Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics

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Cambridge University Press, Dec 23, 2004 - Science - 297 pages
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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.
  

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Contents

1 A simple model of fluid mechanics
1
2 Two routes to hydrodynamics
12
3 Inviscid twodimensional latticegas hydrodynamics
29
4 Viscous twodimensional hydrodynamics
46
5 Some simple threedimensional models
61
6 The latticeBoltzmann method
73
7 Using the Boltzmann method
82
8 Miscible fluids
91
15 Hydrodynamics in the Boltzmann approximation
184
16 Phase separation
203
17 Interfaces
220
18 Complex fluids and patterns
239
Tensor symmetry
253
Poly topes and their symmetry group
265
Classical compressible flow modeling
271
Incompressible limit
276

9 Immiscible lattice gases
106
10 LatticeBoltzmann method for immiscible fluids
119
11 Immiscible lattice gases in three dimensions
128
12 Liquidgas models
141
13 Flow through porous media
151
14 Equilibrium statistical mechanics
168
Derivation of the Gibbs distribution
281
Hydrodynamic responce to force at fluid interfaces
284
Answers to exercises
288
Author Index
290
Subject Index
293
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About the author (2004)

Stephane Zaleski is Professor of Mechanics at the University Pierre et Marie Curie (UPMC) in Paris and Head of the Jean Le Rond d'Alembert Institute (CNRS UMR 7190).