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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
$\mathfrak{S}$ expansion      453
$\mathfrak{S}$ solution      453
Abramowitz function      535
Absolute Maxwell distribution      551
Accommodation coefficient      8 10
Accommodation coefficient, ghost effect of infinitesimal accommodation coefficient      85
Acoustic equation      152 153
Aerosol, thermophoresis of an aerosol particle      248
Almost everywhere      4
Asymptotic theory for small Knudsen numbers      73
Avogadro constant      618
Axially symmetric tensor field      509
BBGKY hierarchy      491
Benard problem      379 389
BGK equation      see "BKW equation"
Bifurcated flow field under infinitesimal curvature      471
Bifurcated temperature field under infinitesimal velocity      396 410
Bifurcation in the Benard problem (a finite Knudsen number)      379
Bifurcation in the Benard problem (the continuum limit)      391 396
Bifurcation in the half-space problem of evaporation and condensation      355
Bifurcation in the Taylor — Couette problem (the continuum limit)      406 410
Bifurcation of flows between rotating cylinders with evaporation and condensation      417
Bifurcation of flows between rotating cylinders with evaporation and condensation, (axially symmetric and nonuniform case)      430 438
Bifurcation of flows between rotating cylinders with evaporation and condensation, (axially symmetric and uniform case)      418
Bifurcation of the plane Couette flow      466
Binary collision      494
BKW equation      12
BKW equation, integral form of the linearized BKW equation      532
BKW equation, linearized      24
BKW equation, nondimensional      17
BKW equation, nondimensional BKW equation in perturbed variables      22
BKW equation, reduced      544
Boltzmann constant      2 618
Boltzmann equation      3
Boltzmann equation in the cylindrical coordinate system      528
Boltzmann equation in the perturbed velocity distribution function      20
Boltzmann equation in the spherical coordinate system      528
Boltzmann equation, derivation of the      481
Boltzmann equation, exponential (multiplier) form of the      531
Boltzmann equation, integral-equation expression of the      531
Boltzmann equation, integrated form of the      531
Boltzmann equation, linearized      23
Boltzmann equation, nondimensional      14
Boltzmann equation, the moment equation of the      579
Boltzmann equation, the weak form of the      579
Boltzmann hierarchy      491
Boltzmann — Krook — Welander equation      see "BKW equation"
Boundary condition for fluid-dynamic-type equations      see "Slip boundary condition"
Boundary condition for fluid-dynamic-type equations with an infinitesimal curvature term      457 463
Boundary condition, complete-condensation      see "Complete-condensation condition"
Boundary condition, diffuse-reflection      see "Diffuse-reflection condition"
Boundary condition, kinetic      8
Boundary condition, kinetic boundary condition in a scattering kernel (on a simple boundary)      8
Boundary condition, kinetic boundary condition in a scattering kernel (on an interface)      10
Boundary condition, kinetic boundary condition in a scattering kernel for linear problems      553
Boundary condition, kinetic boundary condition in a scattering kernel for linear problems, (on a simple boundary)      25
Boundary condition, kinetic boundary condition in a scattering kernel for linear problems, (on an interface)      26
Boundary condition, Maxwell-type      see "Maxwell-type condition"
Boundary condition, mixed-type boundary condition (on an interface)      see "Mixed-type condition (on an interface)"
Boundary condition, nondimensional kinetic boundary condition in a scattering kernel (on a simple boundary)      17
Boundary condition, nondimensional kinetic boundary condition in a scattering kernel (on an interface)      18
Boundary condition, specular-reflection      see "Specular-reflection condition"
Boundary layer      see "Knudsen layer" "S "Suction "Viscous
Boussinesq approximation, inappropriate use of the Boussinesq approximation in the Taylor — Couette problem      417
Bulk viscosity      6
Burnett equation      612
Cartesian tensor notation      1
Cartesian tensor notation, summation convention in      1
Chapman — Enskog expansion      607
Chapman — Enskog expansion, ill-posed equation in      111 612
Classical fluid dynamics, discrepancy (or incompleteness) of classical fluid dynamics in describing the behavior of a gas in the continuum limit      112 122 416 see "Ghost "Non-Navier
