Behavior of upwind scheme in the low Mach number limit: III. Preconditioned dissipation for a five equation two phase model

Abstract

For single phase fluid models, like the Euler equations of compressible gas dynamics, upwind finite volume schemes suffer from a loss of accuracy when computing flows in the near incompressible regime. Preconditioning of the numerical dissipation is necessary to recover results consistent with the asymptotic behaviour of the continuous model. In this paper, we examine this situation for a two-phase flow model. We show that as in the single phase case, the numerical approximation has to be done carefully in the near incompressible regime. We propose to adapt the preconditioning strategy used for single phase problems and present numerical results that show the efficiency of this approach.