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Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics [Kõva köide]

(Université de Paris VI (Pierre et Marie Curie)), (Massachusetts Institute of Technology)
  • Formaat: Hardback, 320 pages, kõrgus x laius x paksus: 254x180x30 mm, kaal: 806 g, Worked examples or Exercises; 4 Tables, unspecified; 87 Line drawings, unspecified
  • Sari: Collection Alea-Saclay: Monographs and Texts in Statistical Physics
  • Ilmumisaeg: 28-Aug-1997
  • Kirjastus: Cambridge University Press
  • ISBN-10: 052155201X
  • ISBN-13: 9780521552011
Teised raamatud teemal:
Lattice-Gas Cellular Automata: Simple Models of Complex HydrodynamicsSuurem pilt
  • Formaat: Hardback, 320 pages, kõrgus x laius x paksus: 254x180x30 mm, kaal: 806 g, Worked examples or Exercises; 4 Tables, unspecified; 87 Line drawings, unspecified
  • Sari: Collection Alea-Saclay: Monographs and Texts in Statistical Physics
  • Ilmumisaeg: 28-Aug-1997
  • Kirjastus: Cambridge University Press
  • ISBN-10: 052155201X
  • ISBN-13: 9780521552011
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780521552011.html
Märksõnad:
A self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases.

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and references are included.

Arvustused

' this book gives a very good review of the main results obtained in the field of lattice-gas models. It will help newcomers to get started. Many of the results shown in the book are impresssive and should attract people who commonly use standard approaches.' P. Lallemand, European Journal of Mechanics

