Hybrid methods that couple atomistic and continuum descriptions of liquids are usually based either on a flux-exchange or a state-exchange coupling. The flux-exchange approaches are designed to explicitly conserve mass and momentum fluxes across the atomistic/continuum boundary. The state-exchange approaches, on the other hand, impose in an alternating way the local velocities and densities from both descriptions to be equal at the overlapping domain until the steady state is reached. In this talk, I will present two hybrid approaches, each from the different class. The AdResS-HybridMD method, based on the flux-exchange, concurrently couples atomistic, mesoscopic, and continuum models of the liquid. This triple-scale approach enables the insertion of large molecules into the atomistic domain via a mesoscopic region and it allows for molecular simulations either in the grand-canonical ensemble or under non-equilibrium conditions. The applicability of the second scheme, which bridges flux-based and Schwarz domain decomposition algorithms, will be demonstrated on a three-dimensional multiscale flow simulation of water past a fullerene.
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