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

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.