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Analytical solution of plane Couette flow in the transition regime and comparison with Direct Simulation Monte Carlo data

机译：过渡状态下飞机库埃特流的解析解及与直接模拟蒙特卡罗数据的比较

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This paper provides analytical solution for the steady-state Couette flow problem in the transition flow regime, while capturing the non-linear Knudsen layer near the walls. Slope at the center obtained from Direct Simulation Monte Carlo (DSMC) data and inherent symmetry in the problem have been utilized for obtaining the solution. A detailed study of the solutions obtained from the linearized super-Burnett, augmented Burnett and R13 equations is presented. The analytical results are compared against DSMC data; good agreement between them is shown till Kn = 10. These are among the first set of analytical solutions in the transition regime. The results indicate that the solution tends to become linear as the Knudsen number increases. The results have allowed formulation of a slip relationship, which can potentially yield more accurate slip velocity than Maxwell's slip model in the transition regime. Our analysis suggests that the Knudsen number envelope over which the R13 and higher-order continuum equations can be employed is substantially extendable.
机译：本文为过渡流态下的稳态库埃特流问题提供了解析解，同时捕获了壁附近的非线性Knudsen层。从直接模拟蒙特卡洛（DSMC）数据获得的中心斜率和问题中的固有对称性已用于获得解决方案。提出了对从线性化超Burnett方程，增强的Burnett方程和R13方程获得的解的详细研究。将分析结果与DSMC数据进行比较;直到Kn = 10为止，它们之间都显示出良好的一致性。这是过渡制度中第一套分析解决方案。结果表明，随着克努森数的增加，解趋于线性化。结果允许建立滑动关系，在过渡状态下，该关系可能比Maxwell的滑动模型产生更精确的滑动速度。我们的分析表明，可以采用R13和高阶连续谱方程的Knudsen数包络是可扩展的。

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