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Sone Y. — Molecular Gas Dynamics Theory, Techniques, and Applications
Sone Y. — Molecular Gas Dynamics Theory, Techniques, and Applications



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Название: Molecular Gas Dynamics Theory, Techniques, and Applications

Автор: Sone Y.

Аннотация:

This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The progress in the field over the last thirty years has greatly enhanced the original theory and has stimulated interesting and critical gas dynamic phenomena and problems. 'Molecular Gas Dynamics,' unique in the literature, presents working knowledge, theory, techniques, and typical phenomena in rarefied gases for theoretical development and application.

Basic theory is developed in a systematic way and presented in a form easily applied for practical use. After presenting various simple flows, such as unidirectional or quasi-unidirectional flows, and flows around a sphere, the author discusses additional topics, including:

* flows induced by temperature fields, which are typical in rarefied gases

* flows with evaporation and condensation

* bifurcation of flows in rarefied gases

* the ghost effect in gases in the continuum limit

An appendix contains many useful fundamental formulas, as well as an explanation of the theoretical background of the direct simulation Monte Carlo method (DSMC method), easily accessible to non-mathematicians, which is not found elsewhere in the literature.

Discovery of the ghost effect has made molecular gas dynamics indispensable to the study of a gas in the continuum limit, which is traditionally treated by classical fluid dynamics. In this work, the ghost effect and non-Navier-Stokes effects are demonstrated for typical examples-Benard and Taylor-Couette problems-in the context of a new framework. A new type of ghost effect is also discussed, and a long-standing problem-bifurcation of the plane Couette flowin classical fluid dynamics-is resolved.

The book is useful for those working in different communities where kinetic theory or fluid dynamics is important: graduate students, researchers, and practitioners in theoretical physics, applied mathematics, and various branches of engineering. The work may be used as a self-study reference or as a textbook in graduate-level courses in fluid dynamics, gas dynamics, molecular gas dynamics, kinetic theory, and applied mathematics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 665

