Connecting lattice Boltzmann methods to physical reality by coarse-graining Molecular Dynamics simulations

The success of lattice Boltzmann methods has been attributed to their mesoscopic nature as a method derivable from a physically consistent microscopic model. Original lattice Boltzmann methods were Boltzmann averages of an underlying lattice gas. In the transition to modern lattice Boltzmann method, this link was broken, and the frequently used over-relaxation to achieve high Reynolds numbers has been seen as lacking physical motivation. While this approach has undeniable utility, it appeared to break the link to any underlying physical reality putting into question the special place of lattice Boltzmann methods among fluid simulation methods. In this letter, we show that over-relaxation arises naturally from physical lattice gases that are derived as a coarse-graining of Molecular Dynamics simulations thereby re-affirming the firm foundation of lattice Boltzmann methods in physical reality.