Molecular modelling of meso- and nanoscale dynamics is concerned with length and time scales that are in the transition zone from molecular to continuum models. Molecular simulation methods, in particular molecular dynamics (MD), only allow the simulation of relatively small nanoscale systems. Continuum methods, such as computational fluid dynamics (CFD), are applicable at macroscopic scales but cease to be valid for nanoscales. This thesis is focused on hybrid MD-CFD methods with geometrical decomposition that seek to bridge the gap between molecular and continuum modelling. The hybrid solution interface (HSI) establishes the coupling between the molecular and the continuum domain. In this work, different realisation approaches for the HSI, flux and state coupling, are discussed and compared. A detailed investigation on MD flux boundary conditions, the most crucial part of a flux based HSI, is carried out. Different schemes for the imposition of mass, momentum and energy fluxes through convective and viscous transport are presented: direct and indirect flux imposition for convective fluxes; the imposition of momentum fluxes through reflective walls, external forces and the reverse velocity scheme; and imposition of energy fluxes through external forces and an energy transfer scheme. Different combinations of these schemes are compared for standard flow situations. The momentum and energy transfer by an external force creates a relaxation zone at the MD boundary. The characteristics of this zone is investigated in detail and a theoretical model for the density profile has been derived. The reverse velocity scheme has been created as part of this work to avoid the problems encountered when using the external force for the momentum transfer. It is shown that indirect convective flux imposition in conjunction with the reverse velocity scheme gives the best results for the standard flow situations. The scheme is also tested for liquid flow past Carbon nanotubes
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