Accuracy of high-order, discrete approximations to the lifting-line equation

Abstract The accuracy of several numerical schemes for solving the lifting-line equation is investigated. Circulation represented on discrete elements using polynomials varying degree, and a novel scheme introduced based discontinuous representation that permits arbitrary polynomial degrees to be used. Satisfying Helmholtz theorems at inter-element boundaries penalises discontinuities in circulation distribution, which helps ensure solution converges towards correct, continuous behaviour as number increases. It found singular vorticity wing tips drives leading-order error solution. With constant panel widths, exhibit suboptimal irrespective basis degree; however, driving width tip zero rate faster than domain average enables improved recovered quadratic-strength elements. In all cases considered, higher-order higher their lower-order counterparts same total freedom also quadratic are more accurate while being flexible geometric representation.