Добавлена в каталог: 09.11.2008

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Предметный указатель
Integral form of the Boltzmann equation      531
Integral-equation expression of the Boltzmann equation      531
Integral-equation expression of the linearized BKW equation      532
Integrated form of the Boltzmann equation      531
Internal energy, specific      2
Inverse-power potential      505
Inverted temperature gradient phenomenon      339
Inviscid region      166
Isotropic operator      509
Jensen inequality      558
Jump condition      83 see
Kernel form of the linearized collision integral      523
Kernel of the linearized collision integral (hard-sphere molecules)      527
Kernel of the linearized collision integral (pseudo inverse-power potential)      527
Kinetic boundary condition      8 see
Knudsen compressor      272
Knudsen layer      79 283
Knudsen layer, analysis of, infinitesimal-curvature problem      455
Knudsen layer, analysis of, linear problem      79
Knudsen layer, analysis of, nonlinear problem      115 130 139
Knudsen layer, analysis of, weakly nonlinear problem      102
Knudsen layer, equation for      80 103 116 131 139 562
Knudsen minimum      183
Knudsen number      15
Knudsen number expansion      see "Grad — Hilbert expansion" "Hilbert "Knudsen-layer "Sexpansion" " "SB "Fluid-dynamic-type "Viscous
Knudsen number expansion, modified      606
Knudsen-layer correction (time-dependent problem)      163
Knudsen-layer correction (time-independent problem), infinitesimal-curvature problem      456
Knudsen-layer correction (time-independent problem), linear problem      79 83 89
Knudsen-layer correction (time-independent problem), nonlinear problem      113 115 130 136 138 139
Knudsen-layer correction (time-independent problem), weakly nonlinear problem      102 104
Knudsen-layer function      85 90 105 106 564
Knudsen-layer function (data)      85 86
Knudsen-layer part      see "Knudsen-layer correction"
Knudsen-layer variables      79 103 115 130
Knudsen-layer-type solution      363
Law of large number      584 586
Law of large number, extended      587
Linear problem (time-dependent problem)      150 155 164
Linear problem (time-independent problem)      74
Linearized collision integral      see "Collision integral"
Liouville equation      481
Local Maxwell distribution      7
Local Maxwell distribution, satisfying the Boltzmann equation      see "Local Maxwell distribution"
Local Maxwellian      see "Local Maxwell distribution"
Loss term of the collision integral      4 505
Lubrication problem in a rarefied gas      196
Mach number      95
Macroscopic variable, relation between a macroscopic variable and the velocity distribution function      2
Macroscopic variable, relation between a macroscopic variable and the velocity distribution function (linearized form)      23
Macroscopic variable, relation between a macroscopic variable and the velocity distribution function (nondimensional variables)      16
Macroscopic variable, relation between a macroscopic variable and the velocity distribution function (perturbed variables)      20
Marginal velocity distribution function      223 303 544
Mass, conservation equation of      6
Mass, flow from a cylindrical condensed phase      307 310 316 319
Mass, flow from a spherical condensed phase      325 326 330
Mass, transfer to a boundary (relation to the velocity distribution function)      2
Mass, transfer to a closed body      94 109
Maxwell distribution      6 546
Maxwell distribution, absolute      551
Maxwell distribution, local      7
Maxwell molecule      506
Maxwell molecule, pseudo      507
Maxwell-type condition      8
Maxwell-type condition in perturbed variables      22
Maxwell-type condition, linearized      24
Maxwell-type condition, nondimensional      17
Maxwellian      see "Maxwell distribution"
Maxwellian, linearized expression for the perturbed local Maxwellian      24
Maxwellian, local      see "Local Maxwell distribution"
Maxwellian, nondimensional local      16
Mean collision frequency      7
Mean collision frequency for a Maxwellian      7 552
Mean free path      7
Mean free path (numerical data)      619
Mean free path (numerical data) for a Maxwellian      7 551
Mean free path (numerical data) for the BKW equation      13
Mean free time      7
Measure zero      4
Micro flow      196
Mixed-type condition (on an interface)      9
Mixed-type condition (on an interface) in perturbed variables      22
Mixed-type condition (on an interface), linearized      25
Mixed-type condition (on an interface), nondimensional      18
Model equation      12
molar mass      618
Molecular chaos      485
Moment method      601
Moment method (Grad thirteen-moment method)      604
Moment method (Mott — Smith analysis of a plane shock wave)      603
Momentum, conservation equation of      6
Momentum, transfer to a boundary (relation to the velocity distribution function)      2
Navier — Stokes set      6 110
