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

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, based on quadratic B-splines or on a combination of a Taylor series expansion and finite difference formulas. The third order methods are based on 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. It is demonstrated that for computational efficiency the third-order methods are superior, with cubic Hermite polynomials being most efficient.