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solver_gs.c
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solver_gs.c
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///////////////////////////////////////////////////////////////////////////////
///
/// \file solver_gs.c
///
/// \brief Gauss-Seidel solvers
///
/// \author Mingang Jin, Qingyan Chen
/// Purdue University
/// Wangda Zuo
/// University of Miami
///
/// \date 8/3/2013
///
///////////////////////////////////////////////////////////////////////////////
#include "solver_gs.h"
///////////////////////////////////////////////////////////////////////////////
/// Gauss-Seidel solver for pressure
///
///\param para Pointer to FFD parameters
///\param var Pointer to FFD simulation variables
///\param Type Type of variable
///\param x Pointer to variable
///
///\return Residual
///////////////////////////////////////////////////////////////////////////////
REAL GS_P(PARA_DATA *para, REAL **var, int Type, REAL *x) {
REAL *as = var[AS], *aw = var[AW], *ae = var[AE], *an = var[AN];
REAL *ap = var[AP], *af = var[AF], *ab = var[AB], *b = var[B];
int imax = para->geom->imax, jmax= para->geom->jmax;
int kmax = para->geom->kmax;
int IMAX = imax+2, IJMAX = (imax+2)*(jmax+2);
int i, j, k, it;
float tmp1, tmp2, residual;
REAL *flagp = var[FLAGP];
/****************************************************************************
| Solve the space using G-S sovler for 5 * 6 = 30 times
****************************************************************************/
for(it=0; it<5; it++) {
/*-------------------------------------------------------------------------
| Solve in X(1->imax), Y(1->jmax), Z(1->kmax)
-------------------------------------------------------------------------*/
for(i=1; i<=imax; i++)
for(j=1; j<=jmax; j++)
for(k=1; k<=kmax; k++) {
if (flagp[IX(i,j,k)]>=0) continue;
x[IX(i,j,k)] = ( ae[IX(i,j,k)]*x[IX(i+1,j,k)]
+ aw[IX(i,j,k)]*x[IX(i-1,j,k)]
+ an[IX(i,j,k)]*x[IX(i,j+1,k)]
+ as[IX(i,j,k)]*x[IX(i,j-1,k)]
+ af[IX(i,j,k)]*x[IX(i,j,k+1)]
+ ab[IX(i,j,k)]*x[IX(i,j,k-1)]
+ b[IX(i,j,k)] ) / ap[IX(i,j,k)];
}
/*-------------------------------------------------------------------------
| Solve in Y(1->kmax), X(1->imax), Z(1->kmax)
-------------------------------------------------------------------------*/
for(j=1; j<=jmax; j++)
for(i=1; i<=imax; i++)
for(k=1; k<=kmax; k++) {
if (flagp[IX(i,j,k)]>=0) continue;
x[IX(i,j,k)] = ( ae[IX(i,j,k)]*x[IX(i+1,j,k)]
+ aw[IX(i,j,k)]*x[IX(i-1,j,k)]
+ an[IX(i,j,k)]*x[IX(i,j+1,k)]
+ as[IX(i,j,k)]*x[IX(i,j-1,k)]
+ af[IX(i,j,k)]*x[IX(i,j,k+1)]
+ ab[IX(i,j,k)]*x[IX(i,j,k-1)]
+ b[IX(i,j,k)] ) / ap[IX(i,j,k)];
}
/*-------------------------------------------------------------------------
| Solve in X(imax->), Y(jmax->1), Z(1->kmax)
-------------------------------------------------------------------------*/
for(i=imax; i>=1; i--)
for(j=jmax; j>=1; j--)
for(k=1; k<=kmax; k++) {
if (flagp[IX(i,j,k)]>=0) continue;
x[IX(i,j,k)] = ( ae[IX(i,j,k)]*x[IX(i+1,j,k)]
+ aw[IX(i,j,k)]*x[IX(i-1,j,k)]
+ an[IX(i,j,k)]*x[IX(i,j+1,k)]
+ as[IX(i,j,k)]*x[IX(i,j-1,k)]
+ af[IX(i,j,k)]*x[IX(i,j,k+1)]
+ ab[IX(i,j,k)]*x[IX(i,j,k-1)]
+ b[IX(i,j,k)] ) / ap[IX(i,j,k)];
}
/*-------------------------------------------------------------------------
| Solve in Y(jmax->1), X(imax->1), Z(1->kmax)
