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We analyze the Lattice Boltzmann method for the simulation of fluctuatinghydrodynamics by Adhikari et al. [Europhys. Lett. 71, 473 (2005)] and find thatit shows excellent agreement with theory even for small wavelengths as long asa stationary system is considered. This is in contrast to other finitedifference and older lattice Boltzmann implementations that show convergenceonly in the limit of large wavelengths. In particular cross correlators vanishto less than 0.5%. For larger mean velocities, however, Galilean invarianceviolations manifest themselves through errors of a magnitude similar to thoseof the earlier implementations.

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