Low-Mach-number limit for two-phase flows

TL;DR

This paper investigates the behavior of two-phase fluid flows as the Mach number approaches zero, extending previous single-phase analyses to more complex multi-phase systems.

Contribution

It provides a formal analysis of the low-Mach-number limit for various two-phase flow models, including different pressure closures and velocity configurations.

Findings

Reviewed existing results for single-phase flows.

Extended analysis to two-phase flows with various modeling assumptions.

Clarified the mathematical behavior of solutions in the low-Mach-number regime.

Abstract

This paper is devoted to the formal study of the low-Mach-number limit for solutions of the compressible Navier-Stokes or Euler equations for different types of fluids.We first review the different results obtained in the case of flows consisting of one phase. Then, we focus on the low-Mach-number limit for two-phase flows, considering different types of systems: with an algebraic closure or a PDE closure for the pressure, with one single or two different velocities, without or with entropy.