Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer
Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer
复制标题
微尺度气流的格子玻尔兹曼方程分析：弛豫时间、边界条件和克努森层
DOI：
10.1080/10618560802253100
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发表时间：
2008-01-01
影响因子：
1.3
通讯作者：
Zheng, Chuguang
中科院分区：
文献类型：
--
作者：
Guo, Zhaoli;Zheng, Chuguang
在这项工作中，我们应用晶格玻尔兹曼方程（LBE）与多重弛豫时间（MRT）来模拟Poiffille流在滑移流区。我们详细分析了LBE的离散扩散和组合反弹-镜面反射边界条件、边界处的离散效应以及滑流区Poiseuille流松弛时间的确定。特别地，我们利用MRT-LBE模型实现了二阶滑移边界条件，并利用解析解验证了我们对Knudsen数Kn ≤ 0.2的滑移Poietonille流的数值结果。我们的分析表明，格点Bhatnagar-Gross-Krook（BGK）模型不能得到正确的结果，Poiquillille流在滑流区。我们还讨论了在微流动中扩展Knudsen层的LBE的可能性。
In this work, we apply the lattice Boltzmann equation (LBE) with multiple relaxation times (MRTs) to simulate the Poiseuille flow in the slip flow regime. We analyse in detail the discrete diffusive and combined bounce-back-specular-reflection boundary conditions for the LBE, the discrete effects at the boundary, and determinations of the relaxation times for the Poiseuille flow in the slip flow regime. In particular, we implement second-order slip boundary conditions with the MRT–LBE model and validate our numerical results for the slip Poiseuille flow with the Knudsen number Kn ≤ 0.2 by using the analytic solution. Our analysis shows that the lattice Bhatnagar–Gross–Krook (BGK) model cannot yield correct results for the Poiseuille flow in the slip-flow regime. We also discuss the possibilities of extending the LBE for the Knudsen layer in micro flows.