A transformation-free HOC scheme for incompressible viscous flows past an impulsively started circular cylinder

In this paper, we present a higher order compact scheme for the unsteady two-dimensional (2D) Navier-Stokes equations on nonuniform polar grids specifically designed for the incompressible viscous flows past a circular cylinder. The scheme is second order accurate in time and at least third order accurate in space. The scheme very efficiently computes both unsteady and time-marching steady-state flow for a wide range of Reynolds numbers (Re) ranging from 10 to 9500 for the impulsively started cylinder. The robustness of the scheme is highlighted when it accurately captures the vortex shedding for moderate Re represented by the von Kármán street and the so called α and β-phenomena for higher Re. Comparisons are made with established numerical and experimental results and excellent agreement is found in all the cases, both qualitatively and quantitatively.