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Cellular automaton fluids 1: Basic theory

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Abstract

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.

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Author notes

  1. Stephen Wolfram

    Present address: Center for Complex Systems Research, and Departments of Physics, Mathematics and Computer Science, University of Illinois, 508 South Sixth Street, 61820, Champaign, Illinois

Authors and Affiliations

  1. The Institute for Advanced Study, Princeton, New Jersey

    Stephen Wolfram

  2. Thinking Machines Corporation, 245 First Street, 02142, Cambridge, Massachusetts

    Stephen Wolfram

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Wolfram, S. Cellular automaton fluids 1: Basic theory. J Stat Phys 45, 471–526 (1986). https://doi.org/10.1007/BF01021083

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  • DOI: https://doi.org/10.1007/BF01021083

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