Numerical simulation of sailing boats: dynamics, FSI, and shape optimization

The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of the sails and appendages under transient external conditions like gusts of wind or wave patterns and, overall, the coupling among all these components [3]. In this talk, we will describe the numerical algorithms that have been developed in the framework of open-source libraries for the simulation of free-surface hydrodynamics and boat dynamics, as well as for the analysis of the fluid-structure interaction between wind and sails. Moreover, an algorithm for shape optimization, based on the solution of the adjoint problem and combined with the Free Form Deformation (FFD) method for the shape parametrization and mesh motion, will be presented and discussed. The OpenFOAM library features many of the key-points needed for our kind of applications, more notably a Navier–Stokes solver, turbulence models, Volume of Fluid models and parallel implementation. Validation of the free-surface solver and its interaction with the rigid-body hull dynamic module have been tested on a classical benchmark problem, namely the Series 60 hull. The steady solution at a fixed attitude has been computed on three-different grid resolutions and the wave profiles on the hull obtained, as well as the drag coefficients, have been compared with the experimental measurements showing good agreement. The behaviour of the model simulating the dynamics of the hull in waves has also been analysed, figure 1. For the fluid structure interaction between wind and sails, we have considered an external structural solver capable to simulate the membranes/shells structural deformations. The coupling algorithm between the fluid and structural solvers is based on a strongly coupled segregated approach. Different approaches have been tested for the the communication and data interpolation between the two independent solvers. The results obtained for a single sail (a gennaker) immersed in a steady atmospheric flow are presented in figure 2. Different sails geometries, boundary conditions and configurations are currently under investigation. Finally, we have moved in the direction of the development of shape optimization algorithms. Based on the method proposed in [2], an