How should lattice Boltzmann methods fluctuate? Evidence from the Molecular Dynamics Lattice Gas method

We recently developed a coarse-graining method for Molecular Dynamics (MD) methods that represent MD results as effective lattice gas methods. We call this coarse-graining procedure Molecular Dynamics Lattice Gas (MDLG). We derived an effective equilibrium distribution that can be related to the lattice Boltzmann equilibrium distribution. For an ideal gas we expect that the occupation numbers are independent and Poisson distributed. Our MDLG method recovers these expected fluctuations for dilute gases, but correlations were observed for higher densities. We discuss how these results should affect the development of fluctuating lattice Boltzmann methods beyond the ideal gas behavior.