Guo Zhaoli, Qin Jishun, Zheng Chuguang
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China and Beijing Computational Science Research Center, Beijing 100084, China.
State Key Laboratory of Enhanced Oil Recovery, Research Institute of Petroleum Exploration and Development, Beijing 100083, P. R. China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):013021. doi: 10.1103/PhysRevE.89.013021. Epub 2014 Jan 28.
It is a challenging task to model nonequilibrium gas flows within a continuum-fluid framework. Recently some extended hydrodynamic models in the Navier-Stokes formulation have been developed for such flows. A key problem in the application of such models is that suitable boundary conditions must be specified. In the present work, a generalized second-order slip boundary condition is developed in which an effective mean-free path considering the wall effect is used. By combining this slip scheme with certain extended Navier-Stokes constitutive relation models, we obtained a method for nonequilibrium gas flows with solid boundaries. The method is applied to several rarefied gas flows involving planar or curved walls, including the Kramers' problem, the planar Poiseuille flow, the cylindrical Couette flow, and the low speed flow over a sphere. The results show that the proposed method is able to give satisfied predictions, indicating the good potential of the method for nonequilibrium flows.
在连续介质流体框架内对非平衡气体流动进行建模是一项具有挑战性的任务。最近，针对此类流动，已经开发了一些纳维-斯托克斯形式的扩展流体动力学模型。应用此类模型的一个关键问题是必须指定合适的边界条件。在本工作中，开发了一种广义二阶滑移边界条件，其中使用了考虑壁面效应的有效平均自由程。通过将这种滑移方案与某些扩展的纳维-斯托克斯本构关系模型相结合，我们获得了一种用于具有固体边界的非平衡气体流动的方法。该方法应用于几种涉及平面或曲面壁的稀薄气体流动，包括克莱默斯问题、平面泊肃叶流动、圆柱库埃特流动以及球体上的低速流动。结果表明，所提出的方法能够给出令人满意的预测，表明该方法在非平衡流动方面具有良好的潜力。
