Computational recipes of transport phenomena in micro and nanofluidics
10.4 HYBRID CONTINUUM-MOLECULAR MODELS
To overcome the limitations of pure molecular models and resolve the inaccuracy of continuum scale description, hybrid continuum-molecular methods have been developed. These hybrid methods bring in the balance between the accuracy of the multiscale phenomena description and the computationally efficiency, bridging the gap between the macroscopic and microscopic length scales and providing a
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unifying description from nanoscale to larger scales. The hybrid methods can be broadly classified into three groups:
• Domain decomposition techniques(DDT) (Flekkoyet al.2000; Drikakis & Kalweit, 2006; Oconnell
& Thompson, 1995)
• Embedding based techniques(EBT) (Ren & Weinan, 2005; Karniadakiset al.2005)
• Equation free approach(EFA) (Samaeyet al.2006; Gear, 1971; Hyman, 2005)
Domain decomposition is appropriate for problems where continuum equations are still valid in large regions of the system, but fail to fully describe the phenomenon in a particular area. In this case two regions are defined, where the one is solved by the continuum solver and the other one, that needs molecular modelling, is solved by molecular dynamics (Drikakis & Kalweit, 2006; Oconnell &
Thompson, 1995). The advantage of this approach is that computationally slow molecular dynamics technique is employed in a small region, which is essential, whereas the rest of the domain is treated with the several orders faster CFD solvers. The idea of the domain decomposition was introduced in 1995 by O’Connell (Oconnell & Thompson, 1995). Since then several coupling approaches have been developed based on the idea of the domain decomposition. These include the relaxation method (Wang
& G, 2007; Oconnell & Thompson, 1995), coupling through state- Schwarz Method (Hadjiconstantinou, 1999; Hadjiconstantinou & Patera, 1997; Hadjiconstantinou, 2005; Werder et al. 2005) and coupling through fluxes (Wagner et al. 2002; Flekkoy et al. 2005). In the embedding multiscale methods, the whole domain is covered with the macroscopic solver and the microscale model, which enters as a refinement, is used to obtain macroscopic properties. An additional property is that the time steps for the macroscale and the microscale are naturally decoupled. These schemes were introduced to handle the time scale constraints introduced by geometrical coupling. The Heterogeneous Multiscale Method when applied to the moving contact line and the Marangoni flow problems inherits the characteristics of the embedding based framework (Ren & Weinan, 2005) Patch Dynamics and equation free approach are techniques initially developed by Yiannis Kevrekidis and James Hyman. The goal of Patch Dynamics is to bridge the time and length scales and predict the macroscale dynamics by performing only microscopic simulation over small batches. More particularly, Patch Dynamics use locally averaged properties for a short period of time and for a small region, in order to advance and predict long space-time scale dynamics. The general framework of the patch dynamics circumvents the need for a closed analytical description of the macroscale systems and delivers macroscopic information.
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