The local error of a low-order boundary element method at the trailing edge of a hydrofoil and its effect on the global solution

Abstract

The performance of a low-order (piecewise constant dipole and source distributions) potential based boundary element method (BEM) is tested when applied for the analysis of the steady flow around two-dimensional hydrofoil geometries. The convergence rate of the results (e.g. the circulation around the foil) with an increasing number of panels N is found to be very slow. The slow convergence is attributed to the O(1/N) local error of the low-order BEM in the vicinity of a sharp trailing edge. To reduce that error an at least linear dipole distribution is shown that must be utilized on each panel. The effect of the difference of the linear from the constant dipole, the so-called “saw-tooth” effect, is accounted for within the low-order BEM in an iterative manner. The inclusion of the “saw-tooth” effect is shown to improve the performance of the low-order BEM substantially.