Hybrid Barnes – Hut/Multipole algorithm application to vortex particles velocities calculation and integral equation solution

Abstract

The approximate fast algorithm is developed that makes it possible to calculate velocities of the vortex particles in two-dimensional flow simulations by using vortex methods. It is adapted to efficient solution of the boundary integral equation arising at each time step of simulation. The proposed method can be considered as generalization of the classical Barnes – Hut method, taking into account some ideas of the Fast Multipole Method. Some model problems are considered that can be solved by using vortex methods, the developed fast algorithm is implemented for multi-cores CPUs and (with some modifications) for GPUs. The scalability of the code is rather high; the developed algorithms can run with millions of vortex particles taking only tens or hundreds of milliseconds per time step; linear systems with dimension of about 104 can be solved on multicore CPU in tens milliseconds.