Numerical simulation method for Brownian particles dispersed in incompressible fluids

TL;DR

This paper introduces a numerical simulation method combining Langevin dynamics and lattice Boltzmann techniques to accurately model Brownian particles in incompressible fluids, capturing key physical phenomena.

Contribution

It presents a novel coupling scheme that accurately reproduces long-time tail behavior and satisfies the fluctuation-dissipation relation in simulations of Brownian particles.

Findings

Reproduces long-time tail in velocity auto-correlation functions

Validates fluctuation-dissipation relation in the simulation

Accurately evaluates friction force based on particle-fluid velocity difference

Abstract

We present a numerical scheme for simulating the dynamics of Brownian particles suspended in a fluid. The motion of the particles is tracked by the Langevin equation, whereas the host fluid flow is analyzed by using the lattice Boltzmann method. The friction force between a particle and the fluid is evaluated correctly based on the velocity difference at the position of the particle. The coupling method accurately reproduces the long-time tail observed in the velocity auto-correlation function. We also show that the fluctuation-dissipation relation holds between the relaxation of a single particle and the velocity autocorrelation function of fluctuating particles.