Fourier Analysis of the Effect of Non-Constant Terms on the Convergence Properties of SIMPLE Algorithm Formulated on a Staggered Grid

Abstract

The Fourier analysis is employed to study the effect of non-constant terms on the convergence properties of SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm formulated on a staggered grid in two-dimension. The results indicate the non-constant items can broaden the convergence range of pressure relaxation factor for a given velocity under-relaxation factor. What’s more, the non-constant items do well to the damping of the lowest error and can accelerate the convergence rate.