Genelarized slip flow theory for stationary micro gas flows and its extension to nonstationary problems

本研究的目的是将传统的流体力学扩展到描述1~1/10000大气压范围内的气体行为。这是现有时间无关情形理论到时间相关情形理论的推广。结果表明，由于气体的可压缩性，在流体型方程中应增加一个新的项。还发现了含时系统所特有的新现象。从技术角度来看，本研究使用了一种新的方法，该方法基于Boltzmann方程的对称性，该方程是描述气体微观特性的基本方程。为了克服一些数学上的困难，最近发展了一种数值方法。

The present research aims at extending the conventional fluid dynamics to describe the gas behavior in the pressure range from 1 to about 1/10000 atmospheric pressure. This is an extension of the existing theory for time-independent cases to the theory for time-dependent cases. It is found that a new term should be added to the fluid-dynamic type equations due to the compressibility of the gas. A new phenomenon that is peculiar to the time-dependent systems are also found. From a technical viewpoint, the present research makes use of a new methodology that is base on a symmetric property of the Boltzmann equation, the equation which is the fundamental equation for a microscopic description of the gas. A numerical method has been newly developed in order to overcome some mathematical difficulties.