Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids

TL;DR

This paper develops a method to incorporate thermal fluctuations into the lattice Boltzmann simulation of non-ideal fluids, ensuring accurate equilibrium behavior and practical applicability for fluctuating hydrodynamics.

Contribution

It derives a fluctuation-dissipation theorem within the lattice Boltzmann framework for non-ideal fluids, enabling accurate thermal noise modeling.

Findings

Thermal noise ensures high-accuracy equilibration of all degrees of freedom.

Long wavelength-limit thermal noise suffices for most practical fluctuating hydrodynamics applications.

The method accurately reproduces linearized fluctuating Navier-Stokes equations.

Abstract

We introduce thermal fluctuations in the lattice Boltzmann method for non-ideal fluids. A fluctuation-dissipation theorem is derived within the Langevin framework and applied to a specific lattice Boltzmann model that approximates the linearized fluctuating Navier-Stokes equations for fluids based on square-gradient free energy functionals. The obtained thermal noise is shown to ensure equilibration of all degrees of freedom in a simulation to high accuracy. Furthermore, we demonstrate that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long wavelength-limit.