Tracking the vortex motion by using Brownian fluid particles

TL;DR

This paper introduces a vortex method using Brownian fluid particles to simulate incompressible flow dynamics, demonstrating convergence and promising simulation results for both 2D and 3D cases.

Contribution

The paper presents a novel vortex approximation scheme based on Brownian particles, with proven convergence in 2D and partial results in 3D.

Findings

Convergence of the method in 2D and small-time 3D cases

Effective simulation results for vortex dynamics

A simple yet powerful approach for incompressible flow simulation

Abstract

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 then follow vortex dynamics along Taylor's Brownian fluid particles. The weak convergences of this approximation scheme are obtained for 2D and 3D cases, though only for small time in 3D case. Based on our method, the simulation results are quite attracting.