Accuracy comparison of different approaches for vortex sheet discretization on the airfoil in vortex particles method

Abstract

The hierarchy of numerical schemes is developed for the solution of the boundary integral equation which arises in the vortex particles method. Two different approaches are considered and numerical schemes are presented, which provide 1-st and 2-nd order of accuracy with respect to two different norms. The developed finite element-type schemes have nearly the same computational cost as the simplest scheme with piecewise-constant solution. The necessary formulae are presented for linear system coefficients for the considered schemes.