The application of numerical methods for the solution of some problems in free-surface hydrodynamics

The aim of this contribution is to present some of the recent developments achieved at INSEAN in the context of accurate and robust algorithms for the solutions of the system of partial differential equations governing complex free-surface flows. The paper addresses several problems of relevant interest in naval hydrodynamics, for example, sloshing, water on deck, microscale breaking waves, bow-stern flows, ship waves, steady and unsteady ship flows. Each problem is solved through the most appropriate numerical method, which is selected on the basis of the approximations that can be done for the particular problem and of the kind of result that the analysis has to provide. Numerical methods adopted involve classical boundary element approaches, smoothed particle hydrodynamics, heterogeneous domain decomposition techniques, level-set methods, steady and unsteady Reynolds averaged Navier-Stokes equations. Validation versus experimental data are presented. Comparisons among different numerical approaches are also established in a few cases with the aim of highlighting their limits and/or capabilities.