Abstract

This chapter presents an overview of some computational methods for the analysis of problems in ship hydrodynamics. Attention is focused on the description of stabilized finite element formulations derived via a finite increment calculus (FIC) procedure. Both arbitrary Lagrangian–Eulerian (ALE) and fully Lagrangian forms are presented. Details of the treatment of the free‐surface waves and the interaction between the ship structure and the sea water are given. Potential flow formulations for seakeeping analysis and calculation of the added resistance in waves are also described. Examples of application of the computational methods presented to a variety of ship hydrodynamics and related problems are given.

Abstract

This presentation introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary Lagrangian–Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235–249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier–Stokes equations are solved using an iterative monolithic predictor–corrector algorithm, where the correction step is based on imposing the divergence‐free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented.