A multiple-relaxation-time collision model by Hermite expansion

The Bhatnagar-Gross-Krook (BGK) single-relaxation-time collision model for the Boltzmann equation serves as foundation of lattice BGK (LBGK) method developed in recent years. description a uniform relaxation process distribution function towards its equilibrium is, many scenarios, simplistic. Based on previous series papers, we present formulated independent relaxations irreducible components Hermit coefficients reference frame moving with fluid. These components, corresponding to representation rotation group, are minimum tensor that can be separately relaxed without violating symmetry. For 2nd, 3rd and 4th moments respectively, two, two three rates exist, giving rise shear bulk viscosity, thermal diffusivity some high-order not explicitly manifested Navier-Stokes-Fourier equations. Using binomial transform, Hermite evaluated absolute avoid numerical dissipation introduced by interpolation. Extensive verification is also provided.