Lattice Gas Hydrodynamics in Two and Three Dimensions
Uriel Frisch
CNRS, Observatoire de Nice, BP 139, 06003 Nice Cedex, France,
Dominique d'Humières
CNRS, Laboratoire de Physique de l'École Normale Supérieure,
24 rue Lhomond, 75231 Paris Cedex 05, France
Brosl Hasslacher
Thoeretical Division and Center for Nonlinear Studies,
Los Alamos National Laboratories, Los Alamos, NM 87544, USA
Pierre Lallemand
CNRS, Laboratoire de Physique de l'École Normale Supérieure,
24 rue Lhomond, 75231 Paris Cedex 05, France
Yves Pomeau
CNRS, Laboratoire de Physique de l'École Normale Supérieure,
24 rue Lhomond, 75231 Paris Cedex 05, France
and
Physique Théorique, Centre d'Études Nucléaires de Saclay,
91191 Gif-sur-Yvette, France
Jean-Pierre Rivet
Observatoire de Nice, BP 139, 06003 Nice Cedex, France
and
École Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France
Abstract
Hydrodynamical phenomena can be simulated by discrete lattice gas models obeying cellular automata rules [1,2]. It is here shown for a class of D-dimensional lattice gas models how the macrodynamical (large-scale) equations for the densities of microscopically conserved quantities can be systematically derived from the underlying exact "microdynamical" Boolean equations. With suitable restrictions on the crystallographic symmetries of the lattice and after proper limits are taken, various standard fluid dynamical equations are obtained, including the incompressible Navier-Stokes equations in two and three dimensions. The transport coefficients appearing in the macrodynamical equations are obtained using variants of the fluctuation-dissipation theorem and Boltzmann formalisms adapted to fully discrete situations.
