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.