A direct boundary integral equation formulation for the Oseen flow past a two-dimensional cylinder of arbitrary cross-section (Q1111849)

The method of linearizing the Navier-Stokes equations to describe the motion of an infinitely long cylinder immersed in a viscous fluid leads to the paradoxical conclusion that solutions obtained in this way are logarithmically unbounded at infinity. To clarify this paradox, Oseen suggested a more rational approximation of the equations in which the convective terms are considered. Further progress was achieved by Imai who found the explicit form for the steady-stream function asymptotically far from the cylinder. The present work gives a new formulation of the Oseen approximate equations in the form of a pair of linear integral equations extended to the boundary of the cylinder and subsequently discretized into a system of linear algebraic equations. Numerical calculations, performed when the boundary is a circle, are compared with other results available in the literature.