Hydrodynamic behavior of lattice Boltzmann and lattice Bhatnagar-Gross-Krook models.

We present a numerical analysis of the ranges of validity of classical and generalized hydrodynamics for lattice Boltzmann and lattice Bhatnagar-Gross-Krook (BGK) methods in two and three dimensions, as a function of the collision parameters of these models. Our analysis is based on the wave-number dependence of the evolution operator. Good ranges of validity are found as long as the BGK relaxation time is chosen smaller than or equal to unity. The additional degree of freedom in a two parameter BGK model can give further improvements.