Supersonic lattice gases: Restoration of Galilean invariance by nonlinear resonance effects

Energy-conserving multispeed lattice simulations of fluid behavior are shown to be capable of maintaining approximate macroscopic Galilean invariance at supersonic flow velocities. This result is due to a resonance between macroscopic flow velocity and discrete microscopic velocities, a nonlinear effect which was suppressed in previous power series expansion derivations of the macroscopic flow equations. The effect is demonstrated by numerical evaluation of the pressure tensor components for two-dimensional lattices with 25, 57, and 129 bits per lattice site and by simulations of a two-dimensional free shear decay flow up to Mach 1.9.