A high order explicit method for the computation of flow about a circular cylinder

In this paper a finite difference method for computing the solutions of the incompressible Navier-Stokes equations for flow about a circular cylinder in two dimensions is presented. A stream function/vorticity formulation of the equation is used and the numerical method incorporates recent developments in the computation of vorticity boundary conditions as well as far field boundary conditions. Three schemes are described, one of second order accuracy, one of fourth order accuracy, and a hybrid method which is second order accurate in the computation of the vorticity transport and fourth order accurate in the determination of the stream function. Fully resolved solutions for flow pasta cylinder have been computed over a range of Reynolds numbers from 1000 to 9500. Comparisons are made between the results obtained with methods of different orders of accuracy as well as of the effectiveness of the vorticity and far field boundary conditions. (C) 1996 Academic Press, Inc.