  In the Hermite-expansion-based multiple-relaxation-time lattice Boltzmann
(LB) model [Shan & Chen, Int. J. Mod. Phys. C, 18, 635, (2007)], a separate
relaxation time is assigned to each of the tensorial moments of the collision
term. Here we point out that to allow maximum flexibility while preserving the
rotational symmetry of the relaxation physics, separate relaxation times can be
assigned to the components of a tensor corresponding to its irreducible
representation of SO(3) but not any finer. By decomposing the second moment in
the LB model for polyatomic gases [Nie, Shan & Chen, Phys. Rev. E 77, 035701,
(2008)], a model with decoupled shear and bulk viscosity is constructed.
Hydrodynamic equation of the model is obtained via Chapman-Enskog calculation
and verified by numerical simulation.
