Analytical and numerical studies of nonlinear problems of a low density gas

本课题的研究成果概括如下：（1）伴随着蒸发和凝结的流动本文从动力学理论出发，分析了长期存在的问题，即从圆柱形或球形凝结相进入真空或进入其蒸汽所占空间的蒸发流动，阐明了流动的综合特征，特别是圆柱形流动与球形流动的决定性区别。B.绕体流动进行绕体流动数值分析的各种困难，即，解决了气体中速度分布函数的不连续性、复杂的碰撞积分和无限域问题。C.温度场诱导的流动从标准Boltzmann方程出发，对球形颗粒的热泳问题进行了全Knudsen数范围的精确分析，阐明了该问题的综合特征。对在热泳中起重要作用的热蠕变流进行了实验研究，并证实了基本的理论结果。D.激波根据硬球分子的标准Boltzmann方程，精确地分析了平面激波的结构。E. Boltzmann方程解的基本性质分析和理解稀薄气体流动中的各种重要性质，即，本文阐明了凸体周围气体速度分布函数间断的存在性及其与Knudsen层底部S层的关系、高稀薄气体定常解的数学性质、近均匀平衡流中的非线性效应及其实例。

The result of this project is summarized as follows.A.Flows accompanying evaporation and condesationLong-standing problems, evaporating flows from a cylindrical or spherical condensed phase into a vacuum or into a space occupied with its vapor, are analyzed on the basis of the kinetic theory, and the comprehensive feature of the flows, especially the decisive difference between the flow from a cylinder and that from the sphere, are clarified. The drag problem of a volatile particle is also studied.B.Flows around a bodyVarious difficulties in carrying out numerical analysis of flows around a body, i.e., discontinuity of the velocity distribution function in a gas, the complicated collision integral, and infinite domain problems, are resolved. With aid of the result, various important flows around bodies are analyzed accurately for the whole range of the Knudsen number.C.Flows induced by temperature fieldsThe thermophoresis problem for a spherical particle is analyzed accurately on the basis of the standard Boltzmann equation for the whole range of the Knudsen number, and its comprehensive feature are clarified. The thermal creep flow, which plays an important role in the thermophoresis, is examined experimentally, and fundamental theoretical results are confirmed.D.Shock wavesThe structure of plane shock waves is analyzed accurately on the basis of the standard Boltzmann equation for hard-sphere molecules. Shock waves that appears in expanding flows are also analyzed.E.Fundamental properties of solutions of Boltzmann equationVarious important properties in analyzing and understanding rarefied gas flows, i.e., existence of discontinuity of the velocity distribution function in a gas around a convex body and its relation with the S layr at the bottom of Knudsen layr, mathematical properties of steady solutions of a highly rarefied gas, nonlinear effects in a nearly uniform equilibrium flow and thier examples, are clarified.