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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.