Fluctuating Multicomponent Lattice Boltzmann Model

TL;DR

This paper extends fluctuating lattice Boltzmann models to multicomponent fluids by incorporating thermal fluctuations at the kinetic level, enabling accurate simulation of complex fluid behaviors with thermal noise.

Contribution

The paper introduces a multicomponent fluctuating lattice Boltzmann model based on the Boltzmann equation, including thermal fluctuations and mean-field interactions.

Findings

Proper thermalization demonstrated in simulations

Model accurately incorporates thermal fluctuations

Extension to non-ideal multicomponent fluids

Abstract

Current implementations of fluctuating lattice Boltzmann equations (FLBE) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem (FDT) directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the ortho-normal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and non-ideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.