Hydrodynamic behaviour of Lattice Boltzmann and Lattice BGK models

We present a numerical analysis of the validity of classical and generalized hydrodynamics for Lattice Boltzmann Equation (LBE) and Lattice 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 for BGK models as long as the relaxation time is chosen smaller than or equal to unity. The additional freedom in the choice of collision parameters for LBE models does not seem to give significant improvement.