Inviscid flow passing a lifting body with a higher order boundary element method

Abstract

A higher order boundary element method (HOBEM) is presented for inviscid flow passing a lifting body. In addition to the boundary integral equation used for the velocity potential, similar integral equation is derived and used for the tangential velocity on the body surface. Higher order elements are used to discretize the body surface, which ensures the continuity of slope at the element nodes. The velocity potential is also expanded using higher order shape function, in which the unknown coefficients involve the tangential velocity. The expansion then ensures the continuity of the velocity at element nodes and it also allows the Kutta condition to be imposed directly through the velocity. A particular shape function is also derived and used near the trailing edge to account for the continuity of the velocity and its sharp variations there. The unknown potential and tangential velocity are then found through solving their integral equations simultaneously. Through extensive comparison of the results for a Karman-Trefftz (KT) foil, it is shown that the present HOBEM is much more accurate than the conventional BEM, in particular for the velocity and local results near the trailing edge.