Convergence of different wake alignment methods in a panel code for steady-state flows

Wake alignment models are always included in the modern panel codes for marine propeller analysis. The wake alignment algorithms influence directly the rate of convergence and the accuracy of calculations. In the present work, firstly, four different numerical methods to implement the wake alignment algorithms for the steady calculation are described. They perform quite differently in terms of convergence history and convergence rate. The comparison with the other methods shows that the direct application of the unsteady method leads to a much slower convergence rate. Secondly, high-order numerical methods including second-order and fourth-order Runge–Kutta methods are introduced into the wake alignment, which results in high-order wake alignment algorithms. The analysis of the results shows that the high-order methods generate a different wake geometry from the low-order method. The thrust coefficient and torque coefficient have also been compared.