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diffusion.c
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diffusion.c
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///////////////////////////////////////////////////////////////////////////////
///
/// \file diffusion.c
///
/// \brief Calculate the diffusion equation
///
/// \author Mingang Jin, Qingyan Chen
/// Purdue University
/// Jin55@purdue.edu, YanChen@purdue.edu
/// Wangda Zuo
/// University of Miami
/// W.Zuo@miami.edu
///
/// \date 8/3/2013
///
/// This file provides functions that are used for calculating the diffusion
/// equations.
///
///////////////////////////////////////////////////////////////////////////////
#include "diffusion.h"
///////////////////////////////////////////////////////////////////////////////
/// 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 index Index of trace substance or species
///\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 0 if no error occurred
///////////////////////////////////////////////////////////////////////////////
int diffusion(PARA_DATA *para, REAL **var, int var_type, int index,
REAL *psi, REAL *psi0, int **BINDEX) {
int flag = 0;
/****************************************************************************
| Define the coeffcients for diffusion euqation
****************************************************************************/
flag = coef_diff(para, var, psi, psi0, var_type, index, BINDEX);
if(flag!=0) {
ffd_log("diffsuion(): Could not calculate coefficents for "
"diffusion equation.", FFD_ERROR);
return flag;
}
// Solve the equations
equ_solver(para, var, var_type, psi);
// Define B.C.
set_bnd(para, var, var_type, index, psi, BINDEX);
// Check residual
if(para->solv->check_residual==1) {
switch(var_type) {
case VX:
sprintf(msg, "diffusion(): Residual of VX is %f",
check_residual(para, var, psi));
ffd_log(msg, FFD_NORMAL);
break;
case VY:
sprintf(msg, "diffusion(): Residual of VY is %f",
check_residual(para, var, psi));
ffd_log(msg, FFD_NORMAL);
break;
case VZ:
sprintf(msg, "diffusion(): Residual of VZ is %f",
check_residual(para, var, psi));
ffd_log(msg, FFD_NORMAL);
break;
case TEMP:
sprintf(msg, "diffusion(): Residual of T is %f",
check_residual(para, var, psi));
ffd_log(msg, FFD_NORMAL);
break;
case TRACE:
sprintf(msg, "diffusion(): Residual of Trace %d is %f",
index, check_residual(para, var, psi));
ffd_log(msg, FFD_NORMAL);
break;
default:
sprintf(msg, "diffusion(): No sovler for varibale type %d",
var_type);
ffd_log(msg, FFD_ERROR);
flag = 1;
}
}
return flag;
} // End of diffusion( )
///////////////////////////////////////////////////////////////////////////////
/// Calcuate coefficients for difussion equation solver
///
///\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 index Index of trace substance or species
///\param BINDEX Pointer to boundary index
///
///\return 0 if no error occurred
///////////////////////////////////////////////////////////////////////////////
int coef_diff(PARA_DATA *para, REAL **var, REAL *psi, REAL *psi0,
int var_type, int index, 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 *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 *pp = var[PP];
REAL *Temp = var[TEMP];
