Kinetic-theoretic studies of the effect of sharp edges of the boundary in low-pressure gases

1.均匀冷却或加热平板边缘诱导稀薄气体流动的研究：在我们以前的论文中，我们用直接模拟蒙特卡罗方法进行了数值分析，结果表明，在放置在稀薄气体中的均匀冷却或加热平板的边缘附近诱导出了相当强的气体流动。在本研究中，为了获得更高可靠性的结果，我们通过对一个动力学方程的精确有限差分分析来研究流动。从而较全面地阐明了气体的行为。特别是在近连续介质情况下，证实了流动比热蠕变流动和热应力引起的流动具有更强的影响。不连续壁温引起的稀薄气体流动的研究：我们研究了当容器壁温具有不连续分布时，在容器内诱导的稀薄气体流动。对于较宽的ra…，流量得到了准确的测量。应用文献[1]中发展的有限差分方法，进一步得到了气体的稀疏度。我们表明，当接近连续介质极限时，虽然有明显流动的区域缩小到壁面温度的间断线，但流动的最大速度趋于有限的值。此外，我们从一个简单的输运方程出发，从数学上阐明了由边界数据中的奇点引起的奇点的传播，该方程具有气体运动论中方程的特征。其他一些基本问题的研究：关注由温度场(热蒸腾)引起的众所周知的流动的另一个方面，我们通过设计管道的温度分布和形状来研究管道中的流动的控制(例如，引起单向流动)。我们还研究了气体混合物连续统极限的基本特征，对它的理解有助于将1和2的分析推广到混合物的情况。较少

1. Study of a rarefied gas flow induced around edges of a uniformly cooled or heated plate :In our previous paper, we showed, by means of a numerical analysis using the direct simulation Monte Carlo method, that a fairly strong gas flow is induced around the edges of a uniformly cooled or heated plate placed in a rarefied gas. In the present study, in order to obtain the result with higher reliability, we investigated the flow by an accurate finite-difference analysis of a kinetic equation. As a result, the behavior of the gas was clarified comprehensively. In particular, it was confirmed that the flow has a stronger effect than the thermal creep flow and the flow induced by the thermal stress in the near continuum case.2. Study of a rarefied gas flow caused by a discontinuous wall temperature :We have investigated a rarefied gas flow induced in a container when the temperature of the wall of the container has a discontinuous distribution. The flow was obtained accurately for a wide ra … More nge of the degree of gas rarefaction by applying the finite-difference method developed in 1. We showed that, as the continuum limit is approached, though the region with an appreciable flow shrinks to the discontinuity line of the wall temperature, the maximum speed of the flow tends to approach a finite value. In addition, we have clarified the propagation of singularities, caused by the singularities in the boundary data, mathematically on the basis of a simple transport equation that possesses the feature of the equations in kinetic theory of gases.3. Studies of some other fundamental problems :Paying attention to another aspect of a well-known flow induced by a temperature field (thermal transpiration), we studied the control of the flow in a pipe (e. g., causing a one-way flow) by devising the temperature distribution as well as the configuration of the pipe. We have also investigated the fundamental features of the continuum limit for gas mixtures, the understanding of which facilitates the extension of the analyses of 1 and 2 to the case of the mixtures. Less