An Application of a Preconditioning Iterative Method to a Three-dimensional Numerical Computation of Fluid Flow

Hiroyuki Hirano, Hiroshi Niki and Naotaka Okamoto

preconditioning iterative method, natural convection, three-dimensional computation
Preconditioning Gauss-Seidel iterative methods were applied to a three-dimensional numerical computation of the natural convection in an enclosure of an incompressible Newtonian fluid using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. A two-dimensional computation was also performed for reference. Preconditioner adopted consists of the entries of the original coefficient matrix, 
and this can be obtained without any additional calculations. The iteration number to solve the linear system of equations of the pressure-correction was reduced to about 45 \% to 70 \% of that without preconditioning. The effect of 
preconditioning was independent of grid system and dimension of the problem adopted in the present computations.

Information, Vol.6, No.1, pp.5-12