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Exploiting timescale separation in micro and nano flows

Lockerby, Duncan A. and Duque-Daza, Carlos A. and Borg, Matthew Karl and Reese, Jason (2011) Exploiting timescale separation in micro and nano flows. In: CECAM Workshop on Multiscale Modelling of Simple and Complex Liquid Flow Using Particle-Continuum Hybrids, 2011-10-05 - 2011-10-07.

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In this paper we describe how timescale separation in micro/nano flows can be exploited for computational acceleration. A modified version of the seamless heterogenous multiscale method (SHMM) is proposed: a multi-step SHMM. This maintains the main advantages of SHMM (e.g., re-initialisation of micro data is not required; temporal gearing (computational speed-up) is easily controlled; and it is applicable to full and intermediate degrees of timescale separation) while improving on accuracy and greatly reducing the number of macroscopic computations and micro/macro coupling instances required. The improved accuracy of the multi-step SHMM is demonstrated for two canonical one-dimensional transient flows (oscillatory Poiseuille and oscillatory Couette flow) and for rarefied-gas oscillatory Poiseuille flow.