Some of the most powerful tools to solve finite difference equations of computational fluid dynamics are the multigrid method and the domain decomposition approach. The present paper (continuing the authors' earlier paper on related topics [Int. J. Numer. Methods Fluids 15, No. 11, 1333-1355 (1992)]) applies those ideas to treat more difficult hydrodynamic problems, based on the representation of the Navier-Stokes equations by an implicit lowest-order reduced Navier-Stokes system and a purely diffusive, higher order, deferred-corrector in conjunction with a global pressure relaxation as described by the second author and \textit{D. R. Reddy} [J. Comput. Fluids 11, 281-306 (1983; Zbl 0526.76042)]. A pressure flux splitting-based discretization scheme ensures the mass conservation. The magnitude of the pressure gradient is used as an effective criterion in the multigrid refinement strategy. Thus, the results are noteworthy: laminar and turbulent flow calculations (at various Reynolds numbers) for an S-shaped duct, laminar flows through a right-angled bend duct, laminar and turbulent flows in a convergent-divergent nozzle (spanning from low subsonic to supersonic range), and the flow in a two-dimensional inlet configuration at supersonic velocity. Good agreement is obtained with the experimental data.