FOURIER ANALYSIS OF THE SIMPLE ALGORITHM FORMULATED ON A COLLOCATED GRID

摘要

The Fourier error amplification matrix has been developed for the SIMPLE algorithm formulated on a collocated grid using the Rhie-Chow approximation. The cause of and remedy for the checkerboard pressure effect associated with collocated grid systems is shown. Comparisons with observations from the technical literature suggest that Fourier analysis is capable of describing algorithm operation. This analysis also suggests that there is a conditional relationship between the momentum underrelaxation factor and the pressure-correction damping factor for convergence of the collocated form, and indicates that the collocated form should serve as a superior multigrid smoother. [References: 15]