Comparison of Boundary Integral and Volume-of-Fluid methods for compressible bubble dynamics

The Boundary Integral Method (BIM) has been widely applied to simulate oscillating bubbles, for its high efficiency and accuracy. A conventional BIM assumes the fluid surrounding the bubble to be inviscid and incompressible. Wang & Blake (J. Fluid Mech., 659, 2010, 191–224) proposed an improved model for bubbles in a weakly compressible flow, which is referred to as CBIM. In this study, an all-Mach method (AMM) implemented in the free software program Basilisk for the simulation of compressible multiphase flows, and using a geometric Volume-of-Fluid (VoF), is employed to study and estimate the accuracy of BIM and CBIM at different Mach numbers. First, for a spherical bubble, an extended Rayleigh-Plesset equation, CBIM and AMM give very close results when Ma≲0.3. However, a deviation between these three schemes gradually becomes evident as Ma increases from 0.3 to 0.6. Second, for the nonspherical deformation of a bubble close to a wall, the results obtained from CBIM and AMM show many similarities, including the evolution of the nonspherical bubble morphology, jet impact velocity, and impact pressure on the wall. Apart from the liquid compressibility, the gas inertia/density is found to be another factor that may affect the applicability of CBIM. In addition, we compare the CBIM and BIM results against an experiment of a spark-generated cavitation bubble, in which the liquid compressibility is found to play a vital role. From the perspective of engineering applications, BIM can reproduce the main features of the bubble dynamics in the first cycle if the initial conditions are set properly. The new findings provide a reference for research of bubble dynamics in both fundamental and applied problems.