Actual source code: ex5.c
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_view
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 <petscdm.h>
70: #include <petscdmda.h>
72: /* stefan-boltzmann constant */
73: #define SIG 0.000000056703
74: /* absorption-emission constant for surface */
75: #define EMMSFC 1
76: /* amount of time (seconds) that passes before new flux is calculated */
77: #define TIMESTEP 1
79: /* variables of interest to be solved at each grid point */
80: typedef struct {
81: PetscScalar Ts,Ta; /* surface and air temperature */
82: PetscScalar u,v; /* wind speed */
83: PetscScalar p; /* density */
84: } Field;
86: /* User defined variables. Used in solving for variables of interest */
87: typedef struct {
88: DM da; /* grid */
89: PetscScalar csoil; /* heat constant for layer */
90: PetscScalar dzlay; /* thickness of top soil layer */
91: PetscScalar emma; /* emission parameter */
92: PetscScalar wind; /* wind speed */
93: PetscScalar dewtemp; /* dew point temperature (moisture in air) */
94: PetscScalar pressure1; /* sea level pressure */
95: PetscScalar airtemp; /* temperature of air near boundary layer inversion */
96: PetscScalar Ts; /* temperature at the surface */
97: PetscScalar fract; /* fraction of sky covered by clouds */
98: PetscScalar Tc; /* temperature at base of lowest cloud layer */
99: PetscScalar lat; /* Latitude in degrees */
100: PetscScalar init; /* initialization scenario */
101: PetscScalar deep_grnd_temp; /* temperature of ground under top soil surface layer */
102: } AppCtx;
104: /* Struct for visualization */
105: typedef struct {
106: PetscBool drawcontours; /* flag - 1 indicates drawing contours */
107: PetscViewer drawviewer;
108: PetscInt interval;
109: } 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 PetscErrorCode 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 */
146: int main(int argc,char **argv)
147: {
148: PetscInt time; /* amount of loops */
149: struct in put;
150: PetscScalar rh; /* relative humidity */
151: PetscScalar x; /* memory varialbe for relative humidity calculation */
152: PetscScalar deep_grnd_temp; /* temperature of ground under top soil surface layer */
153: PetscScalar emma; /* absorption-emission constant for air */
154: PetscScalar pressure1 = 101300; /* surface pressure */
155: PetscScalar mixratio; /* mixing ratio */
156: PetscScalar airtemp; /* temperature of air near boundary layer inversion */
157: PetscScalar dewtemp; /* dew point temperature */
158: PetscScalar sfctemp; /* temperature at surface */
159: PetscScalar pwat; /* total column precipitable water */
160: PetscScalar cloudTemp; /* temperature at base of cloud */
161: AppCtx user; /* user-defined work context */
162: MonitorCtx usermonitor; /* user-defined monitor context */
163: TS ts;
164: SNES snes;
165: DM da;
166: Vec T,rhs; /* solution vector */
167: Mat J; /* Jacobian matrix */
168: PetscReal ftime,dt;
169: PetscInt steps,dof = 5;
170: PetscBool use_coloring = PETSC_TRUE;
171: MatFDColoring matfdcoloring = 0;
172: PetscBool monitor_off = PETSC_FALSE;
174: PetscInitialize(&argc,&argv,(char*)0,help);
176: /* Inputs */
177: readinput(&put);
179: sfctemp = put.Ts;
180: dewtemp = put.Td;
181: cloudTemp = put.Tc;
182: airtemp = put.Ta;
183: pwat = put.pwt;
185: PetscPrintf(PETSC_COMM_WORLD,"Initial Temperature = %g\n",(double)sfctemp); /* input surface temperature */
