Lattice gas automata: A tool for exploring dynamical processes

Abstract

The lattice gas automata (LGA) technique as an alternative to the partial differential equation (PDE) approach for studying dynamical processes, including those in reaction-diffusion systems, is reviewed. The LGA approach gained significance after the simulation of Navier-Stokes equation by Hardyet al (1976). In this approach, the dynamics of a system are simulated by constructing a microlattice on each node of which Boolean bits are associated with the presence or absence of particles indistinct velocity states. A complete description involves the composition of anelastic collision operator, areactive collision operator and apropagation operator. The Hardy, de Pazzis and Pomeau (HPP) model does not have the desired isotropy, but its subsequent modification in 1986, known as the Frisch, Hasselacher and Pomeau (FHP) model (Frischet al 1986), has been applied to a variety of nonequilibrium processes. Reaction-diffusion systems have been simulated in a manner analogous to the master equation approach in a continuum framework. The Boltzmann kinetic equation as well as the expected complex features at the macroscopic level are obtained in LGA simulations. An increasing trend is to use real numbers instead of Boolean bits for the velocity states. This gives the lattice Boltzmann (LB) model which is not only less noisy than LGA but also numerically superior to finite-difference approximations (FDAs) to PDEs. The most significant applications of LGA appear to be in the molecular-level understanding of reactive processes.