This work deals with the application and extention of a RANSE solver to both calculating the turbulent free-surface flow around ships including their running attitude, and simulating the time-accurate dynamic response of freely-floating bodies. The aim of the thesis is threefold: 1. To assess the accuracy of these free-surface RANSE computations for predicting the resistance of a ship advancing at constant speed in calm water; 2. To extend the existing RANSE solver to allow the computation of the ship's running attitude (sinkage, trim and eventually heel), with the aim of improving the resistance prediction by considering the difference in resistance which occurs when the ship changes its running attitude; 3. To extend the method to allow the time-accurate simulation of motions in six degrees of freedom of bodies floating freely at the free surface. A main requirement for this work was to implement the coupling of the body motions and the fluid flow in such a way that any type of analysis, steady or unsteady, could be performed using the same program by simply adjusting the corresponding parameters of the numerical method. Furthermore, the method should be extensible to still more complex tasks, such as those encountered in ship manoeuvring and in ships in waves.

The flow solver is based on a Finite Volume Method with unstructured meshes and an interface-capturing scheme to determine the shape of the free surface. The method was extended to compute the body motions in six degrees of freedom. For this purpose, the equations of motion of the rigid body were implemented as a user-programmed module, which is linked and run simultaneously with the flow solver.

Examples of applications for both steady and unsteady flows around floating bodies at the free surface are presented. Particularly the question concerning the achievable accuracy of the resistance tests simulated with this method -- including the free surface -- is addressed. Three particularities of the computations are analysed. The first one is concerned with grid quality and resolution at the body wall, which is crucial for obtaining an accurate friction resistance prediction. The second one is the size of the time step required for the time integration and its influence on both pressure and friction resistance. The third one is the type of discretization scheme used for the momentum equations and its influence on pressure forces. Furthermore, a novel type of extrapolation procedure for obtaining grid-independent solutions for pressure resistance without having to compute on extremely fine grids is proposed. The numerical approach is also evaluated with respect to its suitability for calculating the ship's running attitude. Two test cases are presented: 1. The Series 60 hull in straight-ahead sailing condition as well as in a drift condition at a small yaw angle. The results are validated with experimental data; 2. The model of a very fat ship with a blunt bow. In this case the emphasis is on the large changes in running attitude and thus resistance, as well as on the bow-wave breaking pattern and its comparison with model tests. Finally, three application cases for the unsteady response of a body released from a position out of equilibrium are presented: 1. 2-D drop tests with a wedge. This case is used to validate the method with existing experimental data; 2. The 2-D large amplitude roll motion of the mid-ship section of a boat. Two configurations are investigated -- the bare hull and the hull with a fin keel -- and the effects of the keel on the damping coefficient and thus on the roll motion are quantified