A Numerical Solution for the Lifting Surface Integral Equation

Abstract

In this paper, we present a new numerical treatment of the lifting surface integral equation (LSIE) in the case of rectangular wing planform. The kernel of this equation possesses a strong singularity in Hadamard sense. First the equation is transformed into one containing weaker singularities, of Cauchy-type, and then the 2D singular integral is discretized by the aid of the Gausstype quadrature formulae. Thus the problem is reduced to a finite system of linear algebraic equations. The numerical simulation reveals a very good agreement, in terms of jump pressure over the wing and aerodynamic coefficients, with the exact solution in the case of the low aspect ratio wing and also with other numerical solutions.

Keywords

• Gauss type quadrature
• singular integral equation
• rectangular wing planform