Navier — Stokes set of equations for a compressible fluid      108
Navier — Stokes set of equations for an incompressible fluid      107 108 144 159
Navier — Stokes system, discrepancy (or incompleteness or inappropriateness) of the Navier — Stokes system in describing the behavior of a gas in the continuum limit      122 402 see "Ghost "Non-Navier "Non-Navier
Navier — Stokes-type set      99
Negative temperature gradient phenomenon      339
Negative thermophoresis      see "Thermophoresis"
Non-Navier — Stokes effect in the continuum limit      120 144 162 416
Non-Navier — Stokes stress      121 459
Nondimensional expression      13
Nondimensional expression in perturbed variables      19
Nondimensional variables, definition of nondimensional variables I      13
Nondimensional variables, definition of nondimensional variables II (perturbed variables)      19
Nonlinear problem (time-dependent problem)      153 160 164 165
Nonlinear problem (time-independent problem)      112 126 137
Nonlinear-thermal-stress flow      121 242
Nonslip condition      86
Normal temperature      325
One-way flow without average temperature and pressure gradients (pipe with ditches)      261
One-way flow without average temperature and pressure gradients (pipe with shelves)      267
Overall solution      73
Overall solution (linear problem)      79
Overall solution (nonlinear problem)      113 131 138
Overall solution (weakly nonlinear problem)      102
Parallel temperature      325
Parity of the collision integral      517
Parity of the linearized collision integral      514
Peculiar velocity      548
Plane Couette flow      see "Couette flow"
Poiseuille flow      178
Poiseuille flow for a square cross section (data)      269
Poiseuille flow for various cross sections (data)      183
Poiseuille flow in a quasi-unidirectional flow      195
Poiseuille flow, software for      183 607
Prandtl boundary layer      see "Viscous boundary layer"
Prandtl number      96
Pressure      2
Pressure stress      79
Pressure, nondimensional      16
Pressure, nondimensional linearized perturbed      23
Pressure, nondimensional perturbed      20
Pressure, work done by      see "Work"
Probability density function, N-particle      481
Probability density function, truncated      482
Pseudo inverse-power molecule      507
Pseudo inverse-power potential, collision integral for the      507
Pseudo Maxwell molecule      507
Quasi-unidirectional flow      189
Quasi-unidirectional flow, Couette flow in a      196
Quasi-unidirectional flow, hear-transfer problem in a      196
Quasi-unidirectional flow, Poiseuille flow in a      195
Quasi-unidirectional flow, thermal transpiration in a      195
Radiometer      234
Rankine — Hugoniot relation      220
Rayleigh number      382
Reynolds number      95
S expansion      97
S layer      93
S solution      97
Saturated gas pressure      10
Saturated gas pressure (numerical data)      619
SB solution      113
Scattering kernel      8 10
Scattering kernel, nondimensional (on a simple boundary)      17
Scattering kernel, nondimensional (on an interface)      18
Second law of thermodynamics, the negative temperature gradient phenomenon and the      339
Self-adjoint property of the linearized collision operator      21 498
Shock condition      220
Shock layer      221 283
Shock wave      166 219 221
Shock wave, formation and propagation of a      222
Shock wave, weak      369
Similarity solution      540
Simple boundary      8
Slightly rarefied gas      73
Slip boundary condition (time-dependent problem)      163
Slip boundary condition (time-independent problem), linear problem      83 89
Slip boundary condition (time-independent problem), nonlinear problem      117 132 140
Slip boundary condition (time-independent problem), weakly nonlinear problem      102 104
Slip coefficient      85 89 105 106 118 135 564
Slip coefficient (data)      85 90 106 119 135
Slip condition      83 see
Slit, flow through a      70 183
Slowly varying approximation      186
Slowly varying function      487
Slowly varying solution      357 365
Sonic speed      96
Sound wave      152 153
Sound wave, speed of      96
Sound wave, speed of, (numerical data)      619
Specular-reflection condition      8
Specular-reflection condition, linearized      24
Specular-reflection condition, nondimensional      17
Speed of sound      96
Speed of sound (numerical data)      619
Spherical symmetry of the velocity distribution function      324
Spherically symmetric state      324
Spherically symmetric tensor field      509
Standard state      618
Stokes set      76 144 157
Stress tensor      2
Stress tensor of the Grad — Hilbert solution      78
Stress tensor of the S solution      101
Stress tensor, Knudsen — layer part of      88 90 105 107
Stress tensor, nondimensional      16
Stress tensor, nondimensional linearized perturbed      23
Stress tensor, nondimensional perturbed      20
Strouhal number      15
