  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.
