:   TSSolve(ts,T);
308:   TSGetSolveTime(ts,&ftime);
309:   TSGetTimeStepNumber(ts,&steps);
310:   if (!rank) PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %d steps\n",ftime/3600,steps);


313:   if (matfdcoloring) {MatFDColoringDestroy(&matfdcoloring);}
314:   if (usermonitor.drawcontours) {
315:     PetscViewerDestroy(&usermonitor.drawviewer);
316:   }
317:   MatDestroy(&J);
318:   VecDestroy(&T);
319:   VecDestroy(&rhs);
320:   TSDestroy(&ts);
321:   DMDestroy(&da);

323:   PetscFinalize();
324:   return 0;
325: }
326: /*****************************end main program********************************/
327: /*****************************************************************************/
328: /*****************************************************************************/
329: /*****************************************************************************/
332: PetscErrorCode calcfluxs(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar fract, PetscScalar cloudTemp, PetscScalar *flux)
333: {
335:   *flux = SIG*((EMMSFC*emma*pow(airtemp,4)) + (EMMSFC*fract*(1 - emma)*pow(cloudTemp,4)) - (EMMSFC*pow(sfctemp,4)));   /* calculates flux using Stefan-Boltzmann relation */
336:   return(0);
337: }

341: PetscErrorCode calcfluxa(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar *flux)   /* this function is not currently called upon */
342: {
343:   PetscScalar emm = 0.001;

346:   *flux = SIG*(-emm*(pow(airtemp,4)));      /* calculates flux usinge Stefan-Boltzmann relation */
347:   return(0);
348: }
351: PetscErrorCode sensibleflux(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar wind, PetscScalar *sheat)
352: {
353:   PetscScalar density = 1;    /* air density */
354:   PetscScalar Cp      = 1005; /* heat capicity for dry air */
355:   PetscScalar wndmix;         /* temperature change from wind mixing: wind*Ch */

358:   wndmix = 0.0025 + 0.0042*wind;                               /* regression equation valid for neutral and stable BL */
359:   *sheat = density*Cp*wndmix*(airtemp - sfctemp);              /* calculates sensible heat flux */
360:   return(0);
361: }

365: PetscErrorCode latentflux(PetscScalar sfctemp, PetscScalar dewtemp, PetscScalar wind, PetscScalar pressure1, PetscScalar *latentheat)
366: {
367:   PetscScalar density = 1;   /* density of dry air */
368:   PetscScalar q;             /* actual specific humitity */
369:   PetscScalar qs;            /* saturation specific humidity */
370:   PetscScalar wndmix;        /* temperature change from wind mixing: wind*Ch */
371:   PetscScalar beta = .4;     /* moisture availability */
372:   PetscScalar mr;            /* mixing ratio */
373:   PetscScalar lhcnst;        /* latent heat of vaporization constant = 2501000 J/kg at 0c */
374:                              /* latent heat of saturation const = 2834000 J/kg */
375:                              /* latent heat of fusion const = 333700 J/kg */

378:   wind   = mph2mpers(wind);                /* converts wind from mph to meters per second */
379:   wndmix = 0.0025 + 0.0042*wind;           /* regression equation valid for neutral BL */
380:   lhcnst = Lconst(sfctemp);                /* calculates latent heat of evaporation */
381:   mr     = calcmixingr(sfctemp,pressure1); /* calculates saturation mixing ratio */
382:   qs     = calc_q(mr);                     /* calculates saturation specific humidty */
383:   mr     = calcmixingr(dewtemp,pressure1); /* calculates mixing ratio */
384:   q      = calc_q(mr);                     /* calculates specific humidty */

386:   *latentheat = density*wndmix*beta*lhcnst*(q - qs); /* calculates latent heat flux */
387:   return(0);
388: }

392: PetscErrorCode potential_temperature(PetscScalar temp, PetscScalar pressure1, PetscScalar pressure2, PetscScalar sfctemp, PetscScalar *pottemp)
393: {
394:   PetscScalar kdry;     /* poisson constant for dry atmosphere */
395:   PetscScalar kmoist;   /* poisson constant for moist atmosphere */
396:   PetscScalar pavg;     /* average atmospheric pressure */
397:   PetscScalar mixratio; /* mixing ratio */

