Atomistic-Continuum Coupling for Liquids

Nanofluidics deals with the study of fluid flows inside and outside nanostructures. Nanoscale flows are often embedded in larger scale systems, when for example nanofluidic channels interface microfluidic domains. Despite the success of atomistic simulation models (like Molecular Dynamics (MD)), their limitations in accessible length and time scales are stringent and allow only the analysis of elementary systems and for short times. As fully atomistic simulations are prohibitively expensive, purely continuum approaches are not possible due to the lack of the correct boundary conditions for the continuum solver (no-slip boundary condition may be not valid at the nanoscale)

Hybrid atomistic-continuum simulations are necessary to study large systems for reasonable times. We develop novel computational concepts based on dynamic control theory for the exchange of information between atomistic and continuum descriptions
Continuum Simulation:
  • Solve for the continuum velocity field subject to appropriate boundary conditions.
MD simulation:
  • Compute the interaction between the atoms including the control boundary force.
  • Impose on the MD system the velocity boundary condition. Move the atoms.
  • Move the interface. bounce the atoms that have hit it, reset it to its initial position to keep a constant frame of reference.
  • Reinsert the particles that have left the domain.
  • Measure the velocities inside the whole MD subdomain and provide them to the continuum solver

Coupling Molecular Dynamics and Navier Stokes solvers
We implement a domain decomposition algorithm, based on the Schwarz alternating method, to couple the MD description of water with a Finite Volume and a Lattice Boltzmann model solving the Navier-Stokes equations.
 
 Liquid Argon flow past a Carbon Nanotube :
 Full MD Simulations
Liquid Argon flow past a Carbon Nanotube :
Hybrid MD - Navier Stokes Simulations

The simulations using the hybrid solvers are (L/l)**3 times faster than the full MD simulations , where L is the size of the continuum and l the size of the atomistic domain in the hybrid solvers [1].
Funding: ETH Zurich

  • T. Werder, J. H. Walther, P. Koumoutsakos, Hybrid atomistic-continuum method for the simulation of dense fluid flow, J. Computational Physics, 205, 373 - 390, 2005 (Abstract) (pdf)
  • Dupuis A., Kotsalis E.M, Koumoutsakos P., Coupling Lattice Boltzmann and Molecular Dynamics Models for Dense Fluids,Physical Review E, 75, 046704, 2007 (Abstract) (pdf)
  • Kotsalis E.M., Walther J.H., Koumoutsakos P., Control of density fluctuations in atomistic-continuum simulations of dense liquids, Physical Review E, 76, 016709, 2007 (Abstract) (pdf)