Clausing's equation      41
Collision frequency      7
Collision frequency for the BKW equation      13
Collision integral      4 494
Collision integral for the pseudo inverse-power potential      507
Collision integral with a cutoff potential      508
Collision integral, gain term of the      4 505
Collision integral, isotropic property of      511
Collision integral, linearized      20 498 517
Collision integral, linearized, integral equation defined by the      518 520
Collision integral, linearized, kernel representation of the      523
Collision integral, linearized, parity of the      514
Collision integral, loss term of the      4 505
Collision integral, parity of the      517
Collision term      4
Collision, effect of intermolecular collision on a free molecular flow      63
Complete system of functions      601
Complete-condensation condition      10
Complete-condensation condition, extension of the result for the complete-condensation condition to that for a generalized kinetic boundary condition      344
Complete-condensation condition, linearized      25
Complete-condensation condition, nondimensional      18
Condensation coefficient      10
Condensation coefficient, effect of the      see "Generalized kinetic boundary condition"
Condensation onto a plane condensed phase      294 362
Condensation under a generalized kinetic boundary condition      347
Conservation equation of energy      6
Conservation equation of mass      6
Conservation equation of momentum      6
Conservation equations      6
Conservation equations in perturbed variables      21
Conservation equations, linearized      24
Conservation equations, nondimensional      16
Contact discontinuity      166
Contact layer      166 283 289
Continuum limit, comment on the      148
Continuum limit, world of the      120
Convex function, strictly      558
Couette flow in a quasi-unidirectional flow      196
Couette flow, bifurcation of the plane      466
Couette flow, cylindrical      421
Couette flow, ghost effect in the cylindrical Couette flow with evaporation and condensation      420 427 430
Couette flow, plane Couette flow problem      170
Couette flow, plane Couette flow problem for a free molecular gas      38
Curvature of a boundary and the discontinuity of the velocity distribution function      see "Discontinuity of the velocity distribution function"
Curvature of a boundary in the Knudsen-layer correction      84 88—90 106 107
Curvature of a boundary in the slip condition      84 89 106
Curvature tensor of a boundary      84
Curvature, bifurcation of the plane Couette flow owing to infinitesimal curvature      466
Curvature, ghost effect of infinitesimal curvature      460 466
Curvature, mean curvature of a boundary      89
Curvature, principal curvature of a boundary      84
Cutoff potential, angular      508
Cutoff potential, collision integral with a      508
Cylindrical Couette flow      421
Darrozes — Guiraud inequality      12 558
Darrozes — Guiraud inequality, the linearized-boundary-condition version of the      560
Dense, definition of dense of a subset      500
density      2
Density, nondimensional      16
Density, nondimensional linearized perturbed      23
Density, nondimensional perturbed      20
Detailed-balance condition      546
Diffuse-reflection condition      8
Diffuse-reflection condition, linearized      24
Diffuse-reflection condition, nondimensional      17
Diffusion region      166
Direct simulation Monte Carlo method      see "DSMC method"
Discontinuity of the velocity distribution function      91
Discontinuity of the velocity distribution function around a convex body      91 305 see
Discontinuity of the velocity distribution function, propagation and decay of the discontinuity of the velocity distribution function in time-dependent problems      224 232 283
Drag      see "Force"
DSMC method      571
DSMC method, economy of computation in      591
DSMC method, process of      574
DSMC method, theoretical background of      579
Eddington's epsilon      94
Energy flow from a cylindrical condensed phase      307 310 316 319
Energy flow from a spherical condensed phase      325 326 330
Energy transfer from a convex body to a free molecular gas      33 54
Energy transfer to a boundary (relation to the velocity distribution function)      2
Energy transfer to a closed body      94 109
Energy, conservation equation of      6
Entropy and H function      11
