Complete Galilean invariant lattice Boltzmann models

Recently, a general theory of constructing lattice Boltzmann models as an approximation to the Boltzmann equation has been introduced [S. Chikatamarla, I. Karlin, Phys. Rev. Lett. 97 (2006) 190601]. We extend this theory to two dimensions and identify a new complete Galilean invariant lattice Boltzmann model. A general theory of constructing discrete velocity sets in higher dimensions is presented. Further implementation and optimization techniques are discussed.