多弛豫时间碰撞模型的Hermite展开
A multiple-relaxation-time collision model by Hermite expansion
摘要：
Boltzmann方程的Bhatnagar-Gross-Krook（BGK）单弛豫碰撞模型是近年来发展起来的格子BGK（LBGK）方法的基础。在许多情况下，将碰撞描述为分布函数朝向其平衡的均匀松弛过程是过于简单的。基于以前的一系列论文，我们提出了一个碰撞模型制定为独立的埃尔米特系数的不可约分量的参考帧移动与流体的松弛。这些分量对应于旋转群的不可约表示，是可以单独松弛而不违反旋转对称性的最小张量分量。对于二阶、三阶和四阶矩，分别可以存在两个、两个和三个独立的弛豫速率，从而引起剪切和体积粘度、热扩散率和一些在Navier-Stokes-Fourier方程中没有明确显示的高阶弛豫过程。利用二项式变换，在绝对坐标系下计算Hermite系数，避免了插值引起的数值耗散。还提供了广泛的数值验证。
英文摘要：
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.
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