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A three-dimensional numerical study has been performed to investigate double-diffusive, natural convection in a cubic enclosure subject to opposing and horizontal gradients of heat and solute. The flow is driven by buoyancy forces due to temperature and solutal gradients. Constant temperature and concentration are imposed along the two vertical side walls of the cubic enclosure, while the remaining walls are impermeable and adiabatic. The numerical simulations presented here span a wide range of thermal Rayleigh number (10.0<Ra<2×105), buoyancy ratio (−2.0<N<0) and Lewis number (0.1<Le<150) to identify the different flow patterns and bifurcations. Nusselt and Sherwood numbers are presented as functions of the governing parameters. Most of the published results approximate the problem as two dimensional. In the present results we indicate that the double diffusive flow in enclosures with opposing buoyancy forces is strictly three dimensional for a certain range of parameters.

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In recent years, there has been an increasing interest in simulating dynamical phenomena of multiscale systems. This was brought about in large part by the ever growing field of nanotechnology, in which nanodevices are often part of larger systems. Molecular Dynamics (MD) provides a valuable tool for modeling systems at the nanoscale. However, the atomistic modeling of macroscopic problems is still beyond the reach of current MD simulations due to their prohibitive computational requirements. The development of hybrid techniques that combine continuum and atomistic descriptions can alleviate such limitations. This can be accomplished by limiting the use of MD to regions where the atomistic scales need to be resolved, while using a continuum-based solver for the remainder of the domain. The computational savings of such a formulation will strongly depend on the relative size of the MD region to that of the continuum, and the extent of the overlap where information is exchanged between the two subdomains. Such methods are crucial for the proficient advancement and better understanding of nanodevices interacting with microscale systems. In this article, an account of the development of hybrid atomistic-continuum (HAC) models for dense flows is presented. The focus is on domain-decomposition-based HAC models. Here, the domain is divided into a relatively small region where atomistic details are important, and a larger region where the continuum description of the fluid is applicable. Of primary concern is how to accurately couple the atomistic and continuum domains, a challenge that manifests itself in the imposition of boundary conditions in an internally consistent manner. Two main approaches: state variable (Dirichlet), and flux-exchange schemes are analyzed and compared. A review of some applications utilizing such HAC models is also provided.

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