A Model for Hybrid Simulations of Molecular Dynamics and CFD
  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. 
Shugo Yasuda and Ryoichi Yamamoto