A fast method to realize the pressure Kutta condition in boundary element method for lifting bodies

The Newton-Raphson method is always employed to realize the zero pressure jump at the trailing edge of lifting bodies, which is required by pressure Kutta condition. This paper describes an analytical method to evaluate the Jacobian matrix during this procedure. With the proposed method, the computation time of the Jacobian matrix is less than that with the conventional method by five orders of magnitude. This allows for calculating the Jacobian matrix in every iteration of the Newton-Raphson method, which accelerates the convergence rate. In addition, a fast method, called the dipole increment method, to update the unknown singularities on the body surface during the Newton-Raphson procedure is also presented. Combination of these two methods makes the time consumed by the nonlinear pressure Kutta condition negligible (less than 2% of the total simulation time) in the boundary element method for both steady and unsteady flows.