187: deep_grnd_temp = sfctemp - 10; /* set underlying ground layer temperature */
188: emma = emission(pwat); /* accounts for radiative effects of water vapor */
190: /* Converts from Fahrenheit to Celsuis */
191: sfctemp = fahr_to_cel(sfctemp);
192: airtemp = fahr_to_cel(airtemp);
193: dewtemp = fahr_to_cel(dewtemp);
194: cloudTemp = fahr_to_cel(cloudTemp);
195: deep_grnd_temp = fahr_to_cel(deep_grnd_temp);
197: /* Converts from Celsius to Kelvin */
198: sfctemp += 273;
199: airtemp += 273;
200: dewtemp += 273;
201: cloudTemp += 273;
202: deep_grnd_temp += 273;
204: /* Calculates initial relative humidity */
205: x = calcmixingr(dewtemp,pressure1);
206: mixratio = calcmixingr(sfctemp,pressure1);
207: rh = (x/mixratio)*100;
209: PetscPrintf(PETSC_COMM_WORLD,"Initial RH = %.1f percent\n\n",(double)rh); /* prints initial relative humidity */
211: time = 3600*put.time; /* sets amount of timesteps to run model */
213: /* Configure PETSc TS solver */
214: /*------------------------------------------*/
216: /* Create grid */
217: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,20,20,PETSC_DECIDE,PETSC_DECIDE,dof,1,NULL,NULL,&da);
218: DMSetFromOptions(da);
219: DMSetUp(da);
220: DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
222: /* Define output window for each variable of interest */
223: DMDASetFieldName(da,0,"Ts");
224: DMDASetFieldName(da,1,"Ta");
225: DMDASetFieldName(da,2,"u");
226: DMDASetFieldName(da,3,"v");
227: DMDASetFieldName(da,4,"p");
229: /* set values for appctx */
230: user.da = da;
231: user.Ts = sfctemp;
232: user.fract = put.fr; /* fraction of sky covered by clouds */
233: user.dewtemp = dewtemp; /* dew point temperature (mositure in air) */
234: user.csoil = 2000000; /* heat constant for layer */
235: user.dzlay = 0.08; /* thickness of top soil layer */
236: user.emma = emma; /* emission parameter */
237: user.wind = put.wnd; /* wind spped */
238: user.pressure1 = pressure1; /* sea level pressure */
239: user.airtemp = airtemp; /* temperature of air near boundar layer inversion */
240: user.Tc = cloudTemp; /* temperature at base of lowest cloud layer */
241: user.init = put.init; /* user chosen initiation scenario */
242: user.lat = 70*0.0174532; /* converts latitude degrees to latitude in radians */
243: user.deep_grnd_temp = deep_grnd_temp; /* temp in lowest ground layer */
245: /* set values for MonitorCtx */
246: usermonitor.drawcontours = PETSC_FALSE;
247: PetscOptionsHasName(NULL,NULL,"-drawcontours",&usermonitor.drawcontours);
248: if (usermonitor.drawcontours) {
249: PetscReal bounds[] = {1000.0,-1000., -1000.,-1000., 1000.,-1000., 1000.,-1000., 1000,-1000, 100700,100800};
250: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer);
251: PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds);
252: }
253: usermonitor.interval = 1;
254: PetscOptionsGetInt(NULL,NULL,"-monitor_interval",&usermonitor.interval,NULL);
256: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
257: Extract global vectors from DA;
258: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
259: DMCreateGlobalVector(da,&T);
260: VecDuplicate(T,&rhs); /* r: vector to put the computed right hand side */
262: TSCreate(PETSC_COMM_WORLD,&ts);
263: TSSetProblemType(ts,TS_NONLINEAR);
264: TSSetType(ts,TSBEULER);
265: TSSetRHSFunction(ts,rhs,RhsFunc,&user);