Muu info

A self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases.
Preface xv(4)
Acknowledgements xix
1 A simple model of fluid mechanics
1(11)
1.1 The lattice gas
1(4)
1.2 Cellular automata
5(1)
1.3 Ramifications
6(2)
1.4 A Boolean analog computer
8(1)
1.5 Notes
9(3)
2 Two routes to hydrodynamics
12(17)
2.1 Molecular dynamics versus continuum mechanics
12(2)
2.2 Mass conservation and the equation of continuity
14(2)
2.3 The Euler equation
16(1)
2.4 Momentum flux density tensor
17(1)
2.5 Viscous flow and the Navier-Stokes equation
18(2)
2.6 Microdynamical equations of the lattice gas
20(3)
2.7 Macrodynamical equations of the lattice gas
23(4)
2.8 Exercises
27(1)
2.9 Notes
28(1)
3 Inviscid two-dimensional lattice-gas hydrodynamics
29(17)
3.1 Homogeneous equilibrium distribution on the square lattice
29(2)
3.2 Low-velocity equilibrium distribution
31(2)
3.3 Euler equation on the square lattice
33(2)
3.4 Fermi-Dirac equilibrium distributions
35(3)
3.5 Euler equation for the hexagonal lattice
38(1)
3.6 The 7-velocity model
39(2)
3.7 Euler equation with rest particles
41(2)
3.8 Exercises
43(1)
3.9 Notes
43(3)
4 Viscous two-dimensional hydrodynamics
46(15)
4.1 Navier-Stokes equation on the square lattice
46(5)
4.2 Hydrodynamic and microscopic scales, and the mean free path
51(1)
4.3 Navier-Stokes equation for the hexagonal model
52(5)
4.4 Viscosity with rest particles
57(1)
4.5 Notes
58(3)
5 Some simple three-dimensional models
61(12)
5.1 Bravais lattices
61(4)
5.2 The FCHC-projection models
65(2)
5.3 Collision operators
67(3)
5.4 Exercises
70(1)
5.5 Notes
70(3)
6 The lattice-Boltzmann method
73(9)
6.1 Basic definitions
73(2)
6.2 Euler equation
75(3)
6.3 Viscous flow
78(1)
6.4 Exercises
79(1)
6.5 Notes
79(3)
7 Using the Boltzmann method
82(9)
7.1 Rescaling to physical variables
82(1)
7.2 Linearized stability and convergence analysis
83(3)
7.3 Forcing the flow
86(1)
7.4 Boundary conditions
86(3)
7.5 Notes
89(2)
8 Miscible fluids
91(15)
8.1 Boolean microdynamics
91(2)
8.2 Convection-diffusion equation
93(1)
8.3 Diffusion coefficient
94(2)
8.4 Lattice-Boltzmann models
96(2)
8.5 Passive tracer dispersion
98(6)
8.6 Notes
104(2)
9 Immiscible lattice gases
106(13)
9.1 Color-dependent collisions
106(4)
9.2 Phase separation
110(1)
9.3 Surface tension
111(5)
9.4 Macroscopic description
116(1)
9.5 Exercises
117(1)
9.6 Notes
117(2)
10 Lattice-Boltzmann method for immiscible fluids
119(9)
10.1 Evolution equations
119(2)
10.2 Calculation of the surface tension
121(3)
10.3 Theory versus simulation
124(1)
10.4 Exercises
125(1)
10.5 Notes
126(2)
11 Immiscible lattice gases in three dimensions
128(13)
11.1 Four familiar steps
128(2)
11.2 The dumbbell method
130(1)
11.3 Symmetric tiling
131(1)
11.4 Surface tension, phase separation, and isotropy
132(5)
11.5 Drag force on a bubble
137(1)
11.6 Exercises
138(1)
11.7 Notes
139(2)
12 Liquid-gas models
141(10)
12.1 Interactions at a distance
141(2)
12.2 Equation of state
143(1)
12.3 Liquid-gas transition
144(3)
12.4 Hydrodynamics
147(2)
12.5 Exercises
149(1)
12.6 Notes
149(2)
13 Flow through porous media
151(17)
13.1 Geometric complexity
151(2)
13.2 Another macroscopic scale
153(2)
13.3 Single-phase flow
155(2)
13.4 Two-phase flow: experiment versus simulation
157(4)
13.5 Two-phase flow: theory versus simulation
161(4)
13.6 Notes
165(3)
14 Equilibrium statistical mechanics
168(16)
14.1 Automata
168(2)
14.2 Probabilistic lattice gases
170(1)
14.3 Markov processes and the first H-theorem
171(3)
14.4 Breaking of ergodicity
174(3)
14.5 Gibbs states
177(3)
14.6 Fermi-Dirac distributions
180(1)
14.7 A summary and critique
181(2)
14.8 Exercises
183(1)
14.9 Notes
183(1)
15 Hydrodynamics in the Boltzmann approximation
184(19)
15.1 General Boolean dynamics
184(2)
15.2 Boltzmann approximation and H-theorems
186(1)
15.3 Chapman-Enskog expansion
187(2)
15.4 First order of the Chapman-Enskog expansion
189(2)
15.5 Second order mass conservation
191(1)
15.6 Second order momentum conservation
191(5)
15.7 Non-uniform global linear invariants
196(2)
15.8 Equilibrium and hydrodynamics with additional invariants
198(3)
15.9 Exercises
201(1)
15.10 Notes
201(2)
16 Phase separation
203(17)
16.1 Phase separation in the real world
203(3)
16.2 Phase transitions in immiscible lattice gases
206(5)
16.3 Structure functions and self-similarity
211(3)
16.4 Growth
214(3)
16.5 Notes
217(3)
17 Interfaces
220(19)
17.1 Surface tension: a Boltzmann approximation
220(4)
17.2 Boltzmann approximation versus simulation
224(2)
17.3 Equilibrium fluctuations and equipartition
226(3)
17.4 Non-equilibrium roughening and dynamical scaling
229(3)
17.5 Fluctuation-dissipation theorem and the frequency spectrum
232(4)
17.6 Notes
236(3)
18 Complex fluids and patterns
239(14)
18.1 Stripes and bubbles
239(3)
18.2 Immiscible three-fluid Boolean mixtures
242(2)
18.3 Three immiscible Boltzmann fluids
244(2)
18.4 A many-bubble model
246(1)
18.5 Microemulsions
247(5)
18.6 Notes
252(1)
Appendix A: Tensor symmetry
253(12)
A.1 Space symmetry: isometry groups
253(2)
A.2 Tensor symmetries
255(2)
A.3 Isotropic tensors
257(2)
A.4 Symmetries of tensors associated with a lattice
259(2)
A.5 Tensors formed with generating vectors
261(1)
A.6 Tensor attached to a given lattice vector
262(2)
A.7 Notes
264(1)
Appendix B: Polytopes and their symmetry group
265(6)
B.1 Polytopes and the Schlafi symbol
265(1)
B.2 The orbit-stabiliser theorem
266(2)
B.3 The structure of the {3,4,3} polytope and its symmetry group
268(2)
B.4 Notes
270(1)
Appendix C: Classical compressible flow modeling
271(5)
C.1 Non-dissipative, inviscid, compressible flow
271(3)
C.2 Compressible viscous flow in three dimensions of space
274(1)
C.3 Generalization to D dimensions of space
275(1)
Appendix D: Incompressible limit
276(5)
D.1 Space, time and velocity scales
276(1)
D.2 Sound waves
277(1)
D.3 Incompressible limit
277(2)
D.4 Viscous case
279(2)
Appendix E: Derivation of the Gibbs distribution
281(3)
Appendix F: Hydrodynamic response to forces at fluid interfaces
284(4)
Appendix G: Answers to exercises
288(2)
Author Index 290(3)
Subject Index 293