Control-volume representation of molecular dynamics - Smith,ER; Heyes,DM; Dini,D; Zaki,TA (Physical Review E, 2012)
A molecular dynamics (MD) parallel to the control volume (CV) formulation of fluid mechanics is developedby integrating the formulas of Irving and Kirkwood [J. Chem. Phys.18, 817 (1950)] over a finite cubic volumeof molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, whichyields an equivalent to Reynolds’ transport theorem for the discrete system. This approach casts the dynamics ofthe molecular system into a form that can be readily compared to the continuum equations. The MD equationsof motion are reinterpreted in terms of a Lagrangian-to-control-volume (LCV) conversion functionθifor eachmoleculei.TheLCVfunction and its spatial derivatives are used to express fluxes and relevant forces across thecontrol 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 [Toddet al.,Phys.Rev.E52, 1627 (1995)]emerges naturally from the treatment. Numerical experiments using the MD CV method are reported forequilibrium and nonequilibrium (start-up Couette flow) model liquids, which demonstrate the advantages ofthe formulation. The CV formulation of the MD is shown to be exactly conservative and is, therefore, ideallysuited to obtain macroscopic properties from a discrete system.