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

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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.