Simulation Of The Interaction Between A Bubble And An Ultrasound Wave By Implementing A Two-Phase Compressible Solver Adapted To Low Mach Number Regime

摘要

This paper is focused on the numerical simulation of the interaction of an ultrasound wave and an air bubble surrounded by water. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific attention must be paid to the effectiveness of the numerical method chosen to solve the compressible Euler equations. Several numerical methods are implemented and confronted on a benchmarck. This preliminary test highlights that the projection method is the most accurate one. Then a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities. A specific velocity/pressure time splitting is thus proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided with the numerical simulation of the interaction between a bubble and a wavefront. Indeed, both the accuracy and the stability of the overall algorithm are enhanced using this new numerical method.