The ACA–BEM approach with a binary-key mosaic partitioning for modelling multiple bubble dynamics

The fast algorithm adaptive cross approximation (ACA) is applied to accelerate the solution of the boundary element method (BEM). A new method for mosaic partitioning is proposed as part of the implementation of the ACA algorithm. It is based on a binary key system, which represents a hierarchical cluster tree and helps to identify the hierarchy within the ℋℋ-matrix generated by the BEM. The employed ACA approach proves efficient even for relatively small problems with the degree of freedom of O(103). As the problem size grows, the superior performance of the fast approach becomes more notable by comparison with that of the conventional boundary element method (CBEM). Modelling of bubble dynamics belongs to the moving boundary problems and can be efficiently analysed by using the BEM. By applying the ACA approach, the dense matrices via the collocation scheme are successfully compressed, and the developed model is capable of investigating the time-dependent evolution process of a relatively large number of bubbles (>100) in an efficient way.