Deriving LBM Collision Operator using the Coarse-Graining MDLG Approach

The Molecular-Dynamics-Lattice-Gas (MDLG) method by Parsa et. al [1] establishes a direct link between a lattice gas method and the coarse-graining of a Molecular Dynamics (MD) approach. Due to its connection to MD, the MDLG rigorously recovers the hydrodynamics and allows to validate the behavior of the Lattice Gas (LG) or Lattice Boltzmann Methods (LBM) without using the standard kinetic theory approach. This MDLG analysis tool has the potential to verify and examine the properties of the LG and the LBM methods for fluctuating, thermal, multi-phase and multi component systems.

In this talk, we present the MDLG analysis to derive the LBM collision operator from an underlying MD simulation of a system undergoing a simple shear flow. This gives us insights into the physical underpinnings of the LBM collision operator. In particular, over-relaxation has been seen as a useful numerical trick without a fundamental physics basis. However, we obtain over-relaxation directly from the MDLG approach which shows that over-relaxation is indeed a physical effect.


[1] Parsa, M. Reza and Wagner, Alexander J., Phys. Rev. E96, 013314 (2017).