400:   mixratio = calcmixingr(sfctemp,pressure1);

402: /* initialize poisson constant */
403:   kdry   = 0.2854;
404:   kmoist = 0.2854*(1 - 0.24*mixratio);

406:   pavg     = ((0.7*pressure1)+pressure2)/2;     /* calculates simple average press */
407:   *pottemp = temp*(pow((pressure1/pavg),kdry)); /* calculates potential temperature */
408:   return(0);
409: }
410: extern PetscScalar calcmixingr(PetscScalar dtemp, PetscScalar pressure1)
411: {
412:   PetscScalar e;        /* vapor pressure */
413:   PetscScalar mixratio; /* mixing ratio */

415:   dtemp    = dtemp - 273;                                /* converts from Kelvin to Celsuis */
416:   e        = 6.11*(pow(10,((7.5*dtemp)/(237.7+dtemp)))); /* converts from dew point temp to vapor pressure */
417:   e        = e*100;                                      /* converts from hPa to Pa */
418:   mixratio = (0.622*e)/(pressure1 - e);                  /* computes mixing ratio */
419:   mixratio = mixratio*1;                                 /* convert to g/Kg */

421:   return mixratio;
422: }
423: extern PetscScalar calc_q(PetscScalar rv)
424: {
425:   PetscScalar specific_humidity;        /* define specific humidity variable */
426:   specific_humidity = rv/(1 + rv);      /* calculates specific humidity */
427:   return specific_humidity;
428: }

432: PetscErrorCode calc_gflux(PetscScalar sfctemp, PetscScalar deep_grnd_temp, PetscScalar* Gflux)
433: {
434:   PetscScalar k;                       /* thermal conductivity parameter */
435:   PetscScalar n                = 0.38; /* value of soil porosity */
436:   PetscScalar dz               = 1;    /* depth of layer between soil surface and deep soil layer */
437:   PetscScalar unit_soil_weight = 2700; /* unit soil weight in kg/m^3 */

440:   k      = ((0.135*(1-n)*unit_soil_weight) + 64.7)/(unit_soil_weight - (0.947*(1-n)*unit_soil_weight)); /* dry soil conductivity */
441:   *Gflux = (k*(deep_grnd_temp - sfctemp)/dz);   /* calculates flux from deep ground layer */
442:   return(0);
443: }
446: extern PetscScalar emission(PetscScalar pwat)
447: {
448:   PetscScalar emma;

450:   emma = 0.725 + 0.17*log10(pwat);

452:   return emma;
453: }
454: extern PetscScalar cloud(PetscScalar fract)
455: {
456:   PetscScalar emma = 0;

458:   /* modifies radiative balance depending on cloud cover */
459:   if (fract >= 0.9)                     emma = 1;
460:   else if (0.9 > fract && fract >= 0.8) emma = 0.9;
461:   else if (0.8 > fract && fract >= 0.7) emma = 0.85;
462:   else if (0.7 > fract && fract >= 0.6) emma = 0.75;
463:   else if (0.6 > fract && fract >= 0.5) emma = 0.65;
464:   else if (0.4 > fract && fract >= 0.3) emma = emma*1.086956;
465:   return emma;
466: }
467: extern PetscScalar Lconst(PetscScalar sfctemp)
468: {
469:   PetscScalar Lheat;
470:   sfctemp -=273;                               /* converts from kelvin to celsius */
471:   Lheat    = 4186.8*(597.31 - 0.5625*sfctemp); /* calculates latent heat constant */
472:   return Lheat;
473: }
474: extern PetscScalar mph2mpers(PetscScalar wind)
475: {
476:   wind = ((wind*1.6*1000)/3600);                 /* converts wind from mph to meters per second */
477:   return wind;
478: }
479: extern PetscScalar fahr_to_cel(PetscScalar temp)
480: {
481:   temp = (5*(temp-32))/9; /* converts from farhrenheit to celsuis */
482:   return temp;
483: }
484: extern PetscScalar cel_to_fahr(PetscScalar temp)
485: {
486:   temp = ((temp*9)/5) + 32; /* converts from celsuis to farhrenheit */
487:   return temp;
488: }
489: void readinput(struct in *put)
490: {
491:   int  i;
492:   char x;
493:   FILE *ifp;

495:   ifp = fopen("ex5_control.txt", "r");

