Elaboration of the Fast Boundary Element Method for 3D Simulation of the Dynamics of a Bubble Cluster with Solid Particles in an Acoustic Field

An efficient numerical approach to the study of the dynamics of a cluster containing bubbles and solid particles under the action of an acoustic field in the 3D case is presented. The numerical method is a combination of the boundary element method (BEM) and the fast multipole method (FMM) for the Laplace equation. The hardware acceleration of the computation of a bubble cluster doped with solid particles is achieved due to parallel computations on graphics processing units (GPU). The efficiency of the proposed method is confirmed by computations for a structured cubic cluster consisting of bubbles and solid spherical particles. The dynamics of the bubble cluster depending on its size is analyzed, and it is shown that as the cluster size increases, the mobility of the bubbles and particles, the amplitude of the change in the cluster volume, the volume of individual bubbles, and the deformation of outermost bubbles of the cluster decrease.