267: /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
268: DMSetMatType(da,MATAIJ);
269: DMCreateMatrix(da,&J);
270: TSGetSNES(ts,&snes);
271: if (use_coloring) {
272: ISColoring iscoloring;
273: DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring);
274: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
275: MatFDColoringSetFromOptions(matfdcoloring);
276: MatFDColoringSetUp(J,iscoloring,matfdcoloring);
277: ISColoringDestroy(&iscoloring);
278: MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);
279: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
280: } else {
281: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);
282: }
284: /* Define what to print for ts_monitor option */
285: PetscOptionsHasName(NULL,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: PetscPrintf(PETSC_COMM_WORLD,"time %D, ftime %g hour, TIMESTEP %g\n",time,(double)(ftime/3600),(double)dt);
294: TSSetTimeStep(ts,dt);
295: TSSetMaxSteps(ts,time);
296: TSSetMaxTime(ts,ftime);
297: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
298: TSSetSolution(ts,T);
299: TSSetDM(ts,da);
301: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302: Set runtime options
303: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
304: TSSetFromOptions(ts);
306: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307: Solve nonlinear system
308: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
309: TSSolve(ts,T);
310: TSGetSolveTime(ts,&ftime);
311: TSGetStepNumber(ts,&steps);
312: PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %D steps\n",(double)(ftime/3600),steps);
314: if (matfdcoloring) MatFDColoringDestroy(&matfdcoloring);
315: if (usermonitor.drawcontours) {
316: PetscViewerDestroy(&usermonitor.drawviewer);
317: }
318: MatDestroy(&J);
319: VecDestroy(&T);
320: VecDestroy(&rhs);
321: TSDestroy(&ts);
322: DMDestroy(&da);
324: PetscFinalize();
325: return 0;
326: }
327: /*****************************end main program********************************/
328: /*****************************************************************************/
329: /*****************************************************************************/
330: /*****************************************************************************/
331: PetscErrorCode calcfluxs(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar fract, PetscScalar cloudTemp, PetscScalar *flux)
332: {
334: *flux = SIG*((EMMSFC*emma*PetscPowScalarInt(airtemp,4)) + (EMMSFC*fract*(1 - emma)*PetscPowScalarInt(cloudTemp,4)) - (EMMSFC*PetscPowScalarInt(sfctemp,4))); /* calculates flux using Stefan-Boltzmann relation */
335: return 0;
336: }
338: PetscErrorCode calcfluxa(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar *flux) /* this function is not currently called upon */
339: {
340: PetscScalar emm = 0.001;
343: *flux = SIG*(-emm*(PetscPowScalarInt(airtemp,4))); /* calculates flux usinge Stefan-Boltzmann relation */
344: return 0;
345: }
346: PetscErrorCode sensibleflux(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar wind, PetscScalar *sheat)
347: {
348: PetscScalar density = 1; /* air density */
349: PetscScalar Cp = 1005; /* heat capicity for dry air */
350: PetscScalar wndmix; /* temperature change from wind mixing: wind*Ch */
353: wndmix = 0.0025 + 0.0042*wind; /* regression equation valid for neutral and stable BL */
354: *sheat = density*Cp*wndmix*(airtemp - sfctemp); /* calculates sensible heat flux */
