Abstract
We present an internal-flow multiscale method (‘unsteady-IMM’) for compressible, time-varying/unsteady flow problems in nano-confined high-aspect-ratio geometries. The IMM is a hybrid molecular–continuum method that provides accurate flow predictions at macroscopic scales because local microscopic corrections to the continuum-fluid formulation are generated by spatially and temporally distributed molecular simulations. Exploiting separation in both time and length scales enables orders of magnitude computational savings, far greater than seen in other hybrid methods. We apply the unsteady-IMM to a converging–diverging channel flow problem with various time- and length-scale separations. Comparisons are made with a full molecular simulation wherever possible; the level of accuracy of the hybrid solution is excellent in most cases. We demonstrate that the sensitivity of the accuracy of a solution to the macro–micro time-stepping, as well as the computational speed-up over a full molecular simulation, is dependent on the degree of scale separation that exists in a problem. For the largest channel lengths considered in this paper, a speed-up of six orders of magnitude has been obtained, compared with a notional full molecular simulation.
Highlights
From rapid point-of-care health diagnostics to alleviating the global problem of diminishing fresh water supplies, nanofluidics is expected to be an important component of many future technological applications
A molecular–continuum method for unsteady compressible multiscale flows 389 (i) The flow occurs in nano-confined geometries that are typically of large aspect ratio
In circumstances where there is no length-scale separation in some parts of the channel flow configuration, i.e. where SL 1 at an arbitrary s, the parallel-flow assumption no longer holds and a suitable alternative is to model the local geometry by an exact Molecular dynamics (MD) representation that is coupled to the other IMM micro elements
Summary
From rapid point-of-care health diagnostics to alleviating the global problem of diminishing fresh water supplies, nanofluidics is expected to be an important component of many future technological applications. We present a simulation technique for problems that are scale-separated in the flow direction (i.e. between the scales over which continuum variables vary and the microscopic molecular scales), but not in the direction perpendicular to the flow For this type of high-aspect-ratio flow geometry we can evaluate the degree of streamwise length-scale separation by a dimensionless number: SL(s) =. In circumstances where there is no length-scale separation in some parts of the channel flow configuration, i.e. where SL 1 at an arbitrary s, the parallel-flow assumption no longer holds and a suitable alternative is to model the local geometry by an exact MD representation that is coupled to the other IMM micro elements This has been demonstrated in Borg, Lockerby & Reese (2013b) and Stephenson et al (2014) for junction components in network channel flows. The separation s of micro elements is assumed uniform along s for numerical simplicity
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