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

Alberto Suárez () and Jean Pierre Boon ()
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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

International Journal of Modern Physics C (IJMPC), 1997, vol. 08, issue 04, 653-674

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.

Keywords: Hydrodynamic Equation; Lattice-Gas Automata; Boltzmann Hypothesis; Nonlinear Response; Green–Kubo Transport Coefficients (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1142/S0129183197000564

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