Lattice Gas Hydrodynamics

A detailed description of lattice-gas hydrodynamics, including theory not presented in other books.

J.-P. Rivet (Author), J. P. Boon (Author)

9780521419444, Cambridge University Press

Hardback, published 4 January 2001

310 pages, 47 b/w illus. 8 tables
25.5 x 18.2 x 2.4 cm, 0.7 kg

'… it may serve as a useful review of the attempts in the last fifteen years, 1986 to present, to apply cellular automata to simulate fluid dynamics.' Zentralblatt MATH

Lattice Gas Hydrodynamics describes the approach to fluid dynamics using a micro-world constructed as an automaton universe, where the microscopic dynamics is based not on a description of interacting particles, but on the laws of symmetry and invariance of macroscopic physics. We imagine point-like particles residing on a regular lattice, where they move from node to node and undergo collisions when their trajectories meet. If the collisions occur according to some simple logical rules, and if the lattice has the proper symmetry, then the automaton shows global behavior very similar to that of real fluids. This book carries two important messages. First, it shows how an automaton universe with simple microscopic dynamics - the lattice gas - can exhibit macroscopic behavior in accordance with the phenomenological laws of classical physics. Second, it demonstrates that lattice gases have spontaneous microscopic fluctuations which capture the essentials of actual fluctuations in real fluids.

1. Introduction
2. Basic ideas
3. Microdynamics: general formalism
4. Microdynamics: various examples
5. Equilibrium statistical mechanics
6. Macrodynamics: Chapman–Enskog method
7. Linearized hydrodynamics
8. Hydrodynamic fluctuations
9. Macrodynamics: projectors approach
10. Hydrodynamic regimes
11. Lattice gas simulations
12. Guide for further reading
Appendix. Mathematical details.

Subject Areas: Fluid mechanics [PHDF], Physics [PH], Nonlinear science [PBWR]