A non-mapped complex variable method for the computation of unseparated airfoil flows

A new complex variable method is developed for the analysis of incompressible potential flow over lifting airfoils. The method is built around the numerical solution of a principal-value Cauchy integral equation. Unlike previous complex variable methods, no mappings are required, and the numerical solution is obtained entirely in the physical ($\text{Z}$) plane. Zero normal velocity over the airfoil is satisfied analytically at every point on the surface, not merely at discrete locations. No restrictions are placed on the airfoil contour, and the solution method producers both the potential distribution around the airfoil and the circulation.