Overrelaxation in a diffusive integer lattice gas

One of the most striking drawbacks 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 multirelaxation time lattice Boltzmann scheme with over-relaxation in the Boltzmann limit.