Aspects of second- and third-order panel methods demonstrated for the two-dimensional flat plate problem

Abstract

Characteristics of three second-order and two third-order panel method formulations for the incompressible flow about a flat plate at incidence are investigated. The second order methods employ quadratic representations for the doublet distribution, either based on quadratic B-splines or on a combination of a Taylor series expansion and finite difference formulas. The third-order methods considered are based on either cubic B-splines or on cubic Hermite Polynomials. The integral equation resulting from imposing the stream surface condition at the flat plate is written in the vorticity formulation. Higher-order accuracy is achieved by employing mode functions which extract the singular behavior of the doublet distribution near the leading and trailing edge to sufficient degree. Only in this way the regular part of the doublet distribution can then be approximated with the polynomial representations to the required degree of accuracy. It is demonstrated that from a viewpoint of computational efficiency the third-order methods are superior over the second-order methods, with the method with the cubic Hermite Polynomials being most efficient.