Isotropy and Galilean invariance of Lattice Boltzmann Method: Theoretical and numerical analysis using oblique dipole benchmark *

Abstract

This work focuses on the two-dimensional, nine-velocity (D2Q9) lattice Boltzmann model. First, we show that the D2Q9 scheme cannot achieve secondorder accuracy unless the cubic velocity terms are neglected, and we explain how some of these parasitic terms can be eliminated. Second, we demonstrate that the standard choice of the equilibrium distribution has no effect on the equivalent PDE at second order. Finally, we numerically investigate the effect of these cubic terms and study different choices of equilibrium distributions using a new benchmark called the Oblique Dipole Benchmark, which describes obliquely propagating 2D vortex dipoles with periodic boundary conditions.