Fourier analysis of the SIMPLE serials

ABSTRACT

In this article, error amplification matrices have been developed for SIMPLE and five revised SIMPLE variants by Fourier decomposition. Comparisons among six algorithms are made to check the effect of pressure–velocity coupling enhancements with respect to SIMPLE in terms of error damping. The Fourier analysis indicates that the SIMPLE variants developed on SIMPLER show better performance on high-frequency error damping, and can be used as better multigrid smoothers. The analysis also demonstrates that some pressure–velocity coupling enhancements can accelerate overall damping rate and promote convergence without weakening the convergence conditions.