  We discuss hybrid atomistic-continuum methods for multiscale hydrodynamic
applications. Both dense fluid and dilute gas formulations are considered. The
choice of coupling method and its relation to the fluid physics is discussed.
The differences in hybrid methods resulting from underlying compressible and
incompressible continuum formulations as well as the importance of timescale
decoupling are highlighted. We also discuss recently developed compressible and
incompressible hybrid methods for dilute gases. The incompressible framework is
based on the Schwarz alternating method whereas the compressible method is a
multi-species, fully adaptive mesh and algorithm refinement approach which
introduces the direct simulation Monte Carlo at the finest level of mesh
refinement.
