Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations (Communications in Computational Physics, 2020)
We analyze the Lattice Boltzmann method for the simulation of fluctuatinghydrodynamics by Adhikari et al. [Europhys. Lett., 71 (2005), 473-479] and find thatit shows excellent agreement with theory even for small wavelengths as long as a stationarysystem is considered. This is in contrast to other finite difference and olderlattice Boltzmann implementations that show convergence only in the limit of largewavelengths. In particular cross correlators vanish to less than 0.5%. For larger meanvelocities, however, Galilean invariance violations manifest themselves.