An all-Mach method for the simulation of bubble dynamics problems in the presence of surface tension

This paper presents a generalization of an all-Mach formulation for multiphase flows accounting for surface tension and viscous forces. The proposed numerical method is based on the consistent advection of conservative quantities and the advection of the color function used in the Volume of Fluid method avoiding any numerical diffusion of mass, momentum and energy across the interface during the advection step. The influence of surface tension and liquid compressibility on the dynamic response of the bubbles is discussed by comparing the full 3D solution with the predictions provided by the Rayleigh-Plesset equation for two relevant problems related to the dynamic response of bubbles to pressure disturbances: The linear oscillation of a single bubble in an acoustic field and the Rayleigh collapse problem. Finally, the problem of the collapse of a bubble close to a wall is compared with experimental results showing the robustness of the method to simulate the collapse of air bubbles in liquids in problems where bubbles generate a high velocity liquid jet.