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| File | Description | Size | Format | |
|---|---|---|---|---|
| LecNote98-KURIR.pdf | 690.63 kB | Adobe PDF | View/Open |
| 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] |
| URI: | http://hdl.handle.net/2433/65065 |
| Appears in Collections: | SONE Yoshio |
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