Monte-Carlo method for incompressible fluid flows past obstacles

TL;DR

This paper introduces a Monte-Carlo approach for simulating incompressible fluid flows past obstacles using stochastic integral representations and random vortex formulations, enabling boundary-free numerical experiments.

Contribution

It develops a novel Monte-Carlo scheme based on stochastic integral representations for wall-bounded incompressible flows, avoiding traditional boundary layer computations.

Findings

Successful numerical experiments demonstrating the method

Efficient boundary-free simulation of fluid flows

Potential for improved computational fluid dynamics techniques

Abstract

We establish stochastic functional integral representations for incompressible fluid flows occupying wall-bounded domains using the conditional law duality for a class of diffusion processes. These representations are used to derive a Monte-Carlo scheme based on the corresponding exact random vortex formulation. We implement several numerical experiments based on the Monte-Carlo method without appealing to the boundary layer flow computations, to demonstrate the methodology.