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Nonlinear Hydrodynamics of Lattice-Gas Automata with Semi-Detailed Balance

Author

Listed:
  • Alberto Suárez

    (Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, C.P. 231, 1050 Brussels, Belgium)

  • Jean Pierre Boon

    (Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, C.P. 231, 1050 Brussels, Belgium)

Abstract

Equations governing the evolution of the hydrodynamic variables in a lattice-gas automaton, arbitrarily far from equilibrium, are derived from the micro-dynamical description of the automaton, under the condition that the local collision rules satisfy semi-detailed balance. This condition guarantees that a factorized local equilibrium distribution (for each node) of the Fermi–Dirac form is invariant under the collision step but not under propagation. The main result is the set of fully nonlinear hydrodynamic equations for the automaton in the lattice-Boltzmann approximation; these equations have a validity domain extending beyond the region close to equilibrium. Linearization of the hydrodynamic equations derived here leads to Green–Kubo formulae for the transport coefficients.

Suggested Citation

  • Alberto Suárez & Jean Pierre Boon, 1997. "Nonlinear Hydrodynamics of Lattice-Gas Automata with Semi-Detailed Balance," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 653-674.
    • Handle: RePEc:wsi:ijmpcx:v:08:y:1997:i:04:n:s0129183197000564
    DOI: 10.1142/S0129183197000564
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