An extended Laplacian smoothing for boundary element analysis of 3D bubble dynamics

Frequently, smoothing techniques have to be applied to tackle the numerical instability and mesh distortion in modelling bubble dynamics using the boundary element method (BEM). Laplacian smoothing (LS) and its variants have been commonly used in the literature due to their ease of implementation and computational efficiency. Nevertheless, these methods are prone to inducing shrinking and oversmoothing effects. To address this issue, an efficient smoothing technique, called the Extended LS (ELS) method, is devised based on the LS method to accurately capture the salient features of the liquid jet of a collapsing bubble near complex boundaries. The efficacy of the ELS method is demonstrated through its application to various test cases for which theoretical, numerical, or experimental data are available in the literature. The ELS method is then used to simulate intricate bubble dynamics, including the oscillation of a 3D gas bubble near two rigid, fixed spherical particles. The influence of the dimensionless distance d^* between the bubble and the particles on the dynamics of the bubble is thoroughly examined. As  d^* decreases, the bubble moves closer to the particles, causing its lower side surface to change from concave to convex.