LATTICE METHODS AND THEIR APPLICATIONS TO REACTING SYSTEMS

The recent development of the lattice gas automata method and its exte nsion to the lattice Boltzmann method have provided new computational schemes for solving a variety of partial differential equations and mo deling chemically reacting systems. The lattice gas method, regarded a s the simplest microscopic and kinetic approach which generates meanin gful macroscopic dynamics, is fully parallel and can, as a result, be easily programmed on parallel machines. In this paper, we introduce th e basic principles of the lattice gas method and the lattice Boltzmann method, their numerical implementations and applications to chemicall y reacting systems. Comparisons of the lattice Boltzmann method with t he lattice gas technique and other traditional numerical schemes, incl uding the finite difference scheme and the pseudo-spectral method, for solving the Navier-Stokes hydrodynamic fluid flows will be discussed. Recent developments of the lattice gas and the lattice Boltzmann meth od and their applications to pattern formation in chemical reaction-di ffusion systems, multiphase fluid flows and polymeric dynamics will be presented.