The Barnes — Hut-type algorithm in 2D Lagrangian vortex particle methods

Abstract

The Lagrangian vortex particle method for two-dimensional flow simulation around airfoils is considered. Generally, the most time-consuming operation in the vortex method is vortex particles interaction simulation, especially if it is performed directly “point-to-point” for all pairs of particles. The result of such operation is vortex particles convective velocities. This problem is similar to the N-body problem and has squared computational complexity O(N2). The only efficient approach for its solution in a reasonable time for large N is to use approximate fast algorithms. The fast method suggested by Barnes and Hut having logarithmic computational complexity is considered for the mentioned problem of convective velocities computation. It also has been adapted for other operations in the vortex method such as a system of algebraic equations iterative solution and efficient right-hand side computation. As the result, the Barnes — Hut method allows reducing the whole time of calculations by several tens of times.