Over-Relaxation in Diffusive Integer Lattice Gas

Abstract

One of the most striking draw-backs of standard lattice gas methods over lattice Boltzmann methods is a much more limited range of transport parameters that can be achieved. It is common for lattice Boltzmann methods to use over-relaxation to achieve arbitrarily small transport parameters in the hydrodynamic equations. Here, we show that it is possible to implement over-relaxation for integer lattice gases. For simplicity we focus here on lattice gases for the diffusion equation. We demonstrate that adding a flipping operation to lattice gases results in a multi-relaxation time lattice Boltzmann scheme with over-relaxation in the Boltzmann limit.

arXiv comment5 pages, 1 figure

References in corpus (6)

• Integer Lattice Gases
• Lattice Gas with Molecular Dynamics Collision Operator
• A Fluctuating Lattice Boltzmann Method for the Diffusion Equation
• Integer Lattice Gas with Monte Carlo collision operator recovers the entropic lattice Boltzmann method with Poisson distributed fluctuations
• Validity of the Molecular-Dynamics-Lattice-Gas Global Equilibrium Distribution Function
• Integer Lattice Gas with a sampling collision operator for the fluctuating Diffusion Equation