Coupling Lattice Boltzmann and Molecular Dynamics models for dense fluids
Institute of Computational Science, ETH Zurich, 8092 Zurich, Switzerland. February 15, 2006
The advent of nanofabrication provides us today with enhanced capabilities for sensors and actuators. A particular challenge involves the embedding of these de- vices in liquid environments when considering biological applications. The difficulty of carrying out controlled experiments on nanoscale systems makes computational studies potent alternatives for characterizing their properties. Molecular Dynamics (MD) simulations are a useful approach that allow the in- vestigation of such flows by modeling the interactions between atoms. State of the art MD have been used to simulate systems that can be described with up to a few millions atoms and a few nanoseconds. However, as nanoscale devices are often embedded in micro and macroscale systems, the computation of such flows requires a proper integration of atomistic simulations with computational methods suitable for larger scales.
Lattice Boltzmann (LB) models are a class of numerical techniques well suited to probing the behavior of fluids at a mesoscopic scale [1]. In this work we use a LB model which solves the Navier-Stokes equations for an incompressible fluid by following the evolution of distribution functions on a lattice at discrete time steps. LB models for meso/macro scale flow modeling enjoy several advantages. They are highly efficient as there is no need to compute a Poisson equation, pressure being locally available. The computational implementation of LB is straightforward and its local character makes it well suited to parallel computing architectures. Finally, the method can handle easily complex boundaries. In this work we propose a domain decomposition algorithm that allows the coupling between an MD description, of a dense fluid, with an LB model solving the Navier-Stokes equations of an incompressible fluid. The flow domain is decomposed into two overlapping regions: an atomistic and a mesoscopic region. The two scales are matched at an overlapping region via an alternating Schwarz method matching the solutions in the two domains [2]. The present novel MD-LB method is tested on nanoscale Couette and Poiseuille flows. The molecular regime is composed of liquid argon, coupled with an LB solver for the Navier-Stokes regime. We compare the results of the present hybrid method with analytical solutions. We report on the convergence of the hybrid method and demonstrate good quantitative agreement in both test cases. The convergence of the method is analyzed in terms of the overlapping region size and the number of iterations performed within the molecular dynamics model.
References
[1] S. Succi. The Lattice Boltzmann Equation, For
Fluid Dynamics and Beyond. Oxford
University Press, 2001.
[2] T. Werder, J.H. Walther, and P. Koumoutsakos.
Hybrid atomistic-continuum method for the simulation of dense fluid flows. J.
Comp. Phys., 205:373, 2005.