Boundary Integral Simulation of Nonlinear Oscillations of Gas Bubbles

Abstract

Nonlinear axisymmetric oscillations of a gas bubble in a liquid are examined using the boundary integral method. The flow in the exterior liquid phase is treated as a potential flow while the gas within the bubble interior is taken to be ideal, having a uniform pressure that depends only on the instantaneous volume of the bubble. The combination of the boundary integral equation and the normal stress balance at the interface — the latter of which includes the use of Bernoulli’s equation to relate the pressure at the surface to the potential — produces a coupled set of nonlinear equations for the potential and the normal velocity at the interface. These can be solved iteratively at each time step and, by moving the nodal points representing the discretized interface according to their normal velocities, the nonlinear evolution of the bubble surface can be followed in time.