Higher-order-compact simulation of unsteady flow past a rotating cylinder at moderate Reynolds numbers

Abstract

A recently developed transformation-free higher-order compact finite difference scheme, in non-uniform cylindrical polar grids, is extended and applied to study the temporal development of two-dimensional viscous incompressible flow past a circular cylinder which starts translating and rotating impulsively from rest, for two moderate Reynolds numbers (\(Re\)) for the rotational parameter \(\alpha \) lying between 0.5 and 3. This scheme does not require transformation from the actual flow domain to the computational domain. The scheme is at least third-order accurate in space and second-order accurate in time. To compute the flow, streamfunction–vorticity (\(\psi \)–\(\omega \)) formulation for the two-dimensional Navier–Stokes equations in polar coordinates is used. The drag and lift coefficients along with various other properties related to stream function and vorticity behavior are investigated. The computed results using present scheme for two (\( Re =500, Re =1{,}000\)) Reynolds numbers with different rotational parameters are compared with existing experimental and numerical results. Excellent agreement is obtained in all the cases, and in most of the cases, our numerical results are closer to the experimental ones than previously published numerical results.