Computation of plane potential flow past multi-element airfoils using conformal mapping, revisited

Abstract

We revisit methods for computing flow over single and multi-element airfoils using more recently developed numerical methods for conformal mapping for simply and multiply connected domains. The corners at the trailing edges of the airfoils are successively removed by Karman–Trefftz maps. The map from the domain exterior to disks to the domain exterior to the smooth images of the airfoils is computed using extensions of a Fourier series method for the disk due to Fornberg. The velocity potential for flow in the circle domain, with circulation calculated to satisfy the Kutta condition in the airfoil domain, is computed by a reflection method based on the Milne-Thomson Circle Theorem. Convergence of the reflection method is proven if the domains are sufficiently well-separated.