We point out that the minimal components of the tensorial moments of the distribution that can be independently relaxed in collision without violating rotational symmetry are its irreducible representation (irrep) of SO(3), and a generic multiple-relaxation-time collision model can be constructed by independently relaxing these components. As the simplest example the irreps of the second moment are the traceless deviatoric stress and an isotropic tensor which is conserved in monatomic gases. Applying the decomposition to the thermal lattice Boltzmann model for polyatomic gases [Phys. Rev. E 77, 035701(R) (2008)], the shear and bulk viscosities are decoupled by two independent relaxation times. The hydrodynamic equation of the model is obtained via Chapman-Enskog calculation and verified by numerical simulation.

中文翻译：

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多重松弛时间碰撞模型的旋转对称

我们指出，可以在碰撞中独立松弛而又不违反旋转对称性的分布张量矩的最小分量是其SO（3）的不可约表示（irrep），而通用的多重松弛时间碰撞模型可以是通过独立地放松这些组件来构造。作为最简单的例子，第二时刻的误差是无痕偏应力和在单原子气体中守恒的各向同性张量。将分解应用于多原子气体的热格子Boltzmann模型[ Phys。启ë 77，035701（R）（2008）]，剪切和本体粘度通过两个独立的弛豫时间解耦。该模型的流体动力学方程通过 Chapman-Enskog计算并通过数值模拟验证。