Molecular dynamics lattice gas equilibrium distribution function for Lennard-Jones particles

Area of Science:

• Mesoscale fluid dynamics simulation
• Computational physics
• Statistical mechanics

Background:

• The lattice Boltzmann method (LBM) is crucial for fluid dynamics simulations.
• Deriving LBM from molecular dynamics (MD) requires accurate equilibrium distribution functions.
• A single Gaussian distribution is insufficient for particle displacements in certain regimes.

Purpose of the Study:

• To derive a novel LBM equilibrium distribution function.
• To improve the accuracy of mesoscale fluid dynamics simulations.
• To address limitations of the single Gaussian assumption in LBM.

Main Methods:

• Coarse-graining molecular dynamics (MD) simulations into a molecular dynamics lattice gas (MDLG) model.
• Applying a Boltzmann average over the MDLG to derive LBM.
• Utilizing a Poisson weighted sum of Gaussians for particle displacement distribution.

Main Results:

• A new LBM equilibrium distribution function was derived from the Poisson weighted sum of Gaussians model.
• The derived function shows improved agreement with MD data compared to single Gaussian models.
• Comparison with measured MD equilibrium distribution functions and analytical approximations was performed.

Conclusions:

• The Poisson weighted sum of Gaussians provides a more accurate representation of particle displacements in LBM.
• This advancement enhances the fundamental basis of LBM for fluid dynamics.
• The study contributes to progress in mesoscale simulation methods.