497:   for (i=0; i<110; i++) fscanf(ifp, "%c", &x);
498:   fscanf(ifp, "%lf", &put->Ts);

500:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
501:   fscanf(ifp, "%lf", &put->Td);

503:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
504:   fscanf(ifp, "%lf", &put->Ta);

506:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
507:   fscanf(ifp, "%lf", &put->Tc);

509:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
510:   fscanf(ifp, "%lf", &put->fr);

512:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
513:   fscanf(ifp, "%lf", &put->wnd);

515:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
516:   fscanf(ifp, "%lf", &put->pwt);

518:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
519:   fscanf(ifp, "%lf", &put->wndDir);

521:   for (i=0; i<43; i++) fscanf(ifp, "%c", &x);
522:   fscanf(ifp, "%lf", &put->time);

524:   for (i=0; i<63; i++) fscanf(ifp, "%c", &x);
525:   fscanf(ifp, "%lf", &put->init);
526: }

528: /* ------------------------------------------------------------------- */
531: PetscErrorCode FormInitialSolution(DM da,Vec Xglobal,void *ctx)
532: {
534:   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
535:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
536:   Field          **X;
537:   PetscScalar    deltT;
538:   PetscReal      hx,hy;
539:   FILE           *ifp;
540:   FILE           *ofp;

543:   ofp   = fopen("swing", "w");
544:   ifp   = fopen("grid.in", "r");
545:   deltT = 0.8;

547:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
548:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

550:   hx = 1/(PetscReal)(Mx-1);
551:   hy = 1/(PetscReal)(My-1);

553:   /* Get pointers to vector data */
554:   DMDAVecGetArray(da,Xglobal,&X);

556:   /* Get local grid boundaries */
557:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

559:   /* Compute function over the locally owned part of the grid */

561:   if (user->init == 1) {
562:     for (j=ys; j<ys+ym; j++) {
563:       for (i=xs; i<xs+xm; i++) {
564:         X[j][i].Ts = user->Ts - i*0.0001;
565:         X[j][i].Ta = X[j][i].Ts - 5;
566:         X[j][i].u  = 0;
567:         X[j][i].v  = 0;
568:         X[j][i].p  = 1.25;
569:         if ((j == 5 || j == 6) && (i == 4 || i == 5))   X[j][i].p += 0.00001;
570:         if ((j == 5 || j == 6) && (i == 12 || i == 13)) X[j][i].p += 0.00001;
571:       }
572:     }
573:   } else {
574:     for (j=ys; j<ys+ym; j++) {
575:       for (i=xs; i<xs+xm; i++) {
576:         X[j][i].Ts = user->Ts;
577:         X[j][i].Ta = X[j][i].Ts - 5;
578:         X[j][i].u  = 0;
579:         X[j][i].v  = 0;
580:         X[j][i].p  = 1.25;
581:       }
582:     }
583:   }

585:   /* Restore vectors */
586:   DMDAVecRestoreArray(da,Xglobal,&X);
587:   return(0);
588: }

592: /*
593:    RhsFunc - Evaluates nonlinear function F(u).

595:    Input Parameters:
596: .  ts - the TS context
597: .  t - current time
598: .  Xglobal - input vector
599: .  F - output vector
600: .  ptr - optional user-defined context, as set by SNESSetFunction()

