A localized momentum constraint for non-equilibrium molecular dynamics simulations

Area of Science:

• Computational Physics
• Chemical Physics
• Fluid Dynamics

Background:

• Controlling momentum in localized regions of molecular dynamics simulations is crucial for studying non-equilibrium systems.
• Existing methods may lack the precision or flexibility required for arbitrary flow control.
• Bridging continuum and discrete system descriptions necessitates robust constraint methodologies.

Purpose of the Study:

• To develop a method for precise momentum control within a sub-region of molecular dynamics simulations.
• To establish a rigorous mathematical framework for localized momentum constraints.
• To enable the simulation of arbitrary flow fields and boundary coupling between continuum and discrete systems.

Main Methods:

• Derivation from Gauss's principle of least constraint.
• Application of Irving and Kirkwood equations in a weak form using the control volume (CV) procedure.
• Inclusion of an advection term for accurate momentum evolution control.

Main Results:

• A numerical procedure that iteratively converges total momentum in the CV to the target value with machine precision.
• Demonstration of the ability to prescribe arbitrary flow fields in non-equilibrium molecular dynamics.
• Successful application to a boundary-driven flow test case, validating continuum-discrete coupling.

Conclusions:

• The developed localized momentum constraint method precisely controls momentum evolution in subvolumes.
• This methodology provides a rigorous framework for continuum-discrete coupling in simulations.
• The technique is applicable to non-equilibrium molecular dynamics and complex flow simulations.