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diffusion.c
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diffusion.c
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///////////////////////////////////////////////////////////////////////////////
///
/// \file diffusion.c
///
/// \brief Subroutines for solving the diffison equation
///
/// \author Mingang Jin, Qingyan Chen
/// Purdue University
/// Jin56@purdue.edu, YanChen@purdue.edu
/// Wangda Zuo
/// University of Miami
/// W.Zuo@miami.edu
///
/// \date 04/02/2014
///
/// This file provides functions that used for solving the diffusion equation
/// in FFD. By calling the function \c diffusion(), the coefficients of the
/// discretized equation can be specified through \c coef_diff(), and then the
/// equation solver will be applied to solve the equation.
///
///////////////////////////////////////////////////////////////////////////////
#include <stdio.h>
#include <stdlib.h>
#include "data_structure.h"
#include "diffusion.h"
#include "boundary.h"
#include "solver.h"
#include "utility.h"
#include "chen_zero_equ_model.h"
///////////////////////////////////////////////////////////////////////////////
///\brief Entrance of calculating diffusion equation
///
///\param para Pointer to FFD parameters
///\param var Pointer to FFD simulation variables
///\param var_type Type of variable
///\param psi Pointer to the variable at current time step
///\param psi0 Pointer to the variable at previous time step
///\param BINDEX Pointer to boundary index
///
///\return void No return needed
///////////////////////////////////////////////////////////////////////////////
void diffusion(PARA_DATA *para, REAL **var, int var_type,
REAL *psi, REAL *psi0, int **BINDEX) {
// Define the coefcients for euqations
coef_diff(para, var, psi, psi0, var_type, BINDEX);
// Solving the discretized equation
equ_solver(para, var, var_type, psi);
// Define the values of variables at B.C.
set_bnd(para, var, var_type, psi, BINDEX);
} // End of diffusion( )
///////////////////////////////////////////////////////////////////////////////
///\brief Specifying the coefficients for equation
///
///\param para Pointer to FFD parameters
///\param var Pointer to FFD simulation variables
///\param psi Pointer to the variable at current time step
///\param psi0 Pointer to the variable at previous time step
///\param var_type Type of variable
///\param BINDEX Pointer to boundary index
///
///\return void No return needed
///////////////////////////////////////////////////////////////////////////////
void coef_diff(PARA_DATA *para, REAL **var, REAL *psi, REAL *psi0,
int var_type, int **BINDEX) {
int i, j, k;
int imax = para->geom->imax, jmax = para->geom->jmax;
int kmax = para->geom->kmax;
int IMAX = imax+2, IJMAX = (imax+2)*(jmax+2);
REAL *u=var[VX],*v=var[VY],*w=var[VZ];
REAL *aw = var[AW], *ae = var[AE], *as = var[AS], *an = var[AN];
REAL *af = var[AF], *ab = var[AB], *ap = var[AP], *ap0 = var[AP0], *b = var[B];
REAL *x = var[X], *y = var[Y], *z = var[Z];
REAL *gx = var[GX], *gy = var[GY], *gz = var[GZ];
REAL *dist= var[DIST],*vt=var[VT];
REAL *Temp = var[TEMP];
REAL *d=var[DEN];
REAL dxe, dxw, dyn, dys, dzf, dzb, Dx, Dy, Dz;
REAL dt = para->mytime->dt, beta = para->prob->beta;
REAL Temp_opt = para->prob->Temp_opt, gravx = para->prob->gravx;
REAL gravy = para->prob->gravy, gravz = para->prob->gravz;
REAL kapa;
REAL *flagp = var[FLAGP],*flagu = var[FLAGU];
REAL *flagv = var[FLAGV],*flagw = var[FLAGW];
REAL Prt= para->prob->Prt;
REAL dtemp=0.0f;
REAL *s_plume=var[ER];
switch (var_type) {
// coefficients for velocity u
case VX:
//Specifying the value for viscosity.
