Viscous flow past circular cylinders

Accurate and efficient calculation of the flow around a circular cylinder are presented for Reynolds number from 1 to 40 (based on the diameter). The semi-analytical method of series truncation is used to express the stream function and the vorticity in a finite Fourier series. Substitution into the Navier-Stokes equation yields a finite system of nonlinear ordinary differential equations. These are approximated by two-point boundary value methods. The resulting nonlinear equation are solved unsing Newton's method. Much attention has been given to numerical errors and errors resulting from the approximation by a finite series. The results are compared with similar calculations by Keller-Takami and Dennis-Chang. The agreement is good. The application of free stream conditions at a finite radius is shown to yield inaccurate results. im