Equilibrium distribution      6 546
Euler region      166
Euler set      6 132 140 144 154
Evaporation and condensation around a sphere      207
Evaporation and condensation between rotating cylinders      417
Evaporation and condensation under a generalized kinetic boundary condition      344
Evaporation and condensation, half-space problem of      140 281 347 355 see
Evaporation and condensation, two-surface problem of      338
Evaporation and condensation, two-surface problem of, under a generalized kinetic boundary condition      352
Evaporation from a cylindrical condensed phase into a gas      315
Evaporation from a cylindrical condensed phase into a gas under a generalized kinetic boundary condition      351
Evaporation from a cylindrical condensed phase into a vacuum      302
Evaporation from a cylindrical condensed phase into a vacuum under a generalized kinetic boundary condition      351
Evaporation from a plane condensed phase      283 356
Evaporation from a plane condensed phase under a generalized kinetic boundary condition      347
Evaporation from a spherical condensed phase into a vacuum      321
Evaporation from a spherical condensed phase into a vacuum under a generalized kinetic boundary condition      351
Exponential (multiplier) form of the Boltzmann equation      531
Extended law of large number      587
Flow      see "Condensation" "Evaporation" "Evaporation
Flow between two parallel plates      181
Flow through a slit      70 183
Flow velocity      2
Flow velocity, nondimensional      16 20
Flow velocity, nondimensional linearized      23
Flow, a uniform flow past a sphere (a sphere with a uniform temperature)      200
Flow, a uniform flow past a sphere (a sphere with an arbitrary thermal conductivity)      207
Flow, bifurcated flow field under infinitesimal velocity      471
Flow, bifurcation of      see "Bifurcation"
Flows induced by temperature fields (flow between elliptic cylinders)      246
Flows induced by temperature fields (Knudsen compressor)      272
Flows induced by temperature fields (nonlinear-thermal-stress flow)      242
Flows induced by temperature fields (thermal creep flow)      233
Flows induced by temperature fields (thermal edge flow)      244
Flows induced by temperature fields (thermal-edge compressor)      277
Flows induced by temperature fields (thermal-stress slip flow)      239
Flows induced by temperature fields (thermophoresis)      248
Flows induced by temperature fields around a sphere with a non-uniform temperature      210
Flows induced by temperature fields through a slit      183
Flows induced by temperature fields, one-way flows induced by temperature fields in a pipe with ditches      261
Flows induced by temperature fields, one-way flows induced by temperature fields in a pipe with shelves      267
Flows through a channel or pipe (Couette flow)      169
Flows through a channel or pipe (Poiseuille flow)      178
Flows through a channel or pipe (quasi-unidirectional flow)      189
Flows through a channel or pipe (straight pipe or channel)      178
Flows through a channel or pipe (thermal transpiration)      178
Flows through a channel or pipe of a free molecular gas      40
Fluid-dynamic part      79 102 113
Fluid-dynamic-type equations (time-dependent problem) with an infinitesimal curvature term      461 465
Fluid-dynamic-type equations (time-dependent problem) with infinitesimal flow velocity      160
Fluid-dynamic-type equations (time-dependent problem), linear problem      150 155
Fluid-dynamic-type equations (time-dependent problem), nonlinear problem      153 160
Fluid-dynamic-type equations (time-dependent problem), weakly nonlinear problem      152 158
Fluid-dynamic-type equations (time-independent problem) with an infinitesimal curvature term      457 462
Fluid-dynamic-type equations (time-independent problem) with infinitesimal flow velocity      117
Fluid-dynamic-type equations (time-independent problem), linear problem      74
Fluid-dynamic-type equations (time-independent problem), nonlinear problem      117 132 140
Fluid-dynamic-type equations (time-independent problem), weakly nonlinear problem      97
Fluid-dynamic-type system, classification of the      144
Flux      2
Force on a closed body      93 109
Force on a heated body or bodies in a free molecular gas      54
Force on a nonuniform temperature      215
Force on a sphere with a nonuniform temperature      211 215
Force, drag (force), on a plate in a free molecular gas      33
