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

Abstract

A novel boundary integral formulation is presented for the direct solution of the classical problem of slow flow past a two-dimensional cylinder of arbitrary cross section in an unbounded viscous medium, the equations of motion having first been linearised by the Oseen approximation. It is shown how the governing partial differential equations of motion, together with the no-slip boundary conditions on the cylinder, may be reformulated as a pair of coupled integral equations of the second kind, which may be manipulated further to yield the lift and drag coefficients explicitly, as well as flow characteristics anywhere in the flowfield. The present formulation requires a non-iterative numerical solution procedure which is applicable to low Reynolds number flows. The method is not restricted in its ability to deal with complicated cylinder geometries, as the discretisation of only the cylinder surface is required. Results of the present method are shown to be in good agreement with those of previous analytical and numerical investigations.