A Fourier analysis of the IPSA/PEA algorithms applied to multiphase flows with mass transfer

The error amplification matrices for two variations of a pressure-based Eulerian-Eulerian multiphase algorithm are developed using the method of Fourier decomposition. The algorithms examined here include Spalding's IPSA/PEA, and a revised form proposed by Siebert and Antal appropriate for flows with mass transfer. The error amplification matrices are developed for a single spatial dimension, but fo an arbitrary number of phases or fluids. The ramifications arising from these amplification matrices are explored in this article. For two-phase applications the revised form produces a broader theoretical range of convergent behavior for different interphase momentum and mass transfer rates. For four-phase applications both methods appear to be conditionally stable, and produce similar convergence behaviors. Large differences in interphase mass and momentum transfer rates between phasic pairs appear to adversely affect the algorithm's stability range.