Lattice-Gas Cellular Automata

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.

Preface
Acknowledgements
1. A simple model of fluid mechanics
2. Two routes to hydrodynamics
3. Inviscid two-dimensional lattice-gas hydrodynamics
4. Viscous two-dimensional hydrodynamics
5. Some simple 3D models
6. The lattice-Boltzmann method
7. Using the Boltzmann method
8. Miscible fluids
9. Immiscible lattice gases
10. Lattice-Boltzmann method for immiscible fluids
11. Immiscible lattice gases in three dimensions
12. Liquid-gas models
13. Flow through porous media
14. Equilibrium statistical mechanics
15. Hydrodynamics in the Boltzmann approximation
16. Phase separation
17. Interfaces
18. Complex fluids and patterns
Appendices
Author Index
Subject Index