Tracking the vortex motion by using Brownian fluid particles

In this paper, we propose a simple yet powerful vortex method to numerically approximate the dynamics of an incompressible flow. The idea is to sample the distribution of the initial vortices of the fluid flow in question and then follow vortex dynamics along Taylor's Brownian fluid particles. The weak convergences of this approximation scheme are obtained for both two-dimensional (2D) and three-dimensional (3D) fluid flows, though only for small time in 3D case. Based on our method, the simulation results are quite attracting.