Journal of Statistical Physics

, Volume 45, Issue 3, pp 471–526

Cellular automaton fluids 1: Basic theory

  • Stephen Wolfram

DOI: 10.1007/BF01021083

Cite this article as:
Wolfram, S. J Stat Phys (1986) 45: 471. doi:10.1007/BF01021083


Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices. Viscosities and other transport coefficients are calculated using the Boltzmann transport equation approximation. Some corrections to the equations of motion for cellular automaton fluids beyond the Navier-Stokes order are given.

Key words

Cellular automataderivation of hydrodynamicsmolecular dynamicskinetic theoryNavier-Stokes equations

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Stephen Wolfram
    • 1
    • 2
  1. 1.The Institute for Advanced StudyPrinceton
  2. 2.Thinking Machines CorporationCambridge
  3. 3.Center for Complex Systems Research, and Departments of Physics, Mathematics and Computer ScienceUniversity of IllinoisChampaign