GPU accelerated fast multipole boundary element method for simulation of 3D bubble dynamics in potential flow

TL;DR

This paper introduces a GPU-accelerated boundary element method combined with the fast multipole method for efficient simulation of 3D bubble dynamics in potential flow, enabling large-scale cluster simulations on standard workstations.

Contribution

It presents a novel GPU-accelerated boundary element method with a new surface smoothing technique for stable, large-scale bubble dynamics simulations in three-dimensional potential flows.

Findings

Enables simulation of thousands of bubbles with millions of boundary elements.

Achieves high accuracy validated against literature and convergence studies.

Demonstrates scalability and performance on personal workstations.

Abstract

A numerical method for simulation of bubble dynamics in three-dimensional potential flows is presented. The approach is based on the boundary element method for the Laplace equation accelerated via the fast multipole method implemented on a heterogeneous CPU/GPU architecture. For mesh stabilization, a new smoothing technique using a surface filter is presented. This technique relies on spherical harmonics expansion of surface functions for bubbles topologically equivalent to a sphere (or Fourier series for toroidal bubbles). The method is validated by comparisons with solutions available in the literature and convergence studies for bubbles in acoustic fields. The accuracy and performance of the algorithm are discussed. It is demonstrated that the approach enables simulation of dynamics of bubble clusters with thousands of bubbles and millions of boundary elements on contemporary personal workstations. The algorithm is scalable and can be extended to larger systems.