Potential flow in a multiply connected circle domain using series methods

Abstract

We study series solutions to potential flow over an assembly of disks in the complex plane. Boundary value problems are solved for both streaming flow uniform at infinity and flow with circulation using Laurent series. If the circles are the images of multi-element airfoils under conformal mapping, the circulations around the disks can be found so that the combined flow satisfies the Kutta condition at the preimages of the trailing edges. Some comparisons with other methods for computing the flow, such as reflection methods, will be given.