kapa = para->prob->nu;
FOR_U_CELL
if(flagu[FIX(i,j,k)]>=0) continue;
dxe = gx[FIX(i+1,j ,k)] - gx[FIX(i ,j,k)];
dxw = gx[FIX(i ,j ,k)] - gx[FIX(i-1,j,k)];
dyn = y[FIX(i ,j+1,k)] - y[FIX(i ,j,k)];
dys=y[FIX(i,j,k)]-y[FIX(i,j-1,k)];
dzf=z[FIX(i,j,k+1)]-z[FIX(i,j,k)];
dzb=z[FIX(i,j,k)]-z[FIX(i,j,k-1)];
Dx=x[FIX(i+1,j,k)]-x[FIX(i,j,k)];
Dy=gy[FIX(i,j,k)]-gy[FIX(i,j-1,k)];
Dz=gz[FIX(i,j,k)]-gz[FIX(i,j,k-1)];
//zero equation model
if(para->prob->tur_model == CHEN) {
aw[FIX(i,j,k)]= (kapa+vt[FIX(i,j,k)])*Dy*Dz/dxw;
ae[FIX(i,j,k)]= (kapa+vt[FIX(i+1,j,k)])*Dy*Dz/dxe;
an[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i+1,j,k)]
+vt[FIX(i,j+1,k)]+vt[FIX(i+1,j+1,k)]))*Dx*Dz/dyn;
as[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i+1,j,k)]
+vt[FIX(i,j-1,k)]+vt[FIX(i+1,j-1,k)]))*Dx*Dz/dys;
af[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i+1,j,k)]
+vt[FIX(i,j,k+1)]+vt[FIX(i+1,j,k+1)]))*Dx*Dy/dzf;
ab[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i+1,j,k)]
+vt[FIX(i,j,k-1)]+vt[FIX(i+1,j,k-1)]))*Dx*Dy/dzb;
}
//laminar model
else {
aw[FIX(i,j,k)]= kapa*Dy*Dz/dxw;
ae[FIX(i,j,k)]= kapa*Dy*Dz/dxe;
an[FIX(i,j,k)]= kapa*Dx*Dz/dyn;
as[FIX(i,j,k)]= kapa*Dx*Dz/dys;
af[FIX(i,j,k)]= kapa*Dx*Dy/dzf;
ab[FIX(i,j,k)]= kapa*Dx*Dy/dzb;
}
ap0[FIX(i,j,k)]= Dx*Dy*Dz/dt;
b[FIX(i,j,k)]= psi0[FIX(i,j,k)]*ap0[FIX(i,j,k)];
//buoyancy forces && plume model correction
if(para->prob->gravdir==GRAVX || para->prob->gravdir==GRAVXN ) {
b[FIX(i,j,k)] -= beta*gravx *(0.5f*(Temp[FIX(i,j,k)]
+Temp[FIX(i+1,j,k)])-Temp_opt)*Dx*Dy*Dz;
if(para->prob->plume_mod==1)
b[FIX(i,j,k)] += s_plume[FIX(i,j,k)]/dt*Dx*Dy*Dz;//plume model
}
ap[FIX(i,j,k)] = ap0[FIX(i,j,k)] + ae[FIX(i,j,k)] + aw[FIX(i,j,k)]
+ an[FIX(i,j,k)] + as[FIX(i,j,k)] + af[FIX(i,j,k)]
+ ab[FIX(i,j,k)];
END_FOR
set_bnd(para, var, var_type, psi, BINDEX);
break;
// coefficients for velocity v
case VY:
kapa = para->prob->nu;
FOR_V_CELL
if(flagv[FIX(i,j,k)]>=0) continue;
dxe=x[FIX(i+1,j,k)]-x[FIX(i,j,k)];
dxw=x[FIX(i,j,k)]-x[FIX(i-1,j,k)];
dyn=gy[FIX(i,j+1,k)]-gy[FIX(i,j,k)];
dys=gy[FIX(i,j,k)]-gy[FIX(i,j-1,k)];
dzf=z[FIX(i,j,k+1)]-z[FIX(i,j,k)];
dzb=z[FIX(i,j,k)]-z[FIX(i,j,k-1)];
