Integer lattice gases, Molecular Dynamics Lattice Gas and an alternative derivation of the lattice Boltzmann method

We report on recent progress in two related areas:

1) that lattice Boltzmann methods can be derived rigorously from Molecular Dynamics simulations through a coarse graining approach (MDLG) that maps Molecular Dynamics onto an integer lattice gas. This gives insights into the surprisingly large correct fluctuations for non-ideal gases and fluids as well as the physical meaning of over-relaxation in lattice Boltzmann.

2) the efficient implementation of integer lattice gases that can be considerably more efficient than the equivalent lattice Boltzmann implementation.