355: return 0;
356: }
358: PetscErrorCode latentflux(PetscScalar sfctemp, PetscScalar dewtemp, PetscScalar wind, PetscScalar pressure1, PetscScalar *latentheat)
359: {
360: PetscScalar density = 1; /* density of dry air */
361: PetscScalar q; /* actual specific humitity */
362: PetscScalar qs; /* saturation specific humidity */
363: PetscScalar wndmix; /* temperature change from wind mixing: wind*Ch */
364: PetscScalar beta = .4; /* moisture availability */
365: PetscScalar mr; /* mixing ratio */
366: PetscScalar lhcnst; /* latent heat of vaporization constant = 2501000 J/kg at 0c */
367: /* latent heat of saturation const = 2834000 J/kg */
368: /* latent heat of fusion const = 333700 J/kg */
371: wind = mph2mpers(wind); /* converts wind from mph to meters per second */
372: wndmix = 0.0025 + 0.0042*wind; /* regression equation valid for neutral BL */
373: lhcnst = Lconst(sfctemp); /* calculates latent heat of evaporation */
374: mr = calcmixingr(sfctemp,pressure1); /* calculates saturation mixing ratio */
375: qs = calc_q(mr); /* calculates saturation specific humidty */
376: mr = calcmixingr(dewtemp,pressure1); /* calculates mixing ratio */
377: q = calc_q(mr); /* calculates specific humidty */
379: *latentheat = density*wndmix*beta*lhcnst*(q - qs); /* calculates latent heat flux */
380: return 0;
381: }
383: PetscErrorCode potential_temperature(PetscScalar temp, PetscScalar pressure1, PetscScalar pressure2, PetscScalar sfctemp, PetscScalar *pottemp)
384: {
385: PetscScalar kdry; /* poisson constant for dry atmosphere */
386: PetscScalar pavg; /* average atmospheric pressure */
387: /* PetscScalar mixratio; mixing ratio */
388: /* PetscScalar kmoist; poisson constant for moist atmosphere */
391: /* mixratio = calcmixingr(sfctemp,pressure1); */
393: /* initialize poisson constant */
394: kdry = 0.2854;
395: /* kmoist = 0.2854*(1 - 0.24*mixratio); */
397: pavg = ((0.7*pressure1)+pressure2)/2; /* calculates simple average press */
398: *pottemp = temp*(PetscPowScalar((pressure1/pavg),kdry)); /* calculates potential temperature */
399: return 0;
400: }
401: extern PetscScalar calcmixingr(PetscScalar dtemp, PetscScalar pressure1)
402: {
403: PetscScalar e; /* vapor pressure */
404: PetscScalar mixratio; /* mixing ratio */
406: dtemp = dtemp - 273; /* converts from Kelvin to Celsuis */
407: e = 6.11*(PetscPowScalar(10,((7.5*dtemp)/(237.7+dtemp)))); /* converts from dew point temp to vapor pressure */
408: e = e*100; /* converts from hPa to Pa */
409: mixratio = (0.622*e)/(pressure1 - e); /* computes mixing ratio */
410: mixratio = mixratio*1; /* convert to g/Kg */
412: return mixratio;
413: }
414: extern PetscScalar calc_q(PetscScalar rv)
415: {
416: PetscScalar specific_humidity; /* define specific humidity variable */
417: specific_humidity = rv/(1 + rv); /* calculates specific humidity */
418: return specific_humidity;
419: }
421: PetscErrorCode calc_gflux(PetscScalar sfctemp, PetscScalar deep_grnd_temp, PetscScalar* Gflux)
422: {
423: PetscScalar k; /* thermal conductivity parameter */
424: PetscScalar n = 0.38; /* value of soil porosity */
425: PetscScalar dz = 1; /* depth of layer between soil surface and deep soil layer */
426: PetscScalar unit_soil_weight = 2700; /* unit soil weight in kg/m^3 */
429: k = ((0.135*(1-n)*unit_soil_weight) + 64.7)/(unit_soil_weight - (0.947*(1-n)*unit_soil_weight)); /* dry soil conductivity */