Dx=gx[FIX(i,j,k)]-gx[FIX(i-1,j,k)];
Dy=y[FIX(i,j+1,k)]-y[FIX(i,j,k)];
Dz=gz[FIX(i,j,k)]-gz[FIX(i,j,k-1)];
if(para->prob->tur_model == CHEN) {
aw[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j+1,k)]
+vt[FIX(i-1,j,k)]+vt[FIX(i-1,j+1,k)]))*Dy*Dz/dxw;
ae[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j+1,k)]
+vt[FIX(i+1,j,k)]+vt[FIX(i+1,j+1,k)]))*Dy*Dz/dxe;
an[FIX(i,j,k)]= (kapa+vt[FIX(i,j+1,k)])*Dx*Dz/dyn;
as[FIX(i,j,k)]= (kapa+vt[FIX(i,j,k)])*Dx*Dz/dys;
af[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j+1,k)]
+vt[FIX(i,j,k+1)]+vt[FIX(i,j+1,k+1)]))*Dx*Dy/dzf;
ab[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j+1,k)]
+vt[FIX(i,j,k-1)]+vt[FIX(i,j+1,k-1)]))*Dx*Dy/dzb;
}
else {
aw[FIX(i,j,k)]= kapa*Dy*Dz/dxw;
ae[FIX(i,j,k)]= kapa*Dy*Dz/dxe;
an[FIX(i,j,k)]= kapa*Dx*Dz/dyn;
as[FIX(i,j,k)]= kapa*Dx*Dz/dys;
af[FIX(i,j,k)]= kapa*Dx*Dy/dzf;
ab[FIX(i,j,k)]= kapa*Dx*Dy/dzb;
}
ap0[FIX(i,j,k)]= Dx*Dy*Dz/dt;
b[FIX(i,j,k)]= psi0[FIX(i,j,k)]*ap0[FIX(i,j,k)];
if(para->prob->gravdir==GRAVY || para->prob->gravdir==GRAVYN ) {
b[FIX(i,j,k)] -= beta*gravy*(0.5f*(Temp[FIX(i,j,k)]
+Temp[FIX(i,j+1,k)])-Temp_opt)*Dx*Dy*Dz;
if(para->prob->plume_mod==1)
b[FIX(i,j,k)] += s_plume[FIX(i,j,k)]/dt*Dx*Dy*Dz;//plume model
}
ap[FIX(i,j,k)] = ap0[FIX(i,j,k)] + ae[FIX(i,j,k)] + aw[FIX(i,j,k)]
+ an[FIX(i,j,k)] + as[FIX(i,j,k)] + af[FIX(i,j,k)]
+ ab[FIX(i,j,k)];
END_FOR
set_bnd(para, var, var_type, psi, BINDEX);
break;
// coefficients for velocity w
case VZ:
kapa = para->prob->nu;
FOR_W_CELL
if(flagw[FIX(i,j,k)]>=0) continue;
dxe=x[FIX(i+1,j,k)]-x[FIX(i,j,k)];
dxw=x[FIX(i,j,k)]-x[FIX(i-1,j,k)];
dyn=y[FIX(i,j+1,k)]-y[FIX(i,j,k)];
dys=y[FIX(i,j,k)]-y[FIX(i,j-1,k)];
dzf=gz[FIX(i,j,k+1)]-gz[FIX(i,j,k)];
dzb=gz[FIX(i,j,k)]-gz[FIX(i,j,k-1)];
Dx=gx[FIX(i,j,k)]-gx[FIX(i-1,j,k)];
Dy=gy[FIX(i,j,k)]-gy[FIX(i,j-1,k)];
Dz=z[FIX(i,j,k+1)]-z[FIX(i,j,k)];
if(para->prob->tur_model == CHEN) {
aw[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j,k+1)]
+vt[FIX(i-1,j,k)]+vt[FIX(i-1,j,k+1)]))*Dy*Dz/dxw;
ae[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j,k+1)]
+vt[FIX(i+1,j,k)]+vt[FIX(i+1,j,k+1)]))*Dy*Dz/dxe;
an[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j,k+1)]
