Fourier Analysis of the Effect of Momentum Interpolation on the SIMPLE Series Formulated on a Collocated Grid

Abstract

The error amplification matrices of three SIMPLE series formulated on a staggered grid and a collocated grid using three momentum interpolation methods are derived. The effects of grid layout and momentum interpolation methods on convergence properties of SIMPLE series are checked. The results indicate that the convergence conditions are available by damping out the highest and lowest errors. The SIMPLE series show almost identical convergence rates under a wide range of useful velocity relaxation factors, regardless of grid layout and interpolation method. However, the high-frequency reduction shows significant variation with grid layout and interpolation method, which maybe referred to in multigrid application.

Acknowledgments

This work was financially supported by the National Key Basic Research Development Program of China (973 Program, Grant No. 2010CB429002), National Natural Science Foundation of China (Grant No. 51009109), and Major Science and Technology Projects for Transportation (Grant No. 201132854850, Grant No. 201132822430)