On the viscous steady flow around a circular cylinder

Abstract

A series truncation method is proposed to obtain approximate solutions to the flow past a circular cylinder. This procedure is based on a change in the radial coordinate ($x$), such that this new coordinate is defined in a finite interval. Solutions are truncated power series in $x$, so that the full Navier-Stokes equations are transformed into three recurrence relations with two independent coefficients. The boundary conditions on the cylinder's surface are satisfied in trivially way, and the conditions at infinity lead to a system of two non linear ordinary differential equations. These are solved using Fourier series in the angular variable and, for the sake of argument, in a power series in $R_{e}$. Results on the convergence of the series, with varying order of truncation, and comparison with earlier results are discussed.