Singularity resolving in solution of the boundary integral equation in two-dimensional vortex methods

Abstract

The problem of 2D incompressible flow simulation around airfoils with sharp edges and corner point is considered. The solution of the boundary integral equation with respect to vortex sheet intensity arising in Lagrangian vortex method has weak singularity that cannot be resolved correctly in the framework of the existing Galerkin-type numerical schemes. It is shown that for piecewise-smooth bounded solutions the known schemes allow for solution reconstruction with high quality and provide the 2-nd order of accuracy, while for singular solution their order of accuracy goes down to the 1-st. A numerical scheme is suggested that allows for solution singularity resolving and provides the 2-nd order of accuracy. As a model problem, the added mass tensor components computation is considered, since its exact value is known for the Joukowsky wing airfoil with sharp edge (cusp point).