A fluctuating lattice-Boltzmann method with improved Galilean invariance

TL;DR

This paper introduces a novel fluctuating lattice Boltzmann method with enhanced Galilean invariance by using a velocity-dependent collision matrix, improving accuracy in non-equilibrium flow simulations.

Contribution

The paper develops a new multi-relaxation time lattice Boltzmann method with a velocity-dependent collision matrix, addressing fundamental Galilean invariance issues.

Findings

The new method significantly improves Galilean invariance.

It maintains near-original computational efficiency with a small numerical trick.

Applicable to non-equilibrium systems with strong flow fields.

Abstract

In this paper we show that standard implementations of fluctuating Lattice Boltzmann methods do not obey Galilean invariance at a fundamental level. In trying to remedy this we are led to a novel kind of multi-relaxation time lattice Boltzmann methods where the collision matrix depends on the local velocity. This new method is conceptually elegant but numerically inefficient. With a small numerical trick, however, this method recovers nearly the original efficiency and allows the practical implementation of fluctuating lattice Boltzmann methods with significantly improved Galilean invariance. This will be important for applications of fluctuating lattice Boltzmann for non-equilibrium systems involving strong flow fields.