Random large eddy simulation for 3-dimensional incompressible viscous flows

TL;DR

This paper introduces a novel numerical approach combining random vortex methods with Large Eddy Simulation techniques to efficiently simulate 3D incompressible viscous flows, including turbulent regimes.

Contribution

It develops a new closure scheme that integrates LES filtering with random vortex methods, enabling Monte Carlo simulations of complex flow systems.

Findings

Successfully simulated laminar and turbulent flows

Validated the method's accuracy and effectiveness

Provided a practical approach for 3D flow simulations

Abstract

We develop a numerical method for simulation of incompressible viscous flows by integrating the technology of random vortex method with the core idea of Large Eddy Simulation (LES). Specifically, we utilize the filtering method in LES, interpreted as spatial averaging, along with the integral representation theorem for parabolic equations, to achieve a closure scheme which may be used for calculating solutions of Navier-Stokes equations. This approach circumvents the challenge associated with handling the non-locally integrable 3-dimensional integral kernel in the random vortex method and facilitates the computation of numerical solutions for flow systems via Monte-Carlo method. Numerical simulations are carried out for both laminar and turbulent flows, demonstrating the validity and effectiveness of the method.