430: *Gflux = (k*(deep_grnd_temp - sfctemp)/dz); /* calculates flux from deep ground layer */
431: return 0;
432: }
433: extern PetscScalar emission(PetscScalar pwat)
434: {
435: PetscScalar emma;
437: emma = 0.725 + 0.17*PetscLog10Real(PetscRealPart(pwat));
439: return emma;
440: }
441: extern PetscScalar cloud(PetscScalar fract)
442: {
443: PetscScalar emma = 0;
445: /* modifies radiative balance depending on cloud cover */
446: if (fract >= 0.9) emma = 1;
447: else if (0.9 > fract && fract >= 0.8) emma = 0.9;
448: else if (0.8 > fract && fract >= 0.7) emma = 0.85;
449: else if (0.7 > fract && fract >= 0.6) emma = 0.75;
450: else if (0.6 > fract && fract >= 0.5) emma = 0.65;
451: else if (0.4 > fract && fract >= 0.3) emma = emma*1.086956;
452: return emma;
453: }
454: extern PetscScalar Lconst(PetscScalar sfctemp)
455: {
456: PetscScalar Lheat;
457: sfctemp -=273; /* converts from kelvin to celsius */
458: Lheat = 4186.8*(597.31 - 0.5625*sfctemp); /* calculates latent heat constant */
459: return Lheat;
460: }
461: extern PetscScalar mph2mpers(PetscScalar wind)
462: {
463: wind = ((wind*1.6*1000)/3600); /* converts wind from mph to meters per second */
464: return wind;
465: }
466: extern PetscScalar fahr_to_cel(PetscScalar temp)
467: {
468: temp = (5*(temp-32))/9; /* converts from farhrenheit to celsuis */
469: return temp;
470: }
471: extern PetscScalar cel_to_fahr(PetscScalar temp)
472: {
473: temp = ((temp*9)/5) + 32; /* converts from celsuis to farhrenheit */
474: return temp;
475: }
476: PetscErrorCode readinput(struct in *put)
477: {
478: int i;
479: char x;
480: FILE *ifp;
481: double tmp;
483: ifp = fopen("ex5_control.txt", "r");
487: put->Ts = tmp;
491: put->Td = tmp;
495: put->Ta = tmp;
499: put->Tc = tmp;
503: put->fr = tmp;
507: put->wnd = tmp;
511: put->pwt = tmp;
515: put->wndDir = tmp;
519: put->time = tmp;
523: put->init = tmp;
524: return 0;
525: }
527: /* ------------------------------------------------------------------- */
528: PetscErrorCode FormInitialSolution(DM da,Vec Xglobal,void *ctx)
529: {
531: AppCtx *user = (AppCtx*)ctx; /* user-defined application context */
532: PetscInt i,j,xs,ys,xm,ym,Mx,My;
533: Field **X;
536: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
537: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
539: /* Get pointers to vector data */
540: DMDAVecGetArray(da,Xglobal,&X);
542: /* Get local grid boundaries */
543: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
545: /* Compute function over the locally owned part of the grid */
547: if (user->init == 1) {
548: for (j=ys; j<ys+ym; j++) {
549: for (i=xs; i<xs+xm; i++) {
550: X[j][i].Ts = user->Ts - i*0.0001;
551: X[j][i].Ta = X[j][i].Ts - 5;
552: X[j][i].u = 0;
553: X[j][i].v = 0;
554: X[j][i].p = 1.25;
555: if ((j == 5 || j == 6) && (i == 4 || i == 5)) X[j][i].p += 0.00001;
556: if ((j == 5 || j == 6) && (i == 12 || i == 13)) X[j][i].p += 0.00001;
557: }
558: }
559: } else {
560: for (j=ys; j<ys+ym; j++) {
561: for (i=xs; i<xs+xm; i++) {
562: X[j][i].Ts = user->Ts;
563: X[j][i].Ta = X[j][i].Ts - 5;
564: X[j][i].u = 0;
565: X[j][i].v = 0;
566: X[j][i].p = 1.25;
567: }
568: }
569: }
571: /* Restore vectors */
572: DMDAVecRestoreArray(da,Xglobal,&X);
573: return 0;
574: }
576: /*
577: RhsFunc - Evaluates nonlinear function F(u).
