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