602:    Output Parameter:
603: .  F - rhs function vector
604:  */
605: PetscErrorCode RhsFunc(TS ts,PetscReal t,Vec Xglobal,Vec F,void *ctx)
606: {
607:   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
608:   DM             da    = user->da;
610:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
611:   PetscReal      dhx,dhy;
612:   Vec            localT;
613:   Field          **X,**Frhs;                            /* structures that contain variables of interest and left hand side of governing equations respectively */
614:   PetscScalar    csoil          = user->csoil;          /* heat constant for layer */
615:   PetscScalar    dzlay          = user->dzlay;          /* thickness of top soil layer */
616:   PetscScalar    emma           = user->emma;           /* emission parameter */
617:   PetscScalar    wind           = user->wind;           /* wind speed */
618:   PetscScalar    dewtemp        = user->dewtemp;        /* dew point temperature (moisture in air) */
619:   PetscScalar    pressure1      = user->pressure1;      /* sea level pressure */
620:   PetscScalar    airtemp        = user->airtemp;        /* temperature of air near boundary layer inversion */
621:   PetscScalar    fract          = user->fract;          /* fraction of the sky covered by clouds */
622:   PetscScalar    Tc             = user->Tc;             /* temperature at base of lowest cloud layer */
623:   PetscScalar    lat            = user->lat;            /* latitude */
624:   PetscScalar    Cp             = 1005.7;               /* specific heat of air at constant pressure */
625:   PetscScalar    Rd             = 287.058;              /* gas constant for dry air */
626:   PetscScalar    diffconst      = 1000;                 /* diffusion coefficient */
627:   PetscScalar    f              = 2*0.0000727*sin(lat); /* coriolis force */
628:   PetscScalar    deep_grnd_temp = user->deep_grnd_temp; /* temp in lowest ground layer */
629:   PetscScalar    Ts,u,v,p,P;
630:   PetscScalar    u_abs,u_plus,u_minus,v_abs,v_plus,v_minus;

632:   PetscScalar sfctemp1,fsfc1,Ra;
633:   PetscScalar sheat;                   /* sensible heat flux */
634:   PetscScalar latentheat;              /* latent heat flux */
635:   PetscScalar groundflux;              /* flux from conduction of deep ground layer in contact with top soil */
636:   PetscInt    xend,yend;

639:   DMGetLocalVector(da,&localT);
640:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
641:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

643:   dhx = (PetscReal)(Mx-1)/(5000*(Mx-1));  /* dhx = 1/dx; assume 2D space domain: [0.0, 1.e5] x [0.0, 1.e5] */
644:   dhy = (PetscReal)(My-1)/(5000*(Mx-1));  /* dhy = 1/dy; */


647:   /*
648:      Scatter ghost points to local vector,using the 2-step process
649:         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
650:      By placing code between these two statements, computations can be
651:      done while messages are in transition.
652:   */
653:   DMGlobalToLocalBegin(da,Xglobal,INSERT_VALUES,localT);
654:   DMGlobalToLocalEnd(da,Xglobal,INSERT_VALUES,localT);

656:   /* Get pointers to vector data */
657:   DMDAVecGetArray(da,localT,&X);
658:   DMDAVecGetArray(da,F,&Frhs);

660:   /* Get local grid boundaries */
661:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

663:   /* Compute function over the locally owned part of the grid */
664:   /* the interior points */
665:   xend=xs+xm; yend=ys+ym;
666:   for (j=ys; j<yend; j++) {
667:     for (i=xs; i<xend; i++) {
668:       Ts = X[j][i].Ts; u = X[j][i].u; v = X[j][i].v; p = X[j][i].p; /*P = X[j][i].P; */

670:       sfctemp1 = (double)Ts;
671:       sfctemp1 = (double)X[j][i].Ts;
672:       calcfluxs(sfctemp1,airtemp,emma,fract,Tc,&fsfc1);        /* calculates surface net radiative flux */
673:       sensibleflux(sfctemp1,airtemp,wind,&sheat);              /* calculate sensible heat flux */
674:       latentflux(sfctemp1,dewtemp,wind,pressure1,&latentheat); /* calculates latent heat flux */
675:       calc_gflux(sfctemp1,deep_grnd_temp,&groundflux);         /* calculates flux from earth below surface soil layer by conduction */
676:       calcfluxa(sfctemp1,airtemp,emma,&Ra);                                  /* Calculates the change in downward radiative flux */
677:       fsfc1    = fsfc1 + latentheat + sheat + groundflux;                               /* adds radiative, sensible heat, latent heat, and ground heat flux yielding net flux */

679:       /* convective coefficients for upwinding */
680:       u_abs   = PetscAbsScalar(u);
681:       u_plus  = .5*(u + u_abs); /* u if u>0; 0 if u<0 */
682:       u_minus = .5*(u - u_abs); /* u if u <0; 0 if u>0 */

684:       v_abs   = PetscAbsScalar(v);
685:       v_plus  = .5*(v + v_abs); /* v if v>0; 0 if v<0 */
686:       v_minus = .5*(v - v_abs); /* v if v <0; 0 if v>0 */

688:       /* Solve governing equations */
689:       P = p*Rd*Ts;

