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

This paper introduces an Extended Laplacian Smoothing (ELS) method to overcome numerical instability and mesh distortion in 3D bubble dynamics simulations using the Boundary Element Method.

This paper introduces an Extended Laplacian Smoothing (ELS) method to overcome numerical instability and mesh distortion in 3D bubble dynamics simulations using the Boundary Element Method. Unlike traditional Laplacian smoothing techniques that suffer from volume shrinkage, the proposed ELS method preserves the initial volume of the triangulated shape while effectively smoothing the mesh. The work validates ELS through three test cases and then applies it to simulate the complex dynamics of a 3D gas bubble oscillating near two rigid spherical particles.

The results demonstrate how the dimensionless distance (d*) between the bubble and particles significantly influences bubble behavior, with decreasing distance causing the bubble’s lower surface to transition from concave to convex. The study shows that ELS produces more accurate results without significant computational cost increases, making it valuable for capturing complex phenomena like jet formation during bubble collapse near boundaries.