Actual source code: ex5.c

petsc-3.4.4 2014-03-13
  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:   PetscInt    interval;
108: } MonitorCtx;


111: /* Inputs read in from text file */
112: struct in {
113:   PetscScalar Ts;     /* surface temperature  */
114:   PetscScalar Td;     /* dewpoint temperature */
115:   PetscScalar Tc;     /* temperature of cloud base */
116:   PetscScalar fr;     /* fraction of sky covered by clouds */
117:   PetscScalar wnd;    /* wind speed */
118:   PetscScalar Ta;     /* air temperature */
119:   PetscScalar pwt;    /* precipitable water */
120:   PetscScalar wndDir; /* wind direction */
121:   PetscScalar lat;    /* latitude */
122:   PetscReal   time;   /* time in hours */
123:   PetscScalar init;
124: };

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

148: int main(int argc,char **argv)
149: {
151:   int            time;           /* amount of loops */
152:   struct in      put;
153:   PetscScalar    rh;             /* relative humidity */
154:   PetscScalar    x;              /* memory varialbe for relative humidity calculation */
155:   PetscScalar    deep_grnd_temp; /* temperature of ground under top soil surface layer */
156:   PetscScalar    emma;           /* absorption-emission constant for air */
157:   PetscScalar    pressure1 = 101300; /* surface pressure */
158:   PetscScalar    mixratio;       /* mixing ratio */
159:   PetscScalar    airtemp;        /* temperature of air near boundary layer inversion */
160:   PetscScalar    dewtemp;        /* dew point temperature */
161:   PetscScalar    sfctemp;        /* temperature at surface */
162:   PetscScalar    pwat;           /* total column precipitable water */
163:   PetscScalar    cloudTemp;      /* temperature at base of cloud */
164:   AppCtx         user;           /*  user-defined work context */
165:   MonitorCtx     usermonitor;    /* user-defined monitor context */
166:   PetscMPIInt    rank,size;
167:   TS             ts;
168:   SNES           snes;
169:   DM             da;
170:   Vec            T,rhs;          /* solution vector */
171:   Mat            J;              /* Jacobian matrix */
172:   PetscReal      ftime,dt;
173:   PetscInt       steps,dof = 5;

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

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

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

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

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

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

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

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

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

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

216:   /* Configure PETSc TS solver */
217:   /*------------------------------------------*/

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

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

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

247:   /* set values for MonitorCtx */
248:   usermonitor.drawcontours = PETSC_FALSE;
249:   PetscOptionsHasName(NULL,"-drawcontours",&usermonitor.drawcontours);
250:   if (usermonitor.drawcontours) {
251:     PetscReal bounds[] = {1000.0,-1000.,  -1000.,-1000.,  1000.,-1000.,  1000.,-1000.,  1000,-1000, 100700,100800};
252:     PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer);
253:     PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds);
254:   }
255:   usermonitor.interval = 1;
256:   PetscOptionsGetInt(NULL,"-monitor_interval",&usermonitor.interval,NULL);

258:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
259:      Extract global vectors from DA;
260:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
261:   DMCreateGlobalVector(da,&T);
262:   VecDuplicate(T,&rhs); /* r: vector to put the computed right hand side */

264:   TSCreate(PETSC_COMM_WORLD,&ts);
265:   TSSetProblemType(ts,TS_NONLINEAR);
266:   TSSetType(ts,TSBEULER);
267:   TSSetRHSFunction(ts,rhs,RhsFunc,&user);

269:   /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
270:   PetscBool     use_coloring  = PETSC_TRUE;
271:   MatFDColoring matfdcoloring = 0;
272:   DMCreateMatrix(da,MATAIJ,&J);
273:   TSGetSNES(ts,&snes);
274:   if (use_coloring) {
275:     ISColoring iscoloring;
276:     DMCreateColoring(da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);
277:     MatFDColoringCreate(J,iscoloring,&matfdcoloring);
278:     MatFDColoringSetFromOptions(matfdcoloring);
279:     ISColoringDestroy(&iscoloring);
280:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);
281:     SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
282:   } else {
283:     SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);
284:   }

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

297:   TSSetInitialTimeStep(ts,0.0,dt);
298:   TSSetDuration(ts,time,ftime);
299:   TSSetSolution(ts,T);
300:   TSSetDM(ts,da);

302:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
303:      Set runtime options
304:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
305:   TSSetFromOptions(ts);

