We develop a method for multiscale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In this method, the usual lattice-mesh based simulations are applied for the CFD level, but each lattice is associated with a small MD cell that generates a "local stress" according to a "local flow field" given from CFD instead of using any constitutive functions at the CFD level. We carried out hybrid simulations for some elemental flow problems involving simple Lennard-Jones liquids and compared the results with those obtained by usual CFD with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduce the correct flow behavior obtained from usual CFD as long as the mesh size Delta x and the time step Delta t of CFD are not too large compared to the system size l(MD) and the sampling duration t(MD) of MD simulations performed at each time step of the CFD. Otherwise, the simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail. (c) 2008 American Institute of Physics.