An Approaching Fourier Analysis of the Relaxation Effect on the SIMPLE Algorithm

The Fourier decomposition is employed to derive the error amplification matrix for the SIMPLE algorithm implemented on a collocated grid with the Rhie-Chow interpolation method incorporated, and an approaching method is developed to study the effect of relaxation factors on the convergence behaviors of SIMPLE based on characteristic analysis of the lowest and highest frequency errors. The study indicates that convergence can be guaranteed by damping out the highest and lowest frequencies with conditional combinations of both factors. In the case of convergence, the optimum convergence rate almost depends on the velocity relaxation factor, and a relatively larger velocity factor can accelerate the optimal rate.