Integer Lattice Gases

Abstract

We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invariance in these models. We show that this prefactor can be set to unity in the generalized model, therby effectively restoring galilean invariance. Moreover, we derive an expression for the kinematic viscosity, and show that it tends to decrease with the maximum number of particles allowed in each direction, so that higher Reynolds numbers may be achieved. Finally, we derive expressions for the statistical noise and the Boltzmann entropy of these models.

23 pages, LaTeX with six PostScript figures included using epsf

References in corpus (4)

• Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part I. Theoretical Foundation
• Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part II. Numerical Results
• Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine
• Correlations and Renormalization in Lattice Gases

Cited by in corpus (8)

• Integer Lattice Gas with Monte Carlo collision operator recovers the entropic lattice Boltzmann method with Poisson distributed fluctuations
• Large fluctuations in non-ideal coarse-grained systems
• Validity of the Molecular-Dynamics-Lattice-Gas Global Equilibrium Distribution Function
• Integer Lattice Gas with a sampling collision operator for the fluctuating Diffusion Equation
• Quantum emulation of classical dynamics
• Over-Relaxation in Diffusive Integer Lattice Gas
• Adaptive Lattice Gas Algorithm: Classical and Quantum implementations
• Integer Lattice Gas with a sampling collision operator for the fluctuating Navier-Stokes Equation