  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 (\CV) conversion function $\vartheta_{i}$, for
each molecule $i$. The \CV 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 (VA,
Lutsko, J. Appl. Phys 64, 1152 (1988)) techniques and the Method of Planes
(MOP, 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 non-equilibrium (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.
