Deriving Lattice Boltzmann Collision Operator Using The Molecular-Dynamics-Lattice-Gas (MDLG) Approach​
December 5 , 2018
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Ms. Aleksandra Pachalieva
Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich
ABSTRACT
We introduce the Molecular-Dynamics-Lattice-Gas (MDLG) method that 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 or lattice Boltzmann methods (LBM) directly without using the standard kinetic theory approach. Through a non-equilibrium ensemble averaging approach, lattice Boltzmann methods can be derived from lattice gas methods. The MDLG analysis is a first principles approach that verify and examine the properties of the lattice gas and lattice Boltzmann methods. Aspects that can be examined include fluctuating, thermal, multi-phase and multicomponent systems. Currently, our quest is to find a universal lattice Boltzmann collision operator that is derived from an underlying Molecular Dynamics simulation. Such collision operator can give significant insight how to construct more stable and robust lattice Boltzmann methods. Until now over-relaxation has been seen as a useful numerical trick without a fundamental physics basis. However, preliminary results from the MDLG analysis show, that we can measure actual over-relaxation from an underlying MD coarsening using the MDLG approach, which means that over-relaxation is indeed a physical effect.
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