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Title: Theory and Numerical Analysis of the Boltzmann Equation : Theory and Analysis of Rarefied Gas Flows Part I (Chapter 1-3)
Authors: Sone, Yoshio
Author's alias: 曾根, 良夫
Issue Date: 17-Aug-1998
Publisher: Department of Aeronautics and Astronautics Graduate School of Engineering Kyoto University
Table of contents: Preface [p.vii]
1 Boltzmann Equation [p.1]
1.1 Velocity distribution function and macroscopic variables [p.1]
1.2 Boltzmann equation [p.2]
1.3 Conservation equation [p.3]
1.4 Maxwell distribution (Equilibrium distribution) [p.3]
1.5 Mean free path [p.3]
1.6 Boundary condition [p.4]
1.6.1 Simple boundary [p.4]
1.6.2 Interface [p.5]
1.7 H theorem [p.6]
1.8 Model equation [p.7]
1.9 Nondimensional expressions [p.8]
1.10 The linearized Boltzmann equation [p.9]
2 Free Molecular Gas: Highly Rarefied Gas Flows [p.11]
2.1 General solution of free molecular flow [p.11]
2.2 Initial-value problem [p.11]
2.3 Boundary-value problem [p.12]
2.3.1 Free molecular gas around a convex body [p.12]
2.3.2 General case [p.13]
2.4 Statics of a free molecular gas: Effect of thetemperature of the boundary [p.13]
2.4.1 Velocity distribution function [p.14]
2.4.2 Macroscopic variables [p.15]
2.4.3 Flow velocity [p.15]
2.4.4 Principle of superposition [p.16]
2.4.5 Application [p.16]
3 Asymptotic Theory of the Boltzmann System for Small Knudsen Numbers: Slightly Rarefied Gas Flows [p.21]
3.1 Linear theory [p.22]
3.1.1 Problem [p.22]
3.1.2 Grad–Hilbert expansion [p.22]
3.1.3 Stress tensor and heat-flow vector of the Grad–Hilbert solution [p.25]
3.1.4 Analysis of Knudsen layer [p.26]
3.1.5 Slip boundary condition and Knudsen-layer correction [p.28]
3.1.6 Discontinuity of the velocity distribution function and S layer [p.35]
3.1.7 Force and mass and energy transfers on a closed body [p.38]
3.1.8 Summary [p.38]
3.1.9 Supplement–viscosity and thermal conductivity [p.39]
3.2 Weakly nonlinear theory [p.39]
3.2.1 Problem [p.39]
3.2.2 S expansion and fluid-dynamic-type equation [p.40]
3.2.3 Knudsen layer and slip boundary condition [p.44]
3.2.4 Rarefaction effect of a gas [p.48]
3.2.5 Force and mass and energy transfers on a closed body [p.49]
3.2.6 Summary [p.50]
3.3 Nonlinear problem [p.51]
3.3.1 Gas around a simple boundary [p.52]
3.3.2 Flow with strong evaporation or condensation [p.59]
3.4 Application [p.61]
3.4.1 Flows induced by temperature field [p.62]
3.4.2 Negative temperature gradient phenomenon [p.65]
3.5 Essential defect of the continuum gas dynamics [p.66]
Bibliography [p.69]
Appears in Collections:SONE Yoshio

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