Lattice Boltzmann algorithms without cubic defects in Galilean invariance on standard lattices
Lattice Boltzmann algorithms without cubic defects in Galilean invariance on standard lattices
复制标题
DOI：
10.1016/j.jcp.2013.11.021
复制
发表时间：
2014-02-15
影响因子：
4.1
通讯作者：
Dellar, Paul J.
中科院分区：
文献类型：
--
作者：
Dellar, Paul J.
绝大多数晶格玻尔兹曼算法产生一个非伽利略不变粘性应力。这种缺陷是由于在第三矩中缺少一项，即与流体速度的立方成正比的平衡热流张量。该矩不能独立于D2Q9、D3Q15、D3Q19或D3Q27等标准格上的较低矩来指定。最近证明了部分校正可以恢复D2Q9和D3Q27张量积格上的一些缺失的立方项。这种修正恢复了与坐标轴对齐的剪切流的伽利略不变性，但以任意角度倾斜的流动可能显示出比以前更大的误差。这些剩余的误差是由于平衡热流张量的对角线项，不能在标准晶格上修正。然而，对于动量通量张量的对角分量，通过引入具有速度相关碰撞率的矩阵碰撞算子，可以在很大程度上吸收剩余的误差。这完全恢复了均匀密度流的伽利略不变性，总体上减小了伽利略不变性缺陷的幅度，从马赫数的立方到马赫数的五次方。通过与标准和部分修正的晶格玻尔兹曼算法对二维和三维流动的比较，证明了所得算法的有效性。(C) 2013出版的爱思唯尔公司。
The vast majority of lattice Boltzmann algorithms produce a non-Galilean invariant viscous stress. This defect arises from the absence of a term in the third moment, the equilibrium heat flow tensor, proportional to the cube of the fluid velocity. This moment cannot be specified independently of the lower moments on the standard lattices such as D2Q9, D3Q15, D3Q19 or D3Q27. A partial correction has recently been demonstrated that restores some of these missing cubic terms on the D2Q9 and D3Q27 tensor product lattices. This correction restores Galilean invariance for shear flows aligned with the coordinate axes, but flows inclined at arbitrary angles may show larger errors than before. These remaining errors are due to the diagonal terms of the equilibrium heat flow tensor, which cannot be corrected on standard lattices. However, the remaining errors may be largely absorbed by introducing a matrix collision operator with velocity-dependent collision rates for the diagonal components of the momentum flux tensor. This completely restores Galilean invariance for flows with uniform density, and in general reduces the magnitude of the defect in Galilean invariance from Mach number cubed to Mach number to the fifth power. The effectiveness of the resulting algorithm is demonstrated by comparisons with the standard and partially corrected lattice Boltzmann algorithms for two- and three-dimensional flows. (C) 2013 Published by Elsevier Inc.