A Model for Hybrid Simulations of Molecular Dynamics and CFD

TL;DR

This paper introduces a multi-scale hybrid simulation method combining molecular dynamics and CFD, where local MD simulations generate stress data for CFD, enabling more accurate flow modeling at different scales.

Contribution

The paper presents a novel hybrid simulation approach that couples MD and CFD without relying on predefined constitutive relations, validated on simple Lennard-Jones liquids.

Findings

Hybrid simulations accurately reproduce traditional CFD results under proper mesh and time-step conditions.

Large fluctuations occur when CFD mesh size and time-step are too large relative to MD sampling.

Fluctuation properties are analyzed to understand their impact on simulation accuracy.

Abstract

We propose a method for multi-scale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, usual lattice-mesh based simulations are applied for CFD level, but each lattice is associated with a small MD cell which generates a "local stress" according to a "local flow field" given from CFD instead of using any constitutive functions at CFD level. We carried out the hybrid simulations for some elemental flow problems of simple Lennard-Jones liquids and compared the results with those obtained by usual CFDs with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduced the correct flow behavior obtained from usual CFDs as far as the mesh size $\Delta x$ and the time-step $\Delta t$ of CFD are not too large comparing to the system size $l_{\rm MD}$ and the sampling duration $t_{\rm MD}$ of MD simulations performed at each time step of CFDs. Otherwise, simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail.