Over-Relaxation in Diffusive Integer Lattice Gas

TL;DR

This paper demonstrates that over-relaxation, a technique used in lattice Boltzmann methods to achieve a wide range of transport parameters, can be implemented in integer lattice gases for the diffusion equation, enhancing their flexibility.

Contribution

The authors introduce a method to implement over-relaxation in integer lattice gases by adding a flipping operation, bridging a gap between lattice gas and lattice Boltzmann methods.

Findings

Over-relaxation can be achieved in integer lattice gases.

Adding a flipping operation enables multi-relaxation time schemes.

The approach extends the range of transport parameters in lattice gases.

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.