Fluctuating lattice Boltzmann

TL;DR

This paper introduces an adaptation of the lattice Boltzmann algorithm that incorporates thermal fluctuations satisfying the fluctuation-dissipation theorem at all wavevectors, enabling more accurate mesoscale fluid simulations.

Contribution

The authors develop a lattice Boltzmann method that includes noise consistent with statistical mechanics at all scales, unlike previous approaches limited to zero wavevector.

Findings

The new algorithm correctly reproduces fluctuations of mass and momentum densities.

It ensures full statistical mechanical consistency in mesoscale simulations.

The method is applicable to fluctuating colloidal hydrodynamics.

Abstract

The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wavevectors $k$. Unlike previous work, which recovers FDT only as $k\to 0$, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.