A Level Set–Boundary Element Method for the Simulation of Underwater Bubble Dynamics

Abstract

The front tracking-boundary element method, though commonly used to simulate underwater bubble dynamics, is not quite well suited for treating the complex topological changes that can occur. In this paper, we present a level set-boundary element method that overcomes this deficiency. This new technique combines the level set method to capture the bubble surface motions and the boundary element method to compute the surface velocities. We propose a level set-type potential function to capture the surface velocity potential, and we formulate a governing equation to evolve this function such that the functional value at the bubble surface is the surface velocity potential consistent with the unsteady Bernoulli equation. A convergence analysis performed using the Rayleigh bubble as reference establishes our implemented procedure to be second-order accurate. We also demonstrate the ease with which our method handles complex topological changes using axisymmetrical examples of bubble merging, bubble splitting, and bubble jet impact. The result for a highly complex problem comprising both jet impact and merging is also presented. Additionally, we develop a more computationally efficient technique that requires computations to be performed only within a narrow band containing the interface.