Introduction to lattice gas cellular automata as a model for simple fluids

Lattice gas cellular automata, introduced by Frisch, Hasslacher and Pomeau in 1986, can be considered as an extremely simplified form of molecular dynamics; for instance, both time and space are discretized. It can be shown that, in a well-defined limit, the behavior of these lattice gases is very close to that of a classical fluid, i.e. the macroscopic equations of motion of the model resemble the Navier-Stokes equations. The advantage of a lattice-gas model over other fluid models is that it is microscopic in character, so it contains all fluctuations and correlations in a natural way. In the present paper we give an introduction to lattice gas cellular automata in their most basic form, presenting the rules, some of the theoretical background, and one application for which these models have been successful.