The paper presents numerical issues with regard to the development of hybrid molecular-continuum computational methods for macro and nanoscale modelling of nanoflows and materials. The implementation is based on a hybrid solution interface between the continuum and molecular regions. Two different approaches for the transfer of the mass, momentum, and energy fluxes onto the boundary of the molecular dynamics domain, are considered: (a) momentum transfer by force and (b) momentum transfer by velocity reversing. Simulations performed for a static fluid and free flow between molecular and continuum boundaries have shown that in the case of the momentum-transfer-by-force approach, the width of the relaxation zone depends linearly on the number of boundary atoms onto which the force is applied to, and for a free-flow this approach is numerically unstable. On the other hand, the momentum transfer by velocity reversing was found to lead to correct results with regard to energy conservation and variables distribution within the hybrid solution interface and was numerically stable both for static and free-flow test cases.
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