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Control-volume representation of molecular dynamics

E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki*

  • Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom

  • *t.zaki@imperial.ac.uk
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Phys. Rev. E 85, 056705 – Published 22 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.056705

Abstract

A molecular dynamics (MD) parallel to the control volume (CV) formulation of fluid mechanics is developed by integrating the formulas of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] over a finite cubic volume of molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, which yields an equivalent to Reynolds’ transport theorem for the discrete system. This approach casts the dynamics of the molecular system into a form that can be readily compared to the continuum equations. The MD equations of motion are reinterpreted in terms of a Lagrangian-to-control-volume (LCV) conversion function ϑi for each molecule i. The LCV function and its spatial derivatives are used to express fluxes and relevant forces across the control surfaces. The relationship between the local pressures computed using the volume average [Lutsko, J. Appl. Phys. 64, 1152 (1988)] techniques and the method of planes [Todd et al., Phys. Rev. E 52, 1627 (1995)] emerges naturally from the treatment. Numerical experiments using the MD CV method are reported for equilibrium and nonequilibrium (start-up Couette flow) model liquids, which demonstrate the advantages of the formulation. The CV formulation of the MD is shown to be exactly conservative and is, therefore, ideally suited to obtain macroscopic properties from a discrete system.

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Phys. Rev. E 85, 056705– Published 22 May, 2012
  • Received 13 October 2011

©2012 American Physical Society

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