Application of a Preconditioning Iterative Method to the Computation of Fluid Flow

Hiroyuki Hirano and Hiroshi Niki

preconditioning Gauss-Seidel method, computational fluid dynamics
In this paper, a new preconditioning iterative method is proposed. It consists of the Gauss-Seidel method with a preconditioning matrix which approximates the inverse matrix of $A$ by a finite Neumann-type expansion. The convergence theorem of the method is given. The validity of the proposed method is illustrated by two numerical examples. We show that the proposed method can be applied to the computation of two-dimensional natural convection problem, and that it is more effective than other standard terative methods.

Numer. Funct. Anal. and Optimiz., Vol.22, No.3&4, pp.405-417