Graphics Processing Unit-Accelerated Boundary Element Method and Vortex Particle Method

Abstract

Vortex particle methods, when combined with boundary element methods, become a powerful tool for the simulation of internal or external vortex-dominated flows. To speed up the simulations substantially, algorithms are presented herein for the implementation of a parallel adaptive multipole-accelerated treecode for evaluating the velocity field induced by vortex particles on a cluster of graphics processing units, as well as the implementation of a graphics processing unit-accelerated treecode for evaluating the velocity field induced by vortex and source boundary panels. The graphics processing unit-accelerated treecode for vortex particles outperforms its eight-core central processing unit counterpart by a factor of 43. Furthermore, the parallel efficiency of the treecode on a 32-node cluster of dual-graphics processingunitsis80%for100millionparticles.Theboundaryelementmethodtreecodecan solveforunknownsource,vortex,orcombinedstrengthsovertriangularsurfacemeshesusing all available central processing unit cores and graphics processing units. Problems with up to 1.4 million unknowns can now be solved on a single commodity desktop computer in 1min, and at that size the hybrid central processing unit/graphics processing unit outperforms a quad-core central processing unit alone by 22.5 times. The method is applied to simulations of the early stages of impulsively started flow over a sphere at Reynolds numbers 500, 1000, 2000, and 4000 based on the diameter and freestream velocity.