REAL dxe, dxw, dyn, dys, dzf, dzb, Dx, Dy, Dz;
REAL dt = para->mytime->dt, beta = para->prob->beta;
REAL Temp_Buoyancy = para->prob->Temp_Buoyancy;
REAL gravx = para->prob->gravx, gravy = para->prob->gravy,
gravz = para->prob->gravz;
REAL kapa;
// define kapa
switch(var_type) {
/*-------------------------------------------------------------------------
| X-velocity
-------------------------------------------------------------------------*/
case VX:
if(para->prob->tur_model==LAM)
kapa = para->prob->nu;
else if(para->prob->tur_model==CONSTANT)
kapa = 101.0f * para->prob->nu;
FOR_U_CELL
dxe = gx[IX(i+1,j ,k)] - gx[IX(i ,j,k)];
dxw = gx[IX(i ,j ,k)] - gx[IX(i-1,j,k)];
dyn = y[IX(i ,j+1,k)] - y[IX(i ,j,k)];
dys = y[IX(i,j,k)] - y[IX(i,j-1,k)];
dzf = z[IX(i,j,k+1)] - z[IX(i,j,k)];
dzb = z[IX(i,j,k)] - z[IX(i,j,k-1)];
Dx = x[IX(i+1,j,k)] - x[IX(i,j,k)];
Dy = gy[IX(i,j,k)] - gy[IX(i,j-1,k)];
Dz = gz[IX(i,j,k)] - gz[IX(i,j,k-1)];
if(para->prob->tur_model==CHEN)
kapa = nu_t_chen_zero_equ(para, var, i, j, k);
aw[IX(i,j,k)] = kapa*Dy*Dz/dxw;
ae[IX(i,j,k)] = kapa*Dy*Dz/dxe;
an[IX(i,j,k)] = kapa*Dx*Dz/dyn;
as[IX(i,j,k)] = kapa*Dx*Dz/dys;
af[IX(i,j,k)] = kapa*Dx*Dy/dzf;
ab[IX(i,j,k)] = kapa*Dx*Dy/dzb;
ap0[IX(i,j,k)] = Dx*Dy*Dz/dt;
b[IX(i,j,k)] = psi0[IX(i,j,k)]*ap0[IX(i,j,k)]
- beta*gravx*(Temp[IX(i,j,k)]-Temp_Buoyancy)*Dx*Dy*Dz
+ (pp[IX(i,j,k)]-pp[IX(i+1,j,k)])*Dy*Dz;
END_FOR
//set_bnd(para, var, var_type, psi, BINDEX);
FOR_U_CELL
ap[IX(i,j,k)] = ap0[IX(i,j,k)] + ae[IX(i,j,k)] + aw[IX(i,j,k)]
+ an[IX(i,j,k)] + as[IX(i,j,k)] + af[IX(i,j,k)]
+ ab[IX(i,j,k)];
END_FOR
break;
/*-------------------------------------------------------------------------
| Y-velocity
-------------------------------------------------------------------------*/
case VY:
if(para->prob->tur_model==LAM)
kapa = para->prob->nu;
else if(para->prob->tur_model==CONSTANT)
kapa = (REAL) 101.0 * para->prob->nu;
FOR_V_CELL
dxe = x[IX(i+1,j,k)] - x[IX(i,j,k)];
dxw = x[IX(i,j,k)] - x[IX(i-1,j,k)];
dyn = gy[IX(i,j+1,k)] - gy[IX(i,j,k)];
dys = gy[IX(i,j,k)] - gy[IX(i,j-1,k)];
dzf = z[IX(i,j,k+1)] - z[IX(i,j,k)];
dzb = z[IX(i,j,k)] - z[IX(i,j,k-1)];
Dx = gx[IX(i,j,k)] - gx[IX(i-1,j,k)];
Dy = y[IX(i,j+1,k)] - y[IX(i,j,k)];
Dz = gz[IX(i,j,k)] - gz[IX(i,j,k-1)];
if(para->prob->tur_model==CHEN)
kapa = nu_t_chen_zero_equ(para, var, i, j, k);
aw[IX(i,j,k)] = kapa*Dy*Dz/dxw;
ae[IX(i,j,k)] = kapa*Dy*Dz/dxe;
an[IX(i,j,k)] = kapa*Dx*Dz/dyn;
as[IX(i,j,k)] = kapa*Dx*Dz/dys;
af[IX(i,j,k)] = kapa*Dx*Dy/dzf;
ab[IX(i,j,k)] = kapa*Dx*Dy/dzb;
ap0[IX(i,j,k)] = Dx*Dy*Dz/dt;
b[IX(i,j,k)] = psi0[IX(i,j,k)]*ap0[IX(i,j,k)]
- beta*gravy*(Temp[IX(i,j,k)]-Temp_Buoyancy)*Dx*Dy*Dz
+ (pp[IX(i,j,k)]-pp[IX(i ,j+1,k)])*Dx*Dz;
END_FOR
//set_bnd(para, var, var_type, psi,BINDEX);
FOR_V_CELL
ap[IX(i,j,k)] = ap0[IX(i,j,k)] + ae[IX(i,j,k)] + aw[IX(i,j,k)]
+ an[IX(i,j,k)] + as[IX(i,j,k)] + af[IX(i,j,k)]
+ ab[IX(i,j,k)];
END_FOR
break;
/*-------------------------------------------------------------------------
| Z-velocity
-------------------------------------------------------------------------*/
case VZ:
if(para->prob->tur_model==LAM)
kapa = para->prob->nu;
else if(para->prob->tur_model==CONSTANT)
kapa = (REAL) 101.0 * para->prob->nu;
FOR_W_CELL
dxe = x[IX(i+1,j,k)] - x[IX(i,j,k)];
