Commun. Comput. Phys.,
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Volume 4.


A Continuum-Atomistic Multi-Timescale Algorithm for Micro/Nano Flows

Jin Liu 1*, Shiyi Chen 2, Xiaobo Nie 3, Mark O. Robbins 4

1 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
2 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA; State Key Laboratory for Turbulence and Complex Systems, College of Engineering and Center for Computational Science and Engineering, Peking University, Beijing, China.
3 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA; Exa Corporation, Burlington, MA 01803, USA.
4 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA; Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA.

Received 20 August 2008; Accepted (in revised version) 5 September 2008
Available online 30 September 2008

Abstract

A multi-timescale algorithm is proposed for simulating time-dependent problems in micro- and nano- fluidics. The total simulation domain is spatially decomposed into two regions. Molecular dynamics is employed in the crucial interfacial regions and continuum hydrodynamics is adopted in the remaining bulk regions. The coupling is through ``constrained dynamics'' in an overlap region. Our time scheme is based on the time scale separation between the continuum macro time step and molecular micro time step. This allows the molecular dynamics during one macro time step to be treated as in quasi-steady state. Therefore, molecular simulation is only performed in two shorter time intervals. Through linear extrapolation of macroscopic velocities and re-initialization of particle configurations, we can significantly reduce the total computational cost. We demonstrate and discuss our time algorithm through hybrid simulation of channel flow driven by a sinusoidally moving top wall. Converging results are achieved for cases of large separation of time scale with much less computational cost than with the original hybrid simulation without time extrapolation.


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PACS: 47.11.St, 47.61.-k, 68.08.De, 47.11.Mn
Key words: Multi-scale simulation, domain decompositions, hybrid simulations, micro-/nano-fluidics.

*Corresponding author.
Email: jliu36@jhu.edu (J. Liu), syc@jhu.edu (S. Chen), xiaobo.nie@ gmail.com (X. Nie), mr@jhu.edu (M. O. Robbins)
 

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