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Relaxation and transport in FCHC lattice gases

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Abstract

FCHC lattice gases are the basic models for studying flow problems in three-dimensional systems. This paper presents a self-contained theoretical analysis and some computer simulations of such lattice gases, extended to include an arbitrary number of rest particles, with special emphasis on non-semi-detailed balance (NSDB) models. The special FCHC lattice symmetry guarantees isotropy of the Navier-Stokes equations, and enumerates the 12 spurious conservation laws (staggered momenta). The kinetic theory is based on the mean field approximation or the nonlinear Boltzmann equation. It is shown how calculation of the eigenvalues of the linearized Boltzmann equation offers a simple alternative to the Chapman-Enskog method or the multi-time-scale methods for calculating transport coefficients and relaxation rates. The simulated values for the speed of sound in NSDB models slightly disagree with the Boltzmann prediction.

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van Coevorden, D.V., Ernst, M.H., Brito, R. et al. Relaxation and transport in FCHC lattice gases. J Stat Phys 74, 1085–1115 (1994). https://doi.org/10.1007/BF02188218

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Key Words

  • Lattice gas automata
  • transport coefficients
  • non-detailed balance
  • staggered invariants
  • Boltzmann equation