We describe a hybrid simulation method that captures the combined effects of molecular and hydrodynamic forces which influence macromolecules in solution. In this method, the solvent contribution is accounted for implicitly as the Navier-Stokes equations are solved on a grid using a finite volume method, while we use coarse-grained molecular dynamics to describe the macromolecule. The two systems are coupled by a dissipative Stokesian force. We show that our method correctly captures the hydrodynamically enhanced self-diffusion of a single monomer for different fluids and grid sizes. Moreover, the monomer diffusion does not depend on the monomer mass for the mass range used, as postulated by polymer dynamics theories. We also show that the dynamical properties of the chain do not depend on the grid size a when the chain radius of gyration R_g ≫ a.