A review of the development of hybrid atomistic-continuum methods for dense fluids

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.