Cellular automaton fluids 1: Basic theory | Zendy

Stephen Wolfram | Zendy

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Cellular automaton fluids 1: Basic theory

Author(s) -

Stephen Wolfram

Publication year - 1986

Publication title -

journal of statistical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.71

H-Index - 115

eISSN - 1572-9613

pISSN - 0022-4715

DOI - 10.1007/bf01021083

Subject(s) - cellular automaton , lattice gas automaton , kinetic theory , statistical physics , stochastic cellular automaton , boltzmann equation , equations of motion , classical mechanics , mathematics , physics , navier–stokes equations , mathematical analysis , mechanics , thermodynamics , algorithm , compressibility

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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