579: Input Parameters:
580: . ts - the TS context
581: . t - current time
582: . Xglobal - input vector
583: . F - output vector
584: . ptr - optional user-defined context, as set by SNESSetFunction()
586: Output Parameter:
587: . F - rhs function vector
588: */
589: PetscErrorCode RhsFunc(TS ts,PetscReal t,Vec Xglobal,Vec F,void *ctx)
590: {
591: AppCtx *user = (AppCtx*)ctx; /* user-defined application context */
592: DM da = user->da;
593: PetscInt i,j,Mx,My,xs,ys,xm,ym;
594: PetscReal dhx,dhy;
595: Vec localT;
596: Field **X,**Frhs; /* structures that contain variables of interest and left hand side of governing equations respectively */
597: PetscScalar csoil = user->csoil; /* heat constant for layer */
598: PetscScalar dzlay = user->dzlay; /* thickness of top soil layer */
599: PetscScalar emma = user->emma; /* emission parameter */
600: PetscScalar wind = user->wind; /* wind speed */
601: PetscScalar dewtemp = user->dewtemp; /* dew point temperature (moisture in air) */
602: PetscScalar pressure1 = user->pressure1; /* sea level pressure */
603: PetscScalar airtemp = user->airtemp; /* temperature of air near boundary layer inversion */
604: PetscScalar fract = user->fract; /* fraction of the sky covered by clouds */
605: PetscScalar Tc = user->Tc; /* temperature at base of lowest cloud layer */
606: PetscScalar lat = user->lat; /* latitude */
607: PetscScalar Cp = 1005.7; /* specific heat of air at constant pressure */
608: PetscScalar Rd = 287.058; /* gas constant for dry air */
609: PetscScalar diffconst = 1000; /* diffusion coefficient */
610: PetscScalar f = 2*0.0000727*PetscSinScalar(lat); /* coriolis force */
611: PetscScalar deep_grnd_temp = user->deep_grnd_temp; /* temp in lowest ground layer */
612: PetscScalar Ts,u,v,p;
613: PetscScalar u_abs,u_plus,u_minus,v_abs,v_plus,v_minus;
615: PetscScalar sfctemp1,fsfc1,Ra;
616: PetscScalar sheat; /* sensible heat flux */
617: PetscScalar latentheat; /* latent heat flux */
618: PetscScalar groundflux; /* flux from conduction of deep ground layer in contact with top soil */
619: PetscInt xend,yend;
622: DMGetLocalVector(da,&localT);
623: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
625: dhx = (PetscReal)(Mx-1)/(5000*(Mx-1)); /* dhx = 1/dx; assume 2D space domain: [0.0, 1.e5] x [0.0, 1.e5] */
626: dhy = (PetscReal)(My-1)/(5000*(Mx-1)); /* dhy = 1/dy; */
628: /*
629: Scatter ghost points to local vector,using the 2-step process
630: DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
631: By placing code between these two statements, computations can be
632: done while messages are in transition.
633: */
634: DMGlobalToLocalBegin(da,Xglobal,INSERT_VALUES,localT);
635: DMGlobalToLocalEnd(da,Xglobal,INSERT_VALUES,localT);
637: /* Get pointers to vector data */
638: DMDAVecGetArrayRead(da,localT,&X);
639: DMDAVecGetArray(da,F,&Frhs);
641: /* Get local grid boundaries */
642: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
644: /* Compute function over the locally owned part of the grid */
645: /* the interior points */
646: xend=xs+xm; yend=ys+ym;
647: for (j=ys; j<yend; j++) {
648: for (i=xs; i<xend; i++) {
649: 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; */
651: sfctemp1 = (double)Ts;
652: calcfluxs(sfctemp1,airtemp,emma,fract,Tc,&fsfc1); /* calculates surface net radiative flux */
653: sensibleflux(sfctemp1,airtemp,wind,&sheat); /* calculate sensible heat flux */
654: latentflux(sfctemp1,dewtemp,wind,pressure1,&latentheat); /* calculates latent heat flux */
