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The aim of hybrid methods in simulations is to communicate regions withdisparate time and length scales. Here, a fluid described at the atomisticlevel within an inner region P is coupled to an outer region C described bycontinuum fluid dynamics. The matching of both descriptions of matter is madeacross an overlapping region and, in general, consists of a two-way couplingscheme (C->P and P->C) which conveys mass, momentum and energy fluxes. Thecontribution of the hybrid scheme hereby presented is two-fold: first it treatsunsteady flows and, more importantly, it handles energy exchange between both Cand P regions. The implementation of the C->P coupling is tested here usingsteady and unsteady flows with different rates of mass, momentum and energyexchange. In particular, relaxing flows described by linear hydrodynamics(transversal and longitudinal waves) are most enlightening as they comprise thewhole set of hydrodynamic modes. Applying the hybrid coupling scheme after theonset of an initial perturbation, the cell-averaged Fourier components of theflow variables in the P region (velocity, density, internal energy, temperatureand pressure) evolve in excellent agreement with the hydrodynamic trends. It isalso shown that the scheme preserves the correct rate of entropy production. Wediscuss some general requirements on the coarse-grained length and time scalesarising from both the characteristic microscopic and hydrodynamic scales.Comment: LaTex, 12 pages, 9 figure

Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow