Multiscale simulation of nanofluidic networks of arbitrary complexity

We present a hybrid molecular-continuum method for the simulation of general nanofluidic networks of long and narrow channels. This builds on the multiscale method of Borg et al. (Microfluid Nanofluid 15(4):541–557, 2013; J Comput Phys 233:400–413, 2013) for systems with a high aspect ratio in three main ways: (a) the method has been generalised to accurately model any nanofluidic network of connected channels, regardless of size or complexity; (b) a versatile density correction procedure enables the modelling of compressible fluids; (c) the method can be utilised as a design tool by applying mass-flow-rate boundary conditions (and then inlet/outlet pressures are the output of the simulation). The method decomposes the network into smaller components that are simulated individually using, in the cases in this paper, molecular dynamics micro-elements that are linked together by simple mass conservation and pressure continuity relations. Computational savings are primarily achieved by exploiting length-scale separation, i.e. modelling long channels as hydrodynamically equivalent shorter channel sections. In addition, these small micro-elements reach steady state much quicker than a full simulation of the network does. We test our multiscale method on several steady, isothermal network flow cases and show that it converges quickly (within three iterations) to good agreement with full molecular simulations of the same cases.