Automatic differentiation for the optimization of a ship propulsion and steering system: a proof of concept

We describe the optimization of the Voith-Schneider-Propeller (VSP) which is an industrial propulsion and steering system of a ship combined in one module. The goal is to optimize efficiency of the VSP with respect to different design variables. In order to determine the efficiency, we have to use numerical simulations for the complex flow around the VSP. Such computations are performed with standard (partly commercial) flow solvers. For the numerical optimization, one would like to use gradient-based methods which requires derivatives of the flow variables with respect to the design parameters. In this paper, we investigate if Automatic Differentiation (AD) offers a method to compute the required derivatives in the described framework. As a proof of concept, we realize AD for the 2D-code Caffa and the 3D-code Comet, for the simplified model of optimizing efficiency with respect to the angle of attack of one single blade (like an airfoil). We show that AD gives smooth derivatives, whereas finite differences show oscillations. This regularization effect is even more pronounced in the 3D-case. Numerical optimization by AD and Newton's method shows almost optimal convergence rates.