Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation

Abstract

Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (θ = 3) and two dimensions (θ = 1) for the Navier-Stokes equation have been obtained.