A multiple-relaxation-time collision model for nonequilibrium flows

Abstract

Despite yielding correct hydrodynamics in the continuum limit, the Bhatnagar–Gross–Krook collision model is too simplistic to model the full details of the collision, which becomes increasingly important as the quasi-equilibrium assumption breaks down. In a recent phenomenological collision model, independent relaxation rates are assigned to the components of the tensorial Hermite expansion of the distribution corresponding to the irreducible representations of SO(3), yielding arguably the most general form of multirelaxation without violating rotation symmetry. Here we show that by using the relaxation rates obtained analytically from Boltzmann collision term with Maxwell molecular model, lattice Boltzmann method yields results in good agreement with the accurate fast spectral method in simulation of the spontaneous Rayleigh–Brillouin scattering problem. The hydrodynamically insignificant relaxation rates of the higher moments are found to be significant as the Knudsen number increases. These results suggest that with properly tuned relaxation rates, the collision model could potentially mimic the behavior of arbitrary collision kernels.