-------------------------------------------------------------------------*/
for(j=jmax; j>=1; j--)
for(i=imax; i>=1; i--)
for(k=1; k<=kmax; k++) {
if (flagp[IX(i,j,k)]>=0) continue;
x[IX(i,j,k)] = ( ae[IX(i,j,k)]*x[IX(i+1,j,k)]
+ aw[IX(i,j,k)]*x[IX(i-1,j,k)]
+ an[IX(i,j,k)]*x[IX(i,j+1,k)]
+ as[IX(i,j,k)]*x[IX(i,j-1,k)]
+ af[IX(i,j,k)]*x[IX(i,j,k+1)]
+ ab[IX(i,j,k)]*x[IX(i,j,k-1)]
+ b[IX(i,j,k)] ) / ap[IX(i,j,k)];
}
}
/****************************************************************************
| Calculate residual
****************************************************************************/
tmp1 = 0;
tmp2 = (REAL)0.0000000001;
FOR_EACH_CELL
if (flagp[IX(i,j,k)]>=0) continue;
tmp1 += (REAL) fabs(ap[IX(i,j,k)]*x[IX(i,j,k)]
- ae[IX(i,j,k)]*x[IX(i+1,j,k)] - aw[IX(i,j,k)]*x[IX(i-1,j,k)]
- an[IX(i,j,k)]*x[IX(i,j+1,k)] - as[IX(i,j,k)]*x[IX(i,j-1,k)]
- af[IX(i,j,k)]*x[IX(i,j,k+1)] - ab[IX(i,j,k)]*x[IX(i,j,k-1)]
- b[IX(i,j,k)]);
tmp2 += (REAL) fabs(ap[IX(i,j,k)]*x[IX(i,j,k)]);
END_FOR
residual = tmp1 /tmp2;
return residual;
} // End of GS_P()
///////////////////////////////////////////////////////////////////////////////
/// Gauss-Seidel solver
///
///\param para Pointer to FFD parameters
///\param var Pointer to FFD simulation variables
///\param flag Pointer to the cell property flag
///\param x Pointer to variable
///
///\return Residual
///////////////////////////////////////////////////////////////////////////////
REAL Gauss_Seidel(PARA_DATA *para, REAL **var, REAL *flag, REAL *x) {
REAL *as = var[AS], *aw = var[AW], *ae = var[AE], *an = var[AN];
REAL *ap = var[AP], *af = var[AF], *ab = var[AB], *b = var[B];
int imax = para->geom->imax, jmax= para->geom->jmax;
int kmax = para->geom->kmax;
int IMAX = imax+2, IJMAX = (imax+2)*(jmax+2);
int i, j, k, it=0;
float tmp1, tmp2, residual;
/****************************************************************************
| Gauss-Seidel solver
****************************************************************************/
for(it=0; it<1; it++) {
for(i=1; i<=imax; i++)
for(j=1; j<=jmax; j++)
for(k=1; k<=kmax; k++) {
if (flag[IX(i,j,k)]>=0) continue;
x[IX(i,j,k)] = ( ae[IX(i,j,k)]*x[IX(i+1,j,k)]
+ aw[IX(i,j,k)]*x[IX(i-1,j,k)]
+ an[IX(i,j,k)]*x[IX(i,j+1,k)]
+ as[IX(i,j,k)]*x[IX(i,j-1,k)]
+ af[IX(i,j,k)]*x[IX(i,j,k+1)]
+ ab[IX(i,j,k)]*x[IX(i,j,k-1)]
+ b[IX(i,j,k)] ) / ap[IX(i,j,k)];
}
for(i=imax; i>=1; i--)
for(j=jmax; j>=1; j--)
for(k=1; k<=kmax; k++) {
if (flag[IX(i,j,k)]>=0) continue;
x[IX(i,j,k)] = ( ae[IX(i,j,k)]*x[IX(i+1,j,k)]
+ aw[IX(i,j,k)]*x[IX(i-1,j,k)]
+ an[IX(i,j,k)]*x[IX(i,j+1,k)]
+ as[IX(i,j,k)]*x[IX(i,j-1,k)]
+ af[IX(i,j,k)]*x[IX(i,j,k+1)]
+ ab[IX(i,j,k)]*x[IX(i,j,k-1)]
+ b[IX(i,j,k)] ) / ap[IX(i,j,k)];
}
}
/****************************************************************************
| Calculate residual
****************************************************************************/
tmp1 = 0;
tmp2 = (REAL)0.0000000001;
FOR_EACH_CELL
if (flag[IX(i,j,k)]>=0) continue;
tmp1 += (REAL) fabs(ap[IX(i,j,k)]*x[IX(i,j,k)]
- ae[IX(i,j,k)]*x[IX(i+1,j,k)] - aw[IX(i,j,k)]*x[IX(i-1,j,k)]
- an[IX(i,j,k)]*x[IX(i,j+1,k)] - as[IX(i,j,k)]*x[IX(i,j-1,k)]
- af[IX(i,j,k)]*x[IX(i,j,k+1)] - ab[IX(i,j,k)]*x[IX(i,j,k-1)]
- b[IX(i,j,k)]);
tmp2 += (REAL) fabs(ap[IX(i,j,k)]*x[IX(i,j,k)]);
END_FOR
residual = tmp1 /tmp2;
return residual;
} // End of Gauss-Seidel( )