691:       /* du/dt -> time change of east-west component of the wind */
692:       Frhs[j][i].u = - u_plus*(u - X[j][i-1].u)*dhx - u_minus*(X[j][i+1].u - u)*dhx       /* - u(du/dx) */
693:                      - v_plus*(u - X[j-1][i].u)*dhy - v_minus*(X[j+1][i].u - u)*dhy       /* - v(du/dy) */
694:                      -(Rd/p)*(Ts*(X[j][i+1].p - X[j][i-1].p)*0.5*dhx  + p*0*(X[j][i+1].Ts - X[j][i-1].Ts)*0.5*dhx) /* -(R/p)[Ts(dp/dx)+ p(dTs/dx)] */
695: /*                     -(1/p)*(X[j][i+1].P - X[j][i-1].P)*dhx */
696:                      + f*v;

698:       /* dv/dt -> time change of north-south component of the wind */
699:       Frhs[j][i].v = - u_plus*(v - X[j][i-1].v)*dhx - u_minus*(X[j][i+1].v - v)*dhx       /* - u(dv/dx) */
700:                      - v_plus*(v - X[j-1][i].v)*dhy - v_minus*(X[j+1][i].v - v)*dhy       /* - v(dv/dy) */
701:                      -(Rd/p)*(Ts*(X[j+1][i].p - X[j-1][i].p)*0.5*dhy + p*0*(X[j+1][i].Ts - X[j-1][i].Ts)*0.5*dhy) /* -(R/p)[Ts(dp/dy)+ p(dTs/dy)] */
702: /*                     -(1/p)*(X[j+1][i].P - X[j-1][i].P)*dhy */
703:                      -f*u;

705:       /* dT/dt -> time change of temperature */
706:       Frhs[j][i].Ts = (fsfc1/(csoil*dzlay))                                            /* Fnet/(Cp*dz)  diabatic change in T */
707:                       -u_plus*(Ts - X[j][i-1].Ts)*dhx - u_minus*(X[j][i+1].Ts - Ts)*dhx  /* - u*(dTs/dx)  advection x */
708:                       -v_plus*(Ts - X[j-1][i].Ts)*dhy - v_minus*(X[j+1][i].Ts - Ts)*dhy  /* - v*(dTs/dy)  advection y */
709:                       + diffconst*((X[j][i+1].Ts - 2*Ts + X[j][i-1].Ts)*dhx*dhx               /* + D(Ts_xx + Ts_yy)  diffusion */
710:                                    + (X[j+1][i].Ts - 2*Ts + X[j-1][i].Ts)*dhy*dhy);

712:       /* dp/dt -> time change of */
713:       Frhs[j][i].p = -u_plus*(p - X[j][i-1].p)*dhx - u_minus*(X[j][i+1].p - p)*dhx     /* - u*(dp/dx) */
714:                      -v_plus*(p - X[j-1][i].p)*dhy - v_minus*(X[j+1][i].p - p)*dhy;    /* - v*(dp/dy) */

716:       Frhs[j][i].Ta = Ra/Cp;  /* dTa/dt time change of air temperature */
717:     }
718:   }

720:   /* Restore vectors */
721:   DMDAVecRestoreArray(da,localT,&X);
722:   DMDAVecRestoreArray(da,F,&Frhs);
723:   DMRestoreLocalVector(da,&localT);
724:   return(0);
725: }

729: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec T,void *ctx)
730: {
732:   PetscScalar    *array;
733:   MonitorCtx     *user  = (MonitorCtx*)ctx;
734:   PetscViewer    viewer = user->drawviewer;
735:   PetscMPIInt    rank;
736:   PetscReal      norm;

739:   MPI_Comm_rank(PetscObjectComm((PetscObject)ts),&rank);
740:   VecNorm(T,NORM_INFINITY,&norm);

742:   VecGetArray(T,&array);
743:   if (!rank) printf("step %4d, time %8.1f,  %6.4f, %6.4f, %6.4f, %6.4f, %6.4f, %6.4f\n",step,time,(((array[0]-273)*9)/5 + 32),(((array[1]-273)*9)/5 + 32),array[2],array[3],array[4],array[5]);
744:   VecRestoreArray(T,&array);

746:   if (user->drawcontours) {
747:     VecView(T,viewer);
748:   }
749:   return(0);
750: }