Low-Mach-number limit for two-phase flows

2025/12/18 by C. Lebot, Lebot, Cassandre
Mathematics · Engineering · #Navier-Stokes equation solutions #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2512.16286

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.

Citations

• Incompressible limits at large Mach number for a reduced compressible MHD system
• Remarks on weak-strong uniqueness for two-fluid model
• On the sound speed in two-fluid mixtures and the implications for CFD model validation
• Existence and stability of dissipative turbulent solutions to a simple bi-fluid model of compressible fluids
• On weak solutions to the compressible inviscid two-fluid model
• Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data
• Global weak solution to the viscous two-fluid model with finite energy
• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids

Related

• Low Mach number limit for the compressible Navier-Stokes equation with a stationary force
• Low Mach number limit of the global solution to the compressible Navier-Stokes system for large data in the critical Besov space
• Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles
• Measure-valued low Mach number limits of ideal fluids
• Low Mach number flows, and combustion