A GPU-accelerated Boundary Element Method and Vortex Particle Method

Vortex particle methods, when combined with multipole-accelerated boundary element methods (BEM), become a complete tool for direct numerical simulation (DNS) of internal or external vortex-dominated flows. In previous work, we presented a method to accelerate the vorticity-velocity inversion at the heart of vortex particle methods by performing a multipole treecode N-body method on parallel graphics hardware. The resulting method achieved a 17-fold speedup over a dual-core CPU implementation. In the present work, we will demonstrate both an improved algorithm for the GPU vortex particle method that outperforms an 8-core CPU by a factor of 43, but also a GPU-accelerated multipole treecode method for the boundary element solution. The new BEM solves for the unknown source, dipole, or combined strengths over a triangulated surface using all available CPU cores and GPUs. Problems with up to 1.4 million unknowns can be solved on a single commodity desktop computer in one minute, and at that size the hybrid CPU/GPU outperforms a quad-core CPU alone by 22.5 times. The method is exercised on DNS of impulsively-started flow over spheres at Re=500, 1000, 2000, and 4000.