A hybrid method of continuum and particle dynamics is developed for micro-and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier-Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.

Abstract-A hybrid numerical method of particle-continuum dynamics designed for micro-fluidics is being developed which solves the Navier-Stokes equations in one domain, where the continuum description is still valid, and uses the molecular dynamics in another domain where the continuum description fails. The matching of these two descriptions can be achieved by a constrained particle dynamics in the overlap region, which exchanges the information between the molecular dynamics and the Navier-Stokes equations. However, the existing models for the constraint particle dynamics often have the empirical parameters such as the coupling parameter, the size of overlap domain and the ratio of the time steps for the molecular dynamics and the Navier-Stokes equation. In this paper, we develop a dynamic Langevin equation, and the coupling parameters in the models can be determined by the velocity consistent constraint. The dynamic scheme is used to simulate the sudden-start Couette flows with either slip or no-slip boundary conditions. The results obtained are quantitatively in agreement with the analytical solutions under the no-slip boundary condition and the full MD simulations under the certain slip boundary conditions. This agreement demonstrates the validity of the dynamic Langevin equation.