Lattice gases and cellular automata

Abstract

We review the class of cellular automata known as lattice gases, and their applications to problems in physics and materials science. The presentation is selfcontained, and assumes very little prior knowledge of the subject. Hydrodynamic lattice gases are emphasized, and non-lattice-gas cellular automata -even those with physical applications -are not treated at all. We begin with a review of lattice gases as the term is understood in equilibrium statistical physics. We then discuss the various methods that have been proposed to simulate hydrodynamics with a lattice gas, leading up to the 1986 discovery of a lattice gas for the isotropic NavierStokes equations. Finally, we discuss variants of lattice-gas models that have been used for the simulation of complex fluids.

Equilibrium Properties of the Cellular Automata Models for Traffic Flow in a Single Lane

“…This class of dynamical systems, now known as lattice gas models, consist of a regular lattice, each site of which can have a finite number of states representing the directions of motion of the gas particles, and evolves in discrete time steps obeying a set of homogeneous local rules which define the system dynamics. These rules are defined in such a way that the physical laws of conservation of mass, momentum and energy are fulfilled during the propagation and collisions of the gas particles (Boghosian, 1999). Typically, only the nearest neighbours are involved in the updating of any lattice site.…”

“…The Kadanoff-Swift model exhibits many features of real fluids, such as sound-wave propagation, and long-time tails in velocity autocorrelation functions. As the authors noted, however, it does not faithfully reproduce the correct motion of a viscous fluid (Boghosian, 1999). The next advance in the lattice modelling of fluids came in the mid 1970's, when J. Hardy, O. de Pazzis and Y. Pomeau introduced a new lattice model (the HPP model, named for its authors) with a number of innovations that warrant discussion here (Hardy et al, 1973(Hardy et al, , 1976.…”

“…At the time, this was not considered a problem, since the real purpose of these models was to study the statistical physics of fluids, and both models could do this well. Traditional computational fluid dynamicists, however, were not inclined to take notice of this as a serious numerical method unless and until a way was found to remove the unphysical anisotropy (Boghosian, 1999). Thirteen years passed from the introduction of the HPP model to the solution of the anisotropy problem in 1986 by Uriel Frisch, Brosl Hasslacher and Yves Pomeau , and simultaneously by Stephen Wolfram (Wolfram, 1986).…”

A cellular automata model for liquid distribution in trickle bed reactors

“…This is to optimize the speed of the model solution. A more complicated Lattice-Boltzmann (LB) model, with some similarities in its structure, can be used instead if more information is needed (Succi, 2001;Boghosian, 1999). Despite the fact that LB models are computationally quite efficient, the present model is faster due to simpler single-event modeling, while being at least as suitable for parallel computing as the LB model.…”

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

“…However, due to its particulate nature, it suffered from considerable stochastic noise and required coarse-graining and other modifications to be mapped onto many systems of interest. It remains useful for exploring concepts of statistical mechanics and dynamical systems theory [4,5], but is less popular for conventional CFD problems.…”