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New Features in Visual Dynamics 3.0

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Control-volume representation of molecular dynamics.

E R Smith¹, D M Heyes, D Dini

¹Department of Mechanical Engineering, Imperial College London, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

A new molecular dynamics (MD) method reformulates fluid mechanics using control volumes (CV). This approach accurately calculates macroscopic properties from discrete molecular systems, offering advantages for fluid dynamics simulations.

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Area of Science:

Computational fluid dynamics
Molecular dynamics simulations
Statistical mechanics

Background:

Continuum fluid mechanics equations are well-established but challenging to apply directly to molecular systems.
Bridging the gap between discrete molecular behavior and continuum fluid dynamics is crucial for accurate simulations.
Existing methods for calculating properties from molecular dynamics have limitations.

Purpose of the Study:

To develop a control volume (CV) formulation for molecular dynamics (MD) that parallels continuum fluid mechanics.
To create a method that accurately computes macroscopic properties from discrete molecular systems.
To establish a conservative formulation for MD simulations.

Main Methods:

Integrating Irving and Kirkwood's formulas over finite cubic volumes of molecular dimensions.
Expressing the Lagrangian molecular system in terms of an Eulerian CV, yielding a discrete equivalent to Reynolds' transport theorem.
Reinterpreting MD equations of motion using a Lagrangian-to-control-volume (LCV) conversion function.

Main Results:

The MD CV formulation provides a direct comparison to continuum fluid dynamics equations.
The method naturally incorporates relationships between local pressures calculated by volume averaging and the method of planes.
Numerical experiments on model liquids demonstrate the formulation's advantages in equilibrium and nonequilibrium flows.
The CV formulation of MD is shown to be exactly conservative.

Conclusions:

The developed MD CV formulation offers a robust framework for simulating fluid dynamics at the molecular level.
This conservative approach is well-suited for deriving macroscopic properties from discrete molecular simulations.
The method provides a unified perspective linking molecular dynamics and continuum fluid mechanics.