Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method (HOBEM) is presented for inviscid flow passing cylinders in bounded or unbounded domain. The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative. In present work, a new integral equation is derived for the tangential velocity. The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes. The velocity potential is also expanded with higher order shape functions, in which the unknown coefficients involve the tangential velocity. The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes. Through extensive comparison of the results for the analytical solution of cylinders, it is shown that the present HOBEM is much more accurate than the conventional BEM.