An easy-to-implement highly efficient algorithm for nonlinear Kutta condition in boundary element method

Abstract

An easy-to-implement highly efficient algorithm for the nonlinear Kutta condition in the boundary element method is proposed. The main innovation is to pre-calculate an inverse matrix and use it to replace a solving system of equations with vector–scalar multiplication and matrix–vector multiplication. This allows calculating the Jacobian matrix in each nonlinear Kutta condition iteration with little computational effort, which is important for fast and robust convergence. The open-water characteristics of four different propellers are calculated with the linear and nonlinear Kutta conditions. The simulations show that the nonlinear Kutta condition results in more accurate open-water characteristics and more physically reasonable surface pressure distributions. In addition, the nonlinear Kutta condition takes no more than 3 extra seconds for an open-water simulation, and this extra time does not increase much with the number of simulation steps. The method proposed in this work is expected to improve the computational speed of the boundary element method while maintaining the same accuracy, or improve the accuracy with little extra computational time.