Lattice Gas Methods For Partial Differential Equations

Background on Cellular Automata and PDEs

Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau.

Historical Context

Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986.

Purpose of the Book

It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.