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


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

326:   PetscFinalize();
327:   return 0;
328: }
329: /*****************************end main program********************************/
330: /*****************************************************************************/
331: /*****************************************************************************/
332: /*****************************************************************************/
335: PetscErrorCode calcfluxs(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar fract, PetscScalar cloudTemp, PetscScalar *flux)
336: {
338:   *flux = SIG*((EMMSFC*emma*pow(airtemp,4)) + (EMMSFC*fract*(1 - emma)*pow(cloudTemp,4)) - (EMMSFC*pow(sfctemp,4)));   /* calculates flux using Stefan-Boltzmann relation */
339:   return(0);
340: }

344: PetscErrorCode calcfluxa(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar *flux)   /* this function is not currently called upon */
345: {
346:   PetscScalar emm = 0.001;

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

361:   wndmix = 0.0025 + 0.0042*wind;                               /* regression equation valid for neutral and stable BL */
362:   *sheat = density*Cp*wndmix*(airtemp - sfctemp);              /* calculates sensible heat flux */
363:   return(0);
364: }

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

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

389:   *latentheat = density*wndmix*beta*lhcnst*(q - qs); /* calculates latent heat flux */
390:   return(0);
391: }

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

403:   mixratio = calcmixingr(sfctemp,pressure1);

405: /* initialize poisson constant */
406:   kdry   = 0.2854;
407:   kmoist = 0.2854*(1 - 0.24*mixratio);

409:   pavg     = ((0.7*pressure1)+pressure2)/2;     /* calculates simple average press */
410:   *pottemp = temp*(pow((pressure1/pavg),kdry)); /* calculates potential temperature */
411:   return(0);
412: }
413: extern PetscScalar calcmixingr(PetscScalar dtemp, PetscScalar pressure1)
414: {
415:   PetscScalar e;        /* vapor pressure */
416:   PetscScalar mixratio; /* mixing ratio */

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

424:   return mixratio;
425: }
426: extern PetscScalar calc_q(PetscScalar rv)
427: {
428:   PetscScalar specific_humidity;        /* define specific humidity variable */
429:   specific_humidity = rv/(1 + rv);      /* calculates specific humidity */
430:   return specific_humidity;
431: }

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

443:   k      = ((0.135*(1-n)*unit_soil_weight) + 64.7)/(unit_soil_weight - (0.947*(1-n)*unit_soil_weight)); /* dry soil conductivity */
444:   *Gflux = (k*(deep_grnd_temp - sfctemp)/dz);   /* calculates flux from deep ground layer */
445:   return(0);
446: }
449: extern PetscScalar emission(PetscScalar pwat)
450: {
451:   PetscScalar emma;

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

455:   return emma;
456: }
457: extern PetscScalar cloud(PetscScalar fract)
458: {
459:   PetscScalar emma = 0;

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

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

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

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

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

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

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

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

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

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

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

527:   for (i=0; i<63; i++) fscanf(ifp, "%c", &x);
528:   fscanf(ifp, "%lf", &put->init);
529: }

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

546:   ofp   = fopen("swing", "w");
547:   ifp   = fopen("grid.in", "r");
548:   deltT = 0.8;

550:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
551:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

553:   hx = 1/(PetscReal)(Mx-1);
554:   hy = 1/(PetscReal)(My-1);

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

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

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

564:   if (user->init == 1) {
565:     for (j=ys; j<ys+ym; j++) {
566:       for (i=xs; i<xs+xm; i++) {
567:         X[j][i].Ts = user->Ts - i*0.0001;
568:         X[j][i].Ta = X[j][i].Ts - 5;
569:         X[j][i].u  = 0;
570:         X[j][i].v  = 0;
571:         X[j][i].p  = 1.25;
572:         if ((j == 5 || j == 6) && (i == 4 || i == 5))   X[j][i].p += 0.00001;
573:         if ((j == 5 || j == 6) && (i == 12 || i == 13)) X[j][i].p += 0.00001;
574:       }
575:     }
576:   } else {
577:     for (j=ys; j<ys+ym; j++) {
578:       for (i=xs; i<xs+xm; i++) {
579:         X[j][i].Ts = user->Ts;
580:         X[j][i].Ta = X[j][i].Ts - 5;
581:         X[j][i].u  = 0;
582:         X[j][i].v  = 0;
583:         X[j][i].p  = 1.25;
584:       }
585:     }
586:   }

588:   /* Restore vectors */
589:   DMDAVecRestoreArray(da,Xglobal,&X);
590:   return(0);
591: }

595: /*
596:    RhsFunc - Evaluates nonlinear function F(u).