+vt[FIX(i,j+1,k)]+vt[FIX(i,j+1,k+1)]))*Dx*Dz/dyn;
as[FIX(i,j,k)]= (kapa+0.25f*(vt[FIX(i,j,k)]+vt[FIX(i,j,k+1)]
+vt[FIX(i,j-1,k)]+vt[FIX(i,j-1,k+1)]))*Dx*Dz/dys;
af[FIX(i,j,k)]= (kapa+vt[FIX(i,j,k+1)])*Dx*Dy/dzf;
ab[FIX(i,j,k)]= (kapa+vt[FIX(i,j,k)])*Dx*Dy/dzb;
}
else {
aw[FIX(i,j,k)]= kapa*Dy*Dz/dxw;
ae[FIX(i,j,k)]= kapa*Dy*Dz/dxe;
an[FIX(i,j,k)]= kapa*Dx*Dz/dyn;
as[FIX(i,j,k)]= kapa*Dx*Dz/dys;
af[FIX(i,j,k)]= kapa*Dx*Dy/dzf;
ab[FIX(i,j,k)]= kapa*Dx*Dy/dzb;
}
ap0[FIX(i,j,k)]= Dx*Dy*Dz/dt;
b[FIX(i,j,k)]= psi0[FIX(i,j,k)]*ap0[FIX(i,j,k)];
if(para->prob->gravdir==GRAVZ || para->prob->gravdir==GRAVZN ) {
b[FIX(i,j,k)] -= beta*gravz*(0.5f*(Temp[FIX(i,j,k)]
+Temp[FIX(i,j,k+1)])-Temp_opt)*Dx*Dy*Dz;
if(para->prob->plume_mod==1)
b[FIX(i,j,k)] += s_plume[FIX(i,j,k)]/dt*Dx*Dy*Dz;//plume model
}
ap[FIX(i,j,k)] = ap0[FIX(i,j,k)] + ae[FIX(i,j,k)] + aw[FIX(i,j,k)]
+ an[FIX(i,j,k)] + as[FIX(i,j,k)] + af[FIX(i,j,k)]
+ ab[FIX(i,j,k)];
END_FOR
set_bnd(para, var, var_type, psi,BINDEX);
break;
//Coefficients for temperature
case TEMP:
kapa = para->prob->nu;
FOR_EACH_CELL
if(flagp[FIX(i,j,k)]>0) continue;
dxe=x[FIX(i+1,j,k)]-x[FIX(i,j,k)];
dxw=x[FIX(i,j,k)]-x[FIX(i-1,j,k)];
dyn=y[FIX(i,j+1,k)]-y[FIX(i,j,k)];
dys=y[FIX(i,j,k)]-y[FIX(i,j-1,k)];
dzf=z[FIX(i,j,k+1)]-z[FIX(i,j,k)];
dzb=z[FIX(i,j,k)]-z[FIX(i,j,k-1)];
Dx=gx[FIX(i,j,k)]-gx[FIX(i-1,j,k)];
Dy=gy[FIX(i,j,k)]-gy[FIX(i,j-1,k)];
Dz=gz[FIX(i,j,k)]-gz[FIX(i,j,k-1)];
if(para->prob->tur_model == CHEN) {
aw[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i-1,j,k)]))/Prt*Dy*Dz/dxw;
ae[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i+1,j,k)]))/Prt*Dy*Dz/dxe;
an[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j+1,k)]))/Prt*Dx*Dz/dyn;
as[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j-1,k)]))/Prt*Dx*Dz/dys;
af[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j,k+1)]))/Prt*Dx*Dy/dzf;
ab[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j,k-1)]))/Prt*Dx*Dy/dzb;
}
else {
aw[FIX(i,j,k)]= kapa/Prt*Dy*Dz/dxw;
ae[FIX(i,j,k)]= kapa/Prt*Dy*Dz/dxe;
an[FIX(i,j,k)]= kapa/Prt*Dx*Dz/dyn;
as[FIX(i,j,k)]= kapa/Prt*Dx*Dz/dys;
af[FIX(i,j,k)]= kapa/Prt*Dx*Dy/dzf;