dxw = x[IX(i,j,k)] - x[IX(i-1,j,k)];
dyn = y[IX(i,j+1,k)] - y[IX(i,j,k)];
dys = y[IX(i,j,k)] - y[IX(i,j-1,k)];
dzf = gz[IX(i,j,k+1)] - gz[IX(i,j,k)];
dzb = gz[IX(i,j,k)] - gz[IX(i,j,k-1)];
Dx = gx[IX(i,j,k)] - gx[IX(i-1,j,k)];
Dy = gy[IX(i,j,k)] - gy[IX(i,j-1,k)];
Dz = z[IX(i,j,k+1)] - z[IX(i,j,k)];
if(para->prob->tur_model==CHEN)
kapa = nu_t_chen_zero_equ(para, var, i, j, k);
aw[IX(i,j,k)] = kapa*Dy*Dz/dxw;
ae[IX(i,j,k)] = kapa*Dy*Dz/dxe;
an[IX(i,j,k)] = kapa*Dx*Dz/dyn;
as[IX(i,j,k)] = kapa*Dx*Dz/dys;
af[IX(i,j,k)] = kapa*Dx*Dy/dzf;
ab[IX(i,j,k)] = kapa*Dx*Dy/dzb;
ap0[IX(i,j,k)] = Dx*Dy*Dz/dt;
b[IX(i,j,k)] = psi0[IX(i,j,k)]*ap0[IX(i,j,k)]
- beta*gravz*(Temp[IX(i,j,k)]-Temp_Buoyancy)*Dx*Dy*Dz
+ (pp[IX(i,j,k)]-pp[IX(i ,j,k+1)])*Dy*Dx;
END_FOR
//set_bnd(para, var, var_type, psi, BINDEX);
FOR_W_CELL
ap[IX(i,j,k)] = ap0[IX(i,j,k)] + ae[IX(i,j,k)] + aw[IX(i,j,k)]
+ an[IX(i,j,k)] + as[IX(i,j,k)] + af[IX(i,j,k)]
+ ab[IX(i,j,k)];
END_FOR
break;
/*-------------------------------------------------------------------------
| Scalar Variable
-------------------------------------------------------------------------*/
case TEMP:
case TRACE:
if(para->prob->tur_model == LAM)
kapa = para->prob->alpha;
else if(para->prob->tur_model == CONSTANT)
kapa = (REAL) 101.0 * para->prob->alpha;
FOR_EACH_CELL
dxe = x[IX(i+1,j,k)] - x[IX(i,j,k)];
dxw = x[IX(i,j,k)] - x[IX(i-1,j,k)];
dyn = y[IX(i,j+1,k)] - y[IX(i,j,k)];
dys = y[IX(i,j,k)] - y[IX(i,j-1,k)];
dzf = z[IX(i,j,k+1)] - z[IX(i,j,k)];
dzb = z[IX(i,j,k)] - z[IX(i,j,k-1)];
Dx = gx[IX(i,j,k)] - gx[IX(i-1,j,k)];
Dy = gy[IX(i,j,k)] - gy[IX(i,j-1,k)];
Dz = gz[IX(i,j,k)] - gz[IX(i,j,k-1)];
aw[IX(i,j,k)] = kapa*Dy*Dz/dxw;
ae[IX(i,j,k)] = kapa*Dy*Dz/dxe;
an[IX(i,j,k)] = kapa*Dx*Dz/dyn;
as[IX(i,j,k)] = kapa*Dx*Dz/dys;
af[IX(i,j,k)] = kapa*Dx*Dy/dzf;
ab[IX(i,j,k)] = kapa*Dx*Dy/dzb;
ap0[IX(i,j,k)] = Dx*Dy*Dz/dt;
b[IX(i,j,k)] = psi0[IX(i,j,k)]*ap0[IX(i,j,k)];
END_FOR
set_bnd(para, var, var_type, index, psi, BINDEX);
FOR_EACH_CELL
ap[IX(i,j,k)] = ap0[IX(i,j,k)] + ae[IX(i,j,k)] + aw[IX(i,j,k)]
+ an[IX(i,j,k)] + as[IX(i,j,k)] + af[IX(i,j,k)] + ab[IX(i,j,k)];
END_FOR
break;
default:
sprintf(msg, "coe_diff(): No function for variable type %d", var_type);
ffd_log(msg, FFD_ERROR);
return 1;
break;
}
return 0;
}// End of coef_diff( )
///////////////////////////////////////////////////////////////////////////////
/// Calcuate source term in the difussion equation
///
///\param para Pointer to FFD parameters
///\param var Pointer to FFD simulation variables
///\param var_type Type of variable
///\param index Index of trace substances or species
///
///\return 0 if no error occurred
///////////////////////////////////////////////////////////////////////////////
int source_diff(PARA_DATA *para, REAL **var, int var_type, int index) {
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 *b = var[B];
FOR_EACH_CELL
switch(var_type) {
case VX:
b[IX(i,j,k)] += var[VXS][IX(i,j,k)];
break;
case VY:
b[IX(i,j,k)] += var[VYS][IX(i,j,k)];
break;
case VZ:
b[IX(i,j,k)] += var[VZS][IX(i,j,k)];
break;
case TEMP:
b[IX(i,j,k)] += var[TEMPS][IX(i,j,k)];
break;
case TRACE:
b[IX(i,j,k)] += var[TRACE+para->bc->nb_Xi+index][IX(i,j,k)];
break;
}
END_FOR
return 0;
} // End of source_diff()