Low-Mach-number limit for multiphase flows
Cassandre Lebot
TL;DR
The paper surveys and formalizes the low-Mach-number limits for compressible multiphase flows, starting from one-phase results and extending to two-phase models with either a single velocity or two velocities. It analyzes both algebraic and PDE closures for pressure and distinguishes isentropic versus non-isentropic regimes, deriving incompressible-like limit systems where the velocity is divergence-free and densities become constrained (often constant or entropy-modulated) in the leading order. It additionally derives the corresponding limit momentum equations, transport equations for volume fractions and entropies, and highlights interfacial terms such as p_int in the momentum balance. The work maps out the formal asymptotics, energy considerations, and open problems that guide future rigorous analysis and numerical methods for low-Mach multiphase flows.
Abstract
This paper is devoted to the 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.