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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.
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Рубрика: Физика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2007
Количество страниц: 665
Добавлена в каталог: 09.11.2008
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Предметный указатель
expansion 453
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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