A hybrid molecular–continuum method for unsteady compressible multiscale flows

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.

Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats

“…The second type of the methods is based on the domain decomposition into a small accurate atomistic region embedded into a coarser macrosopic model, see, e.g., [15]. In the literature we can find several hybrid models combining particle dynamics with the macroscopic continuum model, see, e.g., the hybrid heterogeneous multiscale methods described in [8,6,9,11,33,34,42], the triple-decker atomisticmesoscopic-continuum method [15], the seamless multiscale methods [7,10], the equation-free multiscale methods [22,23] or the internal-flow multiscale method [2,3]. In [24] a overview of multiscale flow simulations using particles is presented.…”

“…In fact all of these techniques can be considered as hybrid particle-continuum methods under the statistical influence of microscale effects since coefficients in coarse-grained equations are estimated from data that are obtained from microscale simulations. As demonstrated in [3] the sensitivity of the accuracy of a solution, 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 case when processes occurring on a small scale are only loosely coupled with the behavior on a much larger scale and the so-called scale separation in the flow direction occurs, the hybrid multiscale schemes can be successfully applied, see [2,3,8,9,14,33,34,41,42,43] and the references therein.…”

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

“…The DSMC simulations are periodic and are carried out with the aid of a body force, which represents the effective pressure gradient at the sub-domain locations. The micro sub-domains then interact indirectly with each other through the constraints applied by the macroscopic conservation laws [36]. For gradually varying micro-channels with very low Reynolds number, the mass flow rate can be characterized in terms of the sum of its fundamental flow components like Couette and Poiseuille flow rates.…”

Simulation of the head-disk interface gap using a hybrid multi-scale method

“…In the present work, excellent estimates of k i has been obtained from the initial iteration simulations with initialisation and ambient pressure boundary condition values relevant to the HDI gap problem. As discussed in Borg et al (2015), the accuracy of these initial simulations and the obtained k i values only determines the convergence characteristics of the method and does not affect the accuracy of the final IMM results. Equation (3) is then used to estimate the change in mass flow rate between successive iterations, n and n + 1:…”