655: calc_gflux(sfctemp1,deep_grnd_temp,&groundflux); /* calculates flux from earth below surface soil layer by conduction */
656: calcfluxa(sfctemp1,airtemp,emma,&Ra); /* Calculates the change in downward radiative flux */
657: fsfc1 = fsfc1 + latentheat + sheat + groundflux; /* adds radiative, sensible heat, latent heat, and ground heat flux yielding net flux */
659: /* convective coefficients for upwinding */
660: u_abs = PetscAbsScalar(u);
661: u_plus = .5*(u + u_abs); /* u if u>0; 0 if u<0 */
662: u_minus = .5*(u - u_abs); /* u if u <0; 0 if u>0 */
664: v_abs = PetscAbsScalar(v);
665: v_plus = .5*(v + v_abs); /* v if v>0; 0 if v<0 */
666: v_minus = .5*(v - v_abs); /* v if v <0; 0 if v>0 */
668: /* Solve governing equations */
669: /* P = p*Rd*Ts; */
671: /* du/dt -> time change of east-west component of the wind */
672: 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) */
673: - v_plus*(u - X[j-1][i].u)*dhy - v_minus*(X[j+1][i].u - u)*dhy /* - v(du/dy) */
674: -(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)] */
675: /* -(1/p)*(X[j][i+1].P - X[j][i-1].P)*dhx */
676: + f*v;
678: /* dv/dt -> time change of north-south component of the wind */
679: 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) */
680: - v_plus*(v - X[j-1][i].v)*dhy - v_minus*(X[j+1][i].v - v)*dhy /* - v(dv/dy) */
681: -(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)] */
682: /* -(1/p)*(X[j+1][i].P - X[j-1][i].P)*dhy */
683: -f*u;
685: /* dT/dt -> time change of temperature */
686: Frhs[j][i].Ts = (fsfc1/(csoil*dzlay)) /* Fnet/(Cp*dz) diabatic change in T */
687: -u_plus*(Ts - X[j][i-1].Ts)*dhx - u_minus*(X[j][i+1].Ts - Ts)*dhx /* - u*(dTs/dx) advection x */
688: -v_plus*(Ts - X[j-1][i].Ts)*dhy - v_minus*(X[j+1][i].Ts - Ts)*dhy /* - v*(dTs/dy) advection y */
689: + diffconst*((X[j][i+1].Ts - 2*Ts + X[j][i-1].Ts)*dhx*dhx /* + D(Ts_xx + Ts_yy) diffusion */
690: + (X[j+1][i].Ts - 2*Ts + X[j-1][i].Ts)*dhy*dhy);
692: /* dp/dt -> time change of */
693: 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) */
694: -v_plus*(p - X[j-1][i].p)*dhy - v_minus*(X[j+1][i].p - p)*dhy; /* - v*(dp/dy) */
696: Frhs[j][i].Ta = Ra/Cp; /* dTa/dt time change of air temperature */
697: }
698: }
700: /* Restore vectors */
701: DMDAVecRestoreArrayRead(da,localT,&X);
702: DMDAVecRestoreArray(da,F,&Frhs);
703: DMRestoreLocalVector(da,&localT);
704: return 0;
705: }
707: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec T,void *ctx)
708: {
709: const PetscScalar *array;
710: MonitorCtx *user = (MonitorCtx*)ctx;
711: PetscViewer viewer = user->drawviewer;
712: PetscReal norm;
715: VecNorm(T,NORM_INFINITY,&norm);
717: if (step%user->interval == 0) {
718: VecGetArrayRead(T,&array);
719: PetscPrintf(PETSC_COMM_WORLD,"step %D, time %8.1f, %6.4f, %6.4f, %6.4f, %6.4f, %6.4f, %6.4f\n",step,(double)time,(double)(((array[0]-273)*9)/5 + 32),(double)(((array[1]-273)*9)/5 + 32),(double)array[2],(double)array[3],(double)array[4],(double)array[5]);
720: VecRestoreArrayRead(T,&array);
721: }
723: if (user->drawcontours) {
724: VecView(T,viewer);
725: }
726: return 0;
727: }
729: /*TEST
731: build:
732: requires: !complex !single
734: test:
735: args: -ts_max_steps 130 -monitor_interval 60
736: output_file: output/ex5.out
737: requires: !complex !single
738: localrunfiles: ex5_control.txt
740: test:
741: suffix: 2
742: nsize: 4
743: args: -ts_max_steps 130 -monitor_interval 60
744: output_file: output/ex5.out
745: localrunfiles: ex5_control.txt
746: requires: !complex !single
748: TEST*/