Galilean invariance of lattice Boltzmann models

It is well known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity-dependent viscosity. This unphysical dependence violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments.