On the use of several compact methods for the study of unsteady incompressible viscous flow round a circular cylinder

Fourth order accurate methods of mehrstellen type are compared to second order accurate methods for the solution of the unsteady incompressible Navier-Stokes equations in their vorticity stream function formulation. These methods are applied to the study of separated flow around a circular cylinder at several Reynolds numbers. The impulsively started cylinder at Re = 200 and 550, is considered without symmetry restrictions. The features illustrated include the bulge phenomenon at Re = 200, the occurrence of secondary vortices depending on the schemes used at Re = 550, and of twin secondary vortices at Re = 3000. The Karman vortex street is investigated at Re = 200 with a uniform flow in the far field and with superimposed motions of the cylinder. In this last case, a frequency analysis has allowed a critical examination of results pertaining to locked-in situations with respect to confinement effects.