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Lattice-gas cellular automata. Simple models of complex hydrodynamics. (English) Zbl 0931.76004
Collection Aléa-Saclay: Monographs and Texts in Statistical Physics. Cambridge: Cambridge University Press. xxi, 297 p. (1997).
This text is a self-contained, comprehensive introduction to the hydrodynamics of 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. At a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics.
The book addresses three important aspects of lattice gases. First, it shows how such simple idealized microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flows. Last, it illustrates how lattice-gas models and related lattice-Boltzmann methods can be used to solve problems in applications as diverse as flows through porous media, phase separation, and interface dynamics.
This book should be of interest to physicists, mathematicians, engineers, earth scientists, and computer scientists interested in the simulation of fluid dynamics.

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76M28 Particle methods and lattice-gas methods
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
82D15 Statistical mechanics of liquids
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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