Asinari Pietro
Department of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016701. doi: 10.1103/PhysRevE.78.016701. Epub 2008 Jul 1.
By realizing the insufficient degree of Galilean invariance of the traditional multiple-relaxation-time collision operators, Geier [Phys. Rev. E 73, 066705 (2006)] proposed to relax differently the moments shifted by the macroscopic velocity, leading to the so-called cascaded lattice Boltzmann method (LBM). This paper points out that (a) the cascaded LBM essentially consists in adopting a generalized local equilibrium in the frame at rest; (b) this new equilibrium does not affect the consistency of LBM; and finally (c) if the raw moments are relaxed in the frame at rest as usual and the number of relaxation frequencies is reduced, the proposed derivation leads to the two-relaxation-time collisional operator with proper polynomial equilibrium.
通过认识到传统多松弛时间碰撞算子的伽利略不变性不足，盖尔 [《物理评论E》73, 066705 (2006)] 提出对由宏观速度偏移的矩进行不同程度的松弛，从而引出了所谓的级联格子玻尔兹曼方法（LBM）。本文指出：(a) 级联LBM本质上在于在静止参考系中采用广义局部平衡；(b) 这种新平衡不影响LBM的一致性；最后 (c) 如果在静止参考系中像往常一样对原始矩进行松弛并且减少松弛频率的数量，所提出的推导会得到具有适当多项式平衡的双松弛时间碰撞算子。
