THE LOCAL ERROR OF A LOW-ORDER BOUNDARY-ELEMENT METHOD AT THE TRAILING-EDGE OF A HYDROFOIL AND ITS EFFECT ON THE GLOBAL SOLUTION

The performance of a low-order (piecewise constant dipole and source d istributions) potential based boundary element method (BEM) is tested when applied for the analysis of the steady flow around two-dimensiona l 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 differenc e of the linear from the constant dipole, the so-called ''saw-tooth'' effect, is accounted for within the low-order BEM in an iterative mann er. The inclusion of the ''saw-tooth'' effect is shown to improve the performance of the low-order BEM substantially.