Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations

TL;DR

This paper evaluates the Lattice Boltzmann method for fluctuating hydrodynamics, demonstrating its accuracy at small wavelengths and identifying Galilean invariance violations at higher velocities.

Contribution

It provides a detailed analysis of the method's agreement with theory and highlights its advantages over previous implementations regarding wavelength accuracy.

Findings

Excellent agreement with theory at small wavelengths for stationary systems

Cross correlators are less than 0.5% at small wavelengths

Galilean invariance violations increase with higher mean velocities

Abstract

We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al. [Europhys. Lett. 71, 473 (2005)] and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered. This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths. In particular cross correlators vanish to less than 0.5%. For larger mean velocities, however, Galilean invariance violations manifest themselves through errors of a magnitude similar to those of the earlier implementations.