Suction boundary layer      145
Summation convention in Cartesian tensor notation      1
Summational invariant of the collision      499
Supersonic accelerating flow      369
Symmetry relation      5 495
Symmetry relation (nondimensional form)      16
System in the overall region      see "Fluid-dynamic-type equations" "Slip
System in the overall region = equations and boundary conditions for the overall region (flow with a finite Mach number around a simple boundary)      132
Taylor — Couette problem      121 403
Taylor — Couette problem, ghost effect in the      416
Temperature      2
Temperature in the $\theta$ direction      306
Temperature in the r direction      306
Temperature in the z direction      306
Temperature, bifurcated temperature field under infinitesimal velocity      396 410
Temperature, flows induced by temperature fields      see "Flow"
Temperature, nondimensional      16
Temperature, nondimensional linearized perturbed      23
Temperature, nondimensional perturbed      20
Temperature, normal      325
Temperature, parallel      325
Tensor      see "Stress tensor"
Tensor, axially symmetric      509
Tensor, axially symmetric field of a symmetric tensor, general form of      511
Tensor, Cartesian tensor notation      1
Tensor, curvature      84
Tensor, spherically symmetric      509
Tensor, spherically symmetric field of a symmetric tensor, general form of      510
Test function      601
thermal conductivity      6
Thermal conductivity (numerical data)      619
Thermal conductivity, mistaken discussion of thermal conductivity in a free molecular flow      41
Thermal conductivity, positivity of      522
Thermal conductivity, relation between thermal conductivity and mean free path      95
Thermal creep flow      86 121 233
Thermal edge flow      246
Thermal force      249 see
Thermal polarization      88 204 280
Thermal stress      79 102 118 120 121 157
Thermal stress slip flow      88 239
Thermal stress, nonlinear thermal stress flow      121 242
Thermal transpiration      178 261
Thermal transpiration for a square cross section (data)      269
Thermal transpiration for various cross sections (data)      183
Thermal transpiration in a quasi-unidirectional flow      195
Thermal transpiration, software for      183 607
Thermal velocity      548
Thermal-edge compressor      278
Thermal-stress slip flow      88 239
Thermophoresis      249
Thermophoresis, negative      261
Transport coefficient, nondimensional      78 100 117 521
Transport coefficient, nondimensional, (data)      78 102 117 522
Truncated probability density function      482
Two-surface problem of evaporation and condensation      338
Two-surface problem of evaporation and condensation under a generalized kinetic boundary condition      352
Unidirectional flow      see "Flow (flows through a channel or pipe)"
Uniqueness of solution of the boundary-value problem of the linearized Boltzmann equation (a bounded domain)      566
Uniqueness of solution of the boundary-value problem of the linearized Boltzmann equation (a half-space)      see "Grad — Bardos theorem"
Uniqueness of solution of the half-space problem of the nonlinear Boltzmann equation (simple boundary)      see "Half-space problem"
Vacuum pump without a moving part (Knudsen compressor)      272
Vacuum pump without a moving part (thermal-edge compressor)      277
Velocity distribution function      2
Velocity distribution function, discontinuity of the velocity distribution function around a convex body      311 319 331
Velocity distribution function, marginal      see "Marginal velocity distribution function"
viscosity      6
Viscosity (numerical data)      619
Viscosity, mistaken discussion of viscosity in a free molecular flow      41
Viscosity, positivity of      522
Viscosity, relation between viscosity and mean free path      95
Viscous boundary layer      126 128 165 461 464
Viscous boundary layer, equations and boundary conditions for the      133
Viscous boundary layer, natural variables in the      128
Viscous boundary-layer set      144
Viscous boundary-layer solution      129
Viscous region      166
Von Karman relation      96
Wave, formation and propagation of a shock wave      222
Wave, speed of sound      see "Speed of sound"
Wave, weak shock      369
Waves formed by a heated or cooled wall      see "Section 4.8"
Waves in condensing flows onto a plane condensed phase      see "Section 6.1.3"
Waves in evaporating flows from a plane condensed phase      see "Section 6.1.2"
Weak form of the Boltzmann equation      579
Weak shock wave      369
Weak solution of the Euler set      166
Weakly nonlinear problem (time-dependent problem)      152 158 164
Weakly nonlinear problem (time-independent problem)      96
Well-posed problem of a partial differential equation      111
Work, done by pressure in the Grad — Hilbert solution      157
Work, done by pressure in the S solution      107 160
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