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: }