Oscillatory shear flow in nanochannels via hybrid particle-continuum scheme

This paper provides an application of our hybrid continuum-particle scheme to liquids by considering unsteady shear flows driven by wall oscillations in nano-slots. The particle region (P) adjacent to the wall, is described at the atomistic level by molecular dynamics, while the outer region (C), described by a continuum equation for the transversal momentum, is solved via a finite volume method. Both regions overlap in the ``handshaking'' region where a two-way coupling scheme (C$\to$P and P$\to$C) is implemented. A protocol for the C$\to$P coupling was presented in a previous paper [Delgado-Buscalioni and Coveney, Phys. Rev. E, {\bf 67}, 046704 (2003)]; here we focus on the the P$\to$C counterpart, that is, on the exchange of information from the microscopic to the continuum domain. We first show how to use the finite volume formalism to balance the momentum and mass fluxes across the P$\to$C surface in such a way that the continuity of velocity is ensured. Then we analyse the effect of the fluctuations of the (P) stress tensor on the stability and accuracy of the numerical scheme. This analysis yields a condition which establishes a restriction on the resolution of the flow field that can be described by the hybrid method, in terms of the maximum frequency and wavenumber of the flow.