Keywords: hybrid molecular-continuum, multiscale modelling, point wise coupling, slip boundary conditions, polymeric fluids, nanofluidics.

A new approach for simulating multiscale phenomena, by incorporating state of the art numerical techniques in a computational fluid dynamics (CFD) - molecular dynamics (MD) hybrid framework is presented. Simulating multiscale phenomena entirely with accurate microscopic description involves an extreme computational effort whereas simulations based only on macroscopic descriptions cannot fully capture the physics of the system. To confront this dilemma multiscale frameworks, called hybrid molecular continuum methods, have been developed to couple the microscopic and macroscopic description of a system and to facilitate the information exchanged.

Several hybrid methods have been developed mainly based on the domain decomposition techniques [1]. Here, two regions are defined, where the first is solved by the continuum solver and the second, that needs molecular modelling, is solved by molecular dynamics. One of the main limitations of these techniques is that they do not decouple the time scales and the computable time. Therefore, the length of computable time scales depends on the time scales of the molecular dynamics solver.

To overcome the former limitations a new family of methods has been developed where the microscale model enters as a refinement to obtain macroscopic properties in a domain, which is basically handled with a macroscopic solver [2]. Thus, the time steps for the macroscale and the microscale are naturally decoupled. In the method pursued by us, named as point wise coupling (PWC), MD simulations are performed around a grid point for a number of time steps at every time step of the macroscopic CFD solver. The MD simulations are constrained from the macroscale by the velocity gradient. In return the shear stresses, measured from the MD simulations, are fed back to the CFD solver.

The new approach is implemented in the in-house fluid flow HIRECOM solver [3] and validated for a number of test cases including the classic solid-liquid slip boundary condition, Couette flows with periodic periodically corrugated surfaces and polymeric fluids under Poiseuille flow. The simulations indicate that PWC effectively decouples the timescales and employs smaller domains for the MD simulations, which leads to increased efficiency in comparison with the classic domain decomposition approach. However, despite the fact that with PWC the molecular simulations are minimised both in time and space the microscopic solver is still the most computationally demanding task of the method.

1

N.G. Hadjiconstantinou, "Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics", Bulletin of the Polish Academy of Sciences: Technical Sciences, 53(4), 335-342, 2005.

2

W. Ren, E. Weinan, "Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics", Journal of Computational Physics, 204(1), 1-26, 2005. doi:10.1016/j.jcp.2004.10.001

3

E. Shapiro, D. Drikakis, "Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. part i. derivation of different formulations and constant density limit", Journal of Computational Physics, 210(2), 584-607, 2005. doi:10.1016/j.jcp.2005.05.001

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