A fast algorithm for modeling multiple bubbles dynamics

This work presents the development of a numerical strategy that combines the fast Fourier transform on multipoles (FFTM) method and the boundary element method (BEM) to study the physics of multiple bubbles dynamics in moving boundary problems. The recent FFTM method can be employed to speedup the resolution of the boundary integral equation. However, one major drawback of the method is that its efficiency deteriorates quite significantly when the problem is spatially sparsely populated, as in the case where multiple bubbles are well separated. To overcome this deficiency, a new version of FFTM with clustering is proposed (henceforth called FFTM Clustering). The new algorithm first identifies and groups closely positioned bubbles. The original FFTM is then used to compute the potential contributions from the bubbles within its own group, while contributions from the other separated groups are evaluated via the multipole to local expansions translations operations directly. We tested the FFTM Clustering on several multiple bubble examples to demonstrate its effectiveness over the original FFTM method and vast improvement over the standard BEM. The high efficiency of the FFTM Clustering method allows us to simulate much larger multiple bubbles dynamics problems within reasonable time. Some physical behaviors of the multiple bubbles are also presented in this work.