Computations on transonic inviscid flows past thin airfoils

Abstract

In this paper we discuss a novel accurate method for computing transonic flow over lifting and non-lifting aerofoils as governed by the steady K´arman-Guderlay equation. The method is based on using finite-differences in the streamwise direction combined with spectral collocation in the other direction. This is combined with Newton iteration and a direct method for the resulting linear system. The method is fast and very robust and we are able to compute steady flows with strong shocks. The work has been extended to discuss the stability of the computed flows using methods based on a global stability analysis. This leads to generalized eigenvalue problem. Some preliminary results are presented. One advantage of the current approach is that for small grid sizes it is possible do the analysis using MATLAB.