Improved algorithm of boundary integral equation approximation in 2D vortex method for flow simulation around curvilinear airfoil

摘要

The problem of the accuracy improving is considered for vortex method. It is shown, that the airfoil surface line representation as a polygon consisting of rectilinear panels can lead to incorrect behavior of the numerical solution of boundary integral equation with respect to unknown vortex sheet intensity, especially in case of considerably different lengths of the neighboring panels. The approach is developed which makes it possible to take into account explicitly the curvature of the surface line. The approximate formulae for the coefficients of linear system are derived which permit to obtain rather "good" numerical solution for arbitrary airfoil discretization.