Author | Sone, Yoshio. author |
---|---|
Title | Kinetic Theory and Fluid Dynamics [electronic resource] / by Yoshio Sone |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0061-1 |
Descript | XI, 353 p. online resource |
1 Introduction -- 2 Boltzmann Equation -- 2.1 Velocity distribution function and macroscopic variables -- 2.2 Boltzmann equation -- 2.3 Conservation equations -- 2.4 Maxwell distribution (Equilibrium distribution) -- 2.5 Mean free path -- 2.6 Boundary condition -- 2.7 H theorem -- 2.8 Model equation -- 2.9 Nondimensional expressions I -- 2.10 Nondimensional expressions II -- 2.11 Linearized Boltzmann equation -- 2.12 Boltzmann equation in the cylindrical and spherical coordinate systems -- 3 Linear Theory โ Small Reynolds Numbers -- 3.1 Problem -- 3.2 GradโHilbert solution and fluid-dynamic-type equations -- 3.3 Stress tensor and heat-flow vector of the GradโHilbert solution -- 3.4 Analysis of the Knudsen layer -- 3.5 Slip condition and Knudsen-layer correction -- 3.6 Determination of macroscopic variables -- 3.7 Discontinuity of the velocity distribution function and S layer. -- 3.8 Force and mass and energy transfers on a closed body -- 3.9 Viscosity and thermal conductivity -- 3.10 Summary of the asymptotic theory -- 3.11 Applications -- 4 Weakly Nonlinear Theory โ Finite Reynolds Numbers -- 4.1 Problem -- 4.2 S solution -- 4.3 Fluid-dynamic-type equations -- 4.4 Knudsen-layer analysis -- 4.5 Slip condition and Knudsen layer -- 4.6 Determination of macroscopic variables -- 4.7 Rarefaction effect -- 4.8 Force and mass and energy transfers on a closed body -- 4.9 Summary of the asymptotic theory and a comment on a time-dependent problem -- 4.10 Applications -- 5 Nonlinear Theory I โ Finite Temperature Variations and Ghost Effect -- 5.1 Problem -- 5.2 SB solution -- 5.3 Fluid-dynamic-type equations -- 5.4 Knudsen layer and slip condition -- 5.5 Determination of macroscopic variables -- 5.6 Ghost effect: Incompleteness of the system of the classical gas dynamics -- 5.7 Half-space problem of evaporation and condensation -- 6 Nonlinear Theory II - Flow with a Finite Mach Number around a Simple Boundary -- 6.1 Problem -- 6.2 Hilbert solution -- 6.3 Viscous boundary-layer solution -- 6.4 Knudsen-layer solution and slip condition -- 6.5 Connection of Hilbert and viscous boundary-layer solutions. -- 6.6 Recipe for construction of solution -- 6.7 Discussions -- 7 Nonlinear Theory III โ Finite Speed of Evaporation and Condensation -- 7.1 Problem -- 7.2 Hilbert solution -- 7.3 Knudsen layer -- 7.4 Half-space problem of evaporation and condensation -- 7.5 System of equations and boundary conditions in the continuum limit -- 7.6 Generalized kinetic boundary condition -- 7.7 Boundary-condition functions $$ h_1 \left( {M_n } \right),h_2 \left( {M_n } \right),F_s \left( {M_n ,\overline M _t ,{T \mathord{\left/ {\vphantom {T {T_w }}} \right. \kern-\nulldelimiterspace} {T_w }}} \right) $$ and $$ F_b \left( {M_n ,\overline M _t ,{T \mathord{\left/ {\vphantom {T {T_w }}} \right. \kern-\nulldelimiterspace} {T_w }}} \right) $$ -- 7.8 Applications -- 8 Bifurcation of Cylindrical Couette Flow with Evaporation -- 8.1 Problem -- 8.2 Solution type I -- 8.3 Solution type II -- 8.4 Bifurcation diagram and transition solution -- 8.5 Discussions for the other parameter range -- 8.6 Concluding remark and supplementary comment -- A Supplementary Explanations and Formulas -- A.1 Formal derivation of the Boltzmann equation from the Liouville equation -- A.3 Derivation of the Stokes set of equations -- A.4 Golseโs theorem on a one-way flow -- A.6 Viscosity and thermal conductivity -- A.9 Equation for the Knudsen layer and Bardosโs theorem -- A.10 The boundary condition for the linearized Euler set of equations -- B Spherically Symmetric Field of Symmetric Tensor -- B.1 Problem -- B.3.1 Preparation -- B.3.3 Summary -- B.4 Applications -- B.4.2 Axially symmetric field -- C Kinetic-Equation Approach to Fluid-Dynamic Equations -- C.1 Introduction -- C.2 Exact kinetic-equation approach -- C.3 Discussion on numerical systems