Partic. vol. 7 no. 6 pp. 501-506 (December 2009)
doi: 10.1016/j.partic.2009.06.012

A fluctuating lattice-Boltzmann model for direct numerical simulation of particle Brownian motion

Deming Nie^{a, b}, Jianzhong Lin^{a, b, *}

mecjzlin@public.zju.edu.cn

Abstract

A single-relaxation-time fluctuating lattice-Boltzmann (LB) model for direct numerical simulation (DNS) of particle Brownian motion is established by adding a fluctuating component to the lattice-Boltzmann equations (LBEs). The fluctuating term is proved to be the random stress tensor in fluctuating hydrodynamics by recovering Navier–Stokes equations from LBEs through a Chapman–Enskog expansion. A three-dimensional implementation of the model is also presented, along with simulations of a single spherical particle and 125 spherical particles at short times. Numerical results including the mean-square displacement, velocity autocorrelation function and self-diffusion coefficient of particles compare favorably with theoretical results and previous numerical results.

Keywords

Fluctuating hydrodynamics; Lattice-Boltzmann method; Brownian motion; Direct numerical simulation