Design of free-surface interfaces using RANS equations

In this paper, the continuous adjoint methodology to compute shape sensitivities in free-surface hydrodynamic design problems (RANS governing systems) has been developed. This technique will allow the specific design of the free-surface interface (typically air/water), which has a great potential in problems where the target is to reduce the wave energy, e.g. ship hull design. A detailed description of the methodology as well as numerical experiments to demonstrate the ability of this new technique to reduce the wave energy will be shown. I. Introduction In the past, lot of work has been done in shape optimization for ship hydrodynamics using Computational Fluid Dynamics. However, in most of the cases, the total resistance of the ship has been selected as the objective function to minimize (subject to geometrical constraints). In this particular paper, a new point of view is presented, and a di↵erent objective function has been defined to minimize the energy of the waves generated by an object submerged in the water. The complete adjoint methodology to evaluate the gradients will be presented in this article as well as some examples that demonstrate the ability of this technique to reduce the total resistance by minimizing the size of the waves. Hydrodynamic applications of optimal shape design in systems governed by partial di↵erential equations are formulated on a fluid domain ⌦ , delimited by disconnected boundaries divided into an inlet, outlet, and solid wall boundaries S. From now on we will restrict ourselves to the analysis of optimization problems involving a functional J defined on the solid wall S, and in the entire domain ⌦ , whose value depends on the flow variables U obtained from the solution of the fluid flow equations. In this context, the generic optimization problem can be succinctly stated as follows: find S min 2 Sad such that