ab[FIX(i,j,k)]= kapa/Prt*Dx*Dy/dzb;
}
if(para->prob->plume_mod==1){
if(BINDEX[20][FIX(i-1,j,k)]==1) aw[FIX(i,j,k)]= 0;
if(BINDEX[20][FIX(i+1,j,k)]==1) ae[FIX(i,j,k)]= 0;
if(BINDEX[20][FIX(i,j,k+1)]==1) af[FIX(i,j,k)]= 0;
if(BINDEX[20][FIX(i,j,k-1)]==1) ab[FIX(i,j,k)]= 0;
if(BINDEX[20][FIX(i,j+1,k)]==1) an[FIX(i,j,k)]= 0;
if(BINDEX[20][FIX(i,j-1,k)]==1) as[FIX(i,j,k)]= 0;
}
ap0[FIX(i,j,k)]= Dx*Dy*Dz/dt;
b[FIX(i,j,k)]= psi0[FIX(i,j,k)]*ap0[FIX(i,j,k)];
END_FOR
set_bnd(para, var, var_type, psi,BINDEX);
FOR_EACH_CELL
ap[FIX(i,j,k)] = ap0[FIX(i,j,k)] + ae[FIX(i,j,k)] + aw[FIX(i,j,k)]
+ an[FIX(i,j,k)] + as[FIX(i,j,k)] + af[FIX(i,j,k)]
+ ab[FIX(i,j,k)];
END_FOR
break;
//Coefficients for species
case DEN:
kapa = para->prob->nu;
FOR_EACH_CELL
if(flagp[FIX(i,j,k)]>0) continue;
dxe=x[FIX(i+1,j,k)]-x[FIX(i,j,k)];
dxw=x[FIX(i,j,k)]-x[FIX(i-1,j,k)];
dyn=y[FIX(i,j+1,k)]-y[FIX(i,j,k)];
dys=y[FIX(i,j,k)]-y[FIX(i,j-1,k)];
dzf=z[FIX(i,j,k+1)]-z[FIX(i,j,k)];
dzb=z[FIX(i,j,k)]-z[FIX(i,j,k-1)];
Dx=gx[FIX(i,j,k)]-gx[FIX(i-1,j,k)];
Dy=gy[FIX(i,j,k)]-gy[FIX(i,j-1,k)];
Dz=gz[FIX(i,j,k)]-gz[FIX(i,j,k-1)];
if(para->prob->tur_model == CHEN) {
aw[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i-1,j,k)]))/Prt*Dy*Dz/dxw;
ae[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i+1,j,k)]))/Prt*Dy*Dz/dxe;
an[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j+1,k)]))/Prt*Dx*Dz/dyn;
as[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j-1,k)]))/Prt*Dx*Dz/dys;
af[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j,k+1)]))/Prt*Dx*Dy/dzf;
ab[FIX(i,j,k)]= (kapa+0.5f*(vt[FIX(i,j,k)]
+vt[FIX(i,j,k-1)]))/Prt*Dx*Dy/dzb;
}
else {
aw[FIX(i,j,k)]= kapa/Prt*Dy*Dz/dxw;
ae[FIX(i,j,k)]= kapa/Prt*Dy*Dz/dxe;
an[FIX(i,j,k)]= kapa/Prt*Dx*Dz/dyn;
as[FIX(i,j,k)]= kapa/Prt*Dx*Dz/dys;
af[FIX(i,j,k)]= kapa/Prt*Dx*Dy/dzf;
ab[FIX(i,j,k)]= kapa/Prt*Dx*Dy/dzb;
}
ap0[FIX(i,j,k)]= Dx*Dy*Dz/dt;
b[FIX(i,j,k)]= psi0[FIX(i,j,k)]*ap0[FIX(i,j,k)];
END_FOR
set_bnd(para, var, var_type, psi,BINDEX);
FOR_EACH_CELL
ap[FIX(i,j,k)] = ap0[FIX(i,j,k)] + ae[FIX(i,j,k)] + aw[FIX(i,j,k)]
+ an[FIX(i,j,k)] + as[FIX(i,j,k)] + af[FIX(i,j,k)]
+ ab[FIX(i,j,k)];
END_FOR
break;
}
}// End of coef_diff( )