A multiscale method for micro/nano flows of high aspect ratio

Abstract

We develop a new multiscale scheme for simulating micro/nano flows of high aspect ratio in the flow direction, e.g. within long ducts, tubes, or channels, of varying section. The scheme couples conventional hydrodynamic conservation equations for mass and momentum-flux with molecular dynamics (MD) in a unified framework. The method is very much different from common 'domain-decomposition' hybrid methods, and is more related to micro-resolution methods, such as the Heterogeneous Multiscale Method. We optimise the use of the computationally-costly MD solvers by applying them only at a limited number of streamwise-distributed cross-sections of the macroscale geometry. The greater the streamwise scale of the geometry, the more significant is the computational speed-up when compared to a full MD simulation. We test our new multiscale method on the case of a converging/diverging nanochannel conveying a simple Lennard-Jones liquid. We validate the results from our simulations by comparing them to a full MD simulation of the same test case

A hybrid molecular–continuum method for unsteady compressible multiscale flows

“…molecular simulation. This is discussed in more detail in Borg, Lockerby & Reese (2013c), Patronis et al (2013) and Patronis & Lockerby (2014). The internal-flow multiscale method (IMM) of Borg et al (2013c) was developed instead for these kind of geometries, and for isothermal, incompressible, steady flows.…”

“…This is discussed in more detail in Borg, Lockerby & Reese (2013c), Patronis et al (2013) and Patronis & Lockerby (2014). The internal-flow multiscale method (IMM) of Borg et al (2013c) was developed instead for these kind of geometries, and for isothermal, incompressible, steady flows. The method consists of iteratively solving a one-dimensional (1D) steady continuity equation; MD simulations are applied at regularly spaced nodes along the streamwise direction of the domain, with heights chosen to match the local geometry of the full channel (see figure 1).…”

“…Substantial fluid compressibility was evident in the flow simulations in Borg et al (2013c), even for a liquid at extremely low Mach numbers (Gad-El-Hak 2005). In these highly confined flows, viscous-related pressure losses can significantly compress the fluid.…”

“…applied locally in the streamwise direction s, where h(s) is the variation of the channel height along s. Equation (2.1) can also be extended to include streamwise variations in hydrodynamic variables and to channel curvature (see Borg et al 2013c;Patronis et al 2013;Patronis & Lockerby 2014). Provided S L 1 it can safely be assumed that, in small streamwise sections of the channel, the walls are approximately parallel to the centre streamline.…”

“…Provided S L 1 it can safely be assumed that, in small streamwise sections of the channel, the walls are approximately parallel to the centre streamline. This is a local parallel-flow assumption, and it enables the representation of small sections of the channel geometry by micro subdomains with exactly parallel walls and periodicity applied in the streamwise direction (Borg et al 2013c). Consequently, this is a convenient set-up for MD ensembles.…”