The Navier-Stokes equations are solved for unsteady, vortical flow problems. It is shown that the solution is sensitive to the formulation of the numerical algorithm, due to the appearance of small characteristic scales in time and space. Several aspects of possible influences will be discussed and demonstrated by computational results. Solutions of the flow problems shown are taken from current studies of vortex breakdown, the development of vortex streets and the simulation of jets. © 1993.