Force, drag (force), on a sphere with a uniform temperature      203 204
Force, drag (force), on a sphere with an arbitrary thermal conductivity      218 219
Force, moment of force on a closed body      93 109
Force, thermal, on a sphere with a uniform temperature      252 253
Force, thermal, on a sphere with an arbitrary thermal conductivity      258 260
Free molecular flow      29
Free molecular flow, effect of intermolecular collisions on      63
Free molecular flow, general solution of a      29
Free molecular gas      29
Free molecular gas between reservoirs      33 37 51
Free molecular gas, boundary-value problem of a      30
Free molecular gas, boundary-value problem of a, (effect of the boundary temperature)      45
Free molecular gas, initial and boundary-value problem of a      42
Free molecular gas, initial-value problem of a      30
Free molecular gas, statics of a      45
Free path      7
Free time      7
Free time, mean      7
Froude number      381
Frozen temperature      329
Gain term of the collision integral      4 505
Galilean invariance and ghost effect      468
Gas constant, per mol (numerical data)      618
Gas constant, specific      2
Gas constant, specific, (numerical data)      618
Generalized kinetic boundary condition, extension of the result for the complete condensation condition to that for a      344
Ghost effect      120 123 144 162 420 449
Ghost effect in the Benard problem      389
Ghost effect in the cylindrical Couette flow with infinitesimal evaporation and condensation      420 427 430
Ghost effect in the plane Couette flow      449
Ghost effect in the Taylor — Couette problem      416
Ghost effect of infinitesimal accommodation coefficient      85
Ghost effect of infinitesimal curvature      460 466
Ghost effect of infinitesimal curvature, in the Navier — Stokes system      478
Ghost effect on the flow velocity field      123 420 427 429 460 466
Ghost effect, Galilean invariance and ghost effect      468
Grad hierarchy      483
Grad thirteen-moment equations      605
Grad thirteen-moment method      604
Grad — Bardos theorem      81
Grad — Boltzmann limit      484
Grad — Hilbert expansion      75
Grad — Hilbert solution      75
Green function of the linearized Boltzmann equation      166
H function      11
H function, the equation for the      11
H function, the equation for the, (nondimensional form)      19
H function, the linearized-Boltzmann-equation version of the      27
H function, the linearized-Boltzmann-equation version of the equation for the      27
H theorem, the Boltzmann      12
H theorem, the H theorem for the linearized Boltzmann equation      27
Half-space problem of evaporation and condensation (time-dependent and independent problems)      281
Half-space problem of evaporation and condensation (time-independent problem)      140 355
Half-space problem of evaporation and condensation, effect of the condensation coefficient on the      347
Half-space problem of the linearized Boltzmann equation      81 104
Half-space problem of the nonlinear Boltzmann equation (on a simple boundary)      196
Half-space problem of the nonlinear Boltzmann equation (on an interface)      140 356 362
Half-space problem of transonic condensation      362
Half-space problem of weak evaporation or condensation      356
Half-space problem, bifurcation in the half-space problem of evaporation and condensation      355
Heat-conduction equation, inappropriateness of the heat-conduction equation in describing the behavior of a gas at rest in the continuum limit      122
Heat-flow vector      2
Heat-flow vector of the Grad — Hilbert solution      78
Heat-flow vector of the S solution      101
Heat-flow vector, Knudsen-layer part of      88 90 105 107
Heat-flow vector, nondimensional      16 20
Heat-flow vector, nondimensional linearized      23
Heat-transfer problem      170
Heat-transfer problem for a free molecular gas      39
Heat-transfer problem in a quasi-unidirectional flow      196
Highly rarefied gas      29
Hilbert expansion      138 155
Hilbert expansion, generalized Hilbert expansion by Yu      166 222
Hybrid difference scheme      224
Hybrid finite-difference method      304
Hypersonic approximation      327 612
Ill-posed equation      111
Incompressible fluid, definition of      107
Incompressible Navier — Stokes set of equations      see "Navier — Stokes set"
Initial layer      166
Integral equation, defined by the linearized collision integral      518 520
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