Journal of Statistical Physics, Vol. 68, Nos. 3/4, 1992. p. 533-566.
Lattice gas automata have received considerable interest for the last several years and possibly may become a powerful numerical method for solving various partial differential equations and modeling different physical
phenomena, because of their discrete and parallel nature and the capability of handling complicated boundaries. In this paper, we present recent studies on the lattice gas model for magnetohydrodynamics. The FHP-type lattice gas model has been extended to include a bidirectional random walk process, which allows well-defined statistical quantities, such as velocity and magnetic field, to be computed from the microscopic particle representation. The model incorporates a new sequential particle collision meth.od to increase the range of useful Reynolds numbers in the model, an improvement that may also be of use in other lattice gas models. In the context of a Chapman-Enskog expansion, the model approximates the incompressible magnetic hydrodynamic equations in the limit of low Mach number and high ft. Simulation results presented here demonstrate the validity Of the model for several basic problems, including sound wave and Alfven wave propagation, and diffusive Kolmogoroff-type flows.