Accuracy improvement of axisymmetric bubble dynamics using low Mach number scaling

• The concept of numerical sound speed is applied in the acoustic Riemann solver.
• A Lagrange-remap method is used to solve the axisymmetric Euler equation.
• The volume-of-fluid method is used to track the interface between two phases.
• The dynamics of bubble motion in ambient water is simulated.
• The low Mach number scaling improves the accuracy considerably.

Bubble collapse and associated shock wave emission are characterized by the compressibility of both gas and liquid. The bubble motion may, however, be in the low Mach number flow regime when the bubble is near the maximum size at the early stage and at its full rebound. Although it is quite well known that a compressible flow solver encounters difficulties in the low Mach number regime, the influence of the low Mach number on the simulation of bubble collapse and rebound is not clear. In the present work, an axisymmetric compressible solver based on the acoustic Riemann solver is used to simulate the dynamics of bubble motion. The artificial viscosity terms in the Riemann solver are rescaled for the low Mach regime by following the concept of numerical sound speed, which was originally developed in the AUSM family scheme. The numerical results are compared with the solutions of the Rayleigh model for bubble collapse and the Keller–Miksis model for bubble collapse and rebound. It is found that the low Mach number scaling improves the accuracy of the size of a collapsing bubble considerably.