Studies on the stability of low pressure gases on the basis of kinetic theory

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1.the Benard problem for a rarefied gas is studied numerically on the basis of kinetic theory. The main results are as follows : (1)The range of the parameters for which a steady convection flow exists and steady flow patterns ; 2)transition processes to various steady patterns from various initial conditions ; and 3)stability of multi-roll solutions, which are arrays of several stable single-roll solutions. In (1) there exists a different branch of the stability boundary, not found in the classical gas dynamies.2)The stability of the cylindrical Couette flow for a rarefied flow is studied by the direct simulation Monte Carlo method, and the parameter range where the steady Taylor vortex flow exists and the structure of the flow are clarified. The analysis is extended to the case where there is a temperature difference between the two cylinders. It is found that the temperature difference acts so as to stabikize flow, against the result inferred from the Benard problem.3.The study of the subject 2 is extended to the case where the cylinders are made of the condensed phase of the gas, and a new type of bifurcation of flow is found in a circumferentially and axially uniform flow.4.Asymptotic analysis in the continuum limit of the problem 3 shows that the rerefaction effect which is supposed to vanish in the continuum limit remains in this limit (a ghost effect). This is a striking result showing the incompleteness of the classical (conventional) gas dynamics and necessity of kinetic theory even in the analysis of the continuum limit (a new role of kinetic theory).5.Flows induced around a heated plate in a rarefied gas in a gravitational field is stucied.6.High speed flows of a rarefied gas past a flat plate are studied.