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

605:    Output Parameter:
606: .  F - rhs function vector
607:  */
608: PetscErrorCode RhsFunc(TS ts,PetscReal t,Vec Xglobal,Vec F,void *ctx)
609: {
610:   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
611:   DM             da    = user->da;
613:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
614:   PetscReal      dhx,dhy;
615:   Vec            localT;
616:   Field          **X,**Frhs;                            /* structures that contain variables of interest and left hand side of governing equations respectively */
617:   PetscScalar    csoil          = user->csoil;          /* heat constant for layer */
618:   PetscScalar    dzlay          = user->dzlay;          /* thickness of top soil layer */
619:   PetscScalar    emma           = user->emma;           /* emission parameter */
620:   PetscScalar    wind           = user->wind;           /* wind speed */
621:   PetscScalar    dewtemp        = user->dewtemp;        /* dew point temperature (moisture in air) */
622:   PetscScalar    pressure1      = user->pressure1;      /* sea level pressure */
623:   PetscScalar    airtemp        = user->airtemp;        /* temperature of air near boundary layer inversion */
624:   PetscScalar    fract          = user->fract;          /* fraction of the sky covered by clouds */
625:   PetscScalar    Tc             = user->Tc;             /* temperature at base of lowest cloud layer */
626:   PetscScalar    lat            = user->lat;            /* latitude */
627:   PetscScalar    Cp             = 1005.7;               /* specific heat of air at constant pressure */
628:   PetscScalar    Rd             = 287.058;              /* gas constant for dry air */
629:   PetscScalar    diffconst      = 1000;                 /* diffusion coefficient */
630:   PetscScalar    f              = 2*0.0000727*sin(lat); /* coriolis force */
631:   PetscScalar    deep_grnd_temp = user->deep_grnd_temp; /* temp in lowest ground layer */
632:   PetscScalar    Ts,u,v,p,P;
633:   PetscScalar    u_abs,u_plus,u_minus,v_abs,v_plus,v_minus;

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

642:   DMGetLocalVector(da,&localT);
643:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
644:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

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


650:   /*
651:      Scatter ghost points to local vector,using the 2-step process
652:         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
653:      By placing code between these two statements, computations can be
654:      done while messages are in transition.
655:   */
656:   DMGlobalToLocalBegin(da,Xglobal,INSERT_VALUES,localT);
657:   DMGlobalToLocalEnd(da,Xglobal,INSERT_VALUES,localT);

659:   /* Get pointers to vector data */
660:   DMDAVecGetArray(da,localT,&X);
661:   DMDAVecGetArray(da,F,&Frhs);

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

666:   /* Compute function over the locally owned part of the grid */
667:   /* the interior points */
668:   xend=xs+xm; yend=ys+ym;
669:   for (j=ys; j<yend; j++) {
670:     for (i=xs; i<xend; i++) {
671:       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; */

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

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

687:       v_abs   = PetscAbsScalar(v);
688:       v_plus  = .5*(v + v_abs); /* v if v>0; 0 if v<0 */
689:       v_minus = .5*(v - v_abs); /* v if v <0; 0 if v>0 */

691:       /* Solve governing equations */
692:       P = p*Rd*Ts;

694:       /* du/dt -> time change of east-west component of the wind */
695:       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) */
696:                      - v_plus*(u - X[j-1][i].u)*dhy - v_minus*(X[j+1][i].u - u)*dhy       /* - v(du/dy) */
697:                      -(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)] */
698: /*                     -(1/p)*(X[j][i+1].P - X[j][i-1].P)*dhx */
699:                      + f*v;

701:       /* dv/dt -> time change of north-south component of the wind */
702:       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) */
703:                      - v_plus*(v - X[j-1][i].v)*dhy - v_minus*(X[j+1][i].v - v)*dhy       /* - v(dv/dy) */
704:                      -(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)] */
705: /*                     -(1/p)*(X[j+1][i].P - X[j-1][i].P)*dhy */
706:                      -f*u;

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

715:       /* dp/dt -> time change of */
716:       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) */
717:                      -v_plus*(p - X[j-1][i].p)*dhy - v_minus*(X[j+1][i].p - p)*dhy;    /* - v*(dp/dy) */

719:       Frhs[j][i].Ta = Ra/Cp;  /* dTa/dt time change of air temperature */
720:     }
721:   }

723:   /* Restore vectors */
724:   DMDAVecRestoreArray(da,localT,&X);
725:   DMDAVecRestoreArray(da,F,&Frhs);
726:   DMRestoreLocalVector(da,&localT);
727:   return(0);
728: }

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

742:   MPI_Comm_rank(PetscObjectComm((PetscObject)ts),&rank);
743:   VecNorm(T,NORM_INFINITY,&norm);

745:   if (step%user->interval == 0) {
746:     VecGetArray(T,&array);
747:     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]);
748:     VecRestoreArray(T,&array);
749:   }

751:   if (user->drawcontours) {
752:     VecView(T,viewer);
753:   }
754:   return(0);
755: }