Research Outline:
Underwater bubble dynamics include features such as jet impact and merging that entail complex topological changes. The front trackingboundary element method, an established computational method for modelling these dynamics, is unable to handle such topological changes well. The level set method, which represents a physical interface implicitly, can handle these topological changes naturally. The objective of our work is to develop a level setboundary element method for the simulation of underwater bubble dynamics.
An important aspect of our work is to formulate the means to evolve the surface velocity potential. We propose a level settype potential function and derive a governing equation to evolve this potential function such that the function value at the interface is the surface velocity potential consistent with Bernoulli’s equation. Based on this formulation, we implement a level setboundary element method for axisymmetric problems. A convergence analysis, performed using the Rayleigh bubble as reference, showed our implemented procedure to be secondorder accurate.
We apply our level setboundary element method to three test problems. The first test problem is a buoyant bubble that develops a liquid jet subsequently resulting in jet impact and the formation of a toroidal bubble. The second test problem comprises two simplyconnected bubbles incepted close to each other eventually merging to form a single bubble. The final test problem consists of a simplyconnected bubble incepted close to a toroidal bubble eventually merging to form a single simplyconnected bubble. The complex topological changes associated with jet impact and merging in the above test problems are all handled naturally by our level setboundary element method.
