Control-volume representation of molecular dynamics
File(s)
Accepted version
Author(s)
Smith, ER
Heyes, DM
Dini, D
Zaki, TA
Type
Journal Article
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
θ
i
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.
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
θ
i
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.
Date Issued
2012-05-22
Date Acceptance
2012-03-02
Citation
Physical Review E, 2012, 85, pp.056705-056705
ISSN
1539-3755
Publisher
American Physical Society
Start Page
056705
End Page
056705
Journal / Book Title
Physical Review E
Volume
85
Copyright Statement
© 2012 American Physical Society
Subjects
Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Physics
PHYSICS, FLUIDS & PLASMAS
PHYSICS, MATHEMATICAL
INHOMOGENEOUS FLUIDS
CONTINUUM DYNAMICS
STRESS CALCULATION
SIMULATIONS
TRANSITION
PARTICLE
SOLIDS
TENSOR
FLOWS
math-ph
math.MP
76A02, 74A25
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Fluids & Plasmas
Publication Status
Published