Integer Lattice Gas with a sampling collision operator for the fluctuating Diffusion Equation

TL;DR

This paper introduces an efficient integer lattice gas method for the fluctuating diffusion equation, featuring a novel sampling collision operator that enhances stability and computational speed while accurately reproducing the Poisson distribution.

Contribution

The paper presents a new sampling collision operator for integer lattice gases, significantly improving efficiency and stability in simulating the fluctuating diffusion equation.

Findings

Unconditionally stable lattice gas method developed

Accurately recovers Poisson distribution for microscopic densities

Achieves several orders of magnitude speedup

Abstract

We developed an integer lattice gas method for the fluctuating diffusion equation. Such a method is unconditionally stable and able to recover the Poisson distribution for the microscopic densities. A key advance for integer lattice gases introduced in this paper is a new sampling collision operator that replaces particle collisions with sampling from an equilibrium distribution. This can increase the efficiency of our integer lattice gas by several orders of magnitude.