Derivation of lattice Boltzmann from coarse graining Molecular Dynamics and lattice gases

Fluids can be modelled at different scales, on the macroscopic scale through conservation equations for mass, momentum, and energy (i.e. Navier Stokes) and on the microscopic scale through Newtonian mechanics of molecules (or even more rigorous quantum descriptions). These descriptions have to match (at least in principle) and a bridging of those scales is accomplished using kinetic theory through Liouville's equation, the equivalent BBGKY hirarchy, its lowest order approximation the Boltzmann equation and from this, by taking the hydrodynamic limit, the macroscopic conservation equations.

Numerical methods span a similar scale from Molecular Dynamics over lattice gases and lattice Boltzmann to tradtional CFD discretizations of the macroscopic equations. We are focusing in this talk on deriving lattice gas and lattice Boltzmann methods directly from Molecular Dynamics simulations. Such an approach is a promising alternative to deriving lattice Boltzmann methods from demanding a match to macroscopic equations, and this approach suggests interesting alternative implementations. In particular this approach suggested novel integer lattice gases that can recover modern lattice Boltzmann methods as their hydrodynamic limit. We wil report on some recent progress in this area.