Discrete Rotational Symmetry, Moment Isotropy, and High Order Lattice Boltzmann Models

Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe improtant physical effects beyond the isothermal Navier-Stokes fluid regime, higher order isotropy is required. In this paper, we present some basic results on moment isotropy and its relationship to the rotational symmetry of a generating discrete vector set. The anslysis provides a geometric understanding for popular lattice Boltzmann models, while offering a systematic procedure to construct higher order models.