Simulating fluid flows in micro and nano devices: the challenge of non-equilibrium behaviour
Simulating fluid flows in micro and nano devices: the challenge of non-equilibrium behaviour
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DOI：
10.1166/jctn.2009.1263
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发表时间：
2009-10
影响因子：
--
通讯作者：
J. Reese;Yonghao Zhang
中科院分区：
文献类型：
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作者：
J. Reese;Yonghao Zhang
我们回顾了微米和纳米尺度非平衡（稀薄）气流建模的一些最新进展，重点关注两种不同但有前途的方法：扩展流体动力学模型和晶格玻尔兹曼方法。在简要阐述非平衡在微米和纳米尺度气流中带来的挑战之后，我们首先转向扩展流体动力学，概述了伯内特型模型的有效放弃，转而采用高阶正则化矩方程。我们表明，具有正确构建的边界条件的后一个模型可以很好地捕获关键的非平衡流动现象。然后，我们回顾了在微观尺度上应用传统的纳维-斯托克斯-傅立叶 (NSF) 流体动力学模型所需的边界条件，描述了如何使用二阶麦克斯韦型条件来补偿固体表面附近的一些非平衡流动行为。虽然扩展流体动力学由于其固有的复杂性尚未广泛用于实际流动问题，但我们以最近的“唯象扩展流体动力学”（PEH）技术的概述结束本节，本质上是 NSF 方程，其缩放以包含接近固体表面的非平衡行为，这为工程模型提供了前景。对格子玻尔兹曼 (LB) 框架内非平衡的理解并不像在流体动力学框架中那样先进，尽管 LB 可以借用后者正在开发的一些技术，特别是某些流体特性的近壁缩放，这些技术已被证明在 PEH 中有效。我们描述了通过这种修改，标准二阶 LB 方法如何在预测一些稀疏现象方面显示出希望，这表明，与开发具有大量离散速度的高阶离格 LB 方法不同，具有近壁缩放的简化高阶 LB 方法可能被证明与模拟工具一样有效。
We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool.