Boundary conditions for the lattice Boltzmann method
Boundary conditions for the lattice Boltzmann method
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DOI：
10.1063/1.868961
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发表时间：
1996-07-01
影响因子：
4.6
通讯作者：
Grunau, DW
中科院分区：
文献类型：
--
作者：
Maier, RS;Bernard, RS;Grunau, DW
当用格子Boltzmann方法(LBM)模拟连续流体流动时，离散质量分布必须满足格子边界上的密度和动量约束。只有当外部(向内指向)晶格链接的数量不超过四个时，这些约束才唯一地确定边界节点的三维(3-D)质量分布。我们提出了计算边界分布的补充规则，当外部链接的数目超过四个时，除了简单的矩形晶格之外，所有的情况都是如此。给出了三维体心立方格子对Poiseuille流、多孔板Couette流、管流和矩形管道流的计算结果。当碰撞之间的平均自由程很大时，二维Poiseuille和Couette缺陷的精度仍然存在，但当平均自由程超过晶格间距时，三维管道流动的精度显著恶化。精度一般随Knudsen数和Mach数的增加而降低，这两个量的乘积是衡量LBM对三维低雷诺数流动适用性的一个有用指标。(C)1996年美国物理研究所。
When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three-dimensional (3-D) mass distribution for boundary nodes only when the number of external (inward-pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3-D body-centered-cubic lattices are presented for Poiseuille flow, porous-plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two-dimensional (2-D) Poiseuille and Couette flaws persists even when the mean free path between collisions is large, but that of the 3-D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3-D low-Reynolds-number flow. (C) 1996 American Institute of Physics.