Computation of Steady Laminar Flow over a Circular Cylinder with Third-Order Boundary Conditions

An analytic-numerical solution to the Navier-Stokes equations is developed for the steady laminar flow past a circular cylinder. The method of series truncation is employed to reduce the governing partial differential equation to a system of ordinary differential equations, which are then numerically integrated. The Reynolds numbers Re, based on the diameter, range from 0.4 to 40. Beyond that, the flow field should be represented by cosine as well as sine series, and is to be treated later. The accuracy of the solution is enhanced by third-order boundary conditions at infinity. Quantities of interest such as the drag and pressure coefficients, tangential and radial velocities, streamlines, and vorticity lines are computed, plotted, and compared with previous results. Applying Shanks' transformation to each of three successive truncations improves the accuracy of the surface quantities.