A numerical method for the simulation of low Mach number liquid-gas flows

V. Daru*, P. Le Quéré, M. C. Duluc, O. Le Maître

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This work is devoted to the numerical simulation of liquid-gas flows. The liquid phase is considered as incompressible, while the gas phase is treated as compressible in the low Mach number approximation. A single fluid two pressure model is developed and the front-tracking method is used to track the interface. Navier-Stokes equations coupled with that of temperature are solved in the whole computational domain. Velocity, pressure and temperature fields are computed yielding a complete description of the dynamics for both phases. We show that our method is much more efficient than the so-called all-Mach methods involving a single pressure, since large time steps can be used while retaining time accuracy. The model is first validated on a reference test problem solved using an accurate ALE technique to track the interface. Numerical examples in two space dimensions are next presented. They consist of air bubbles immersed in a closed cavity filled up with liquid water. The forced oscillations of the system consisting of the air bubbles and the liquid water are investigated. They are driven by a heat supply or a thermodynamic pressure difference between the bubbles.

Original languageEnglish (US)
Pages (from-to)8844-8867
Number of pages24
JournalJournal of Computational Physics
Issue number23
StatePublished - Nov 2010
Externally publishedYes


  • Compressibility
  • Front-tracking
  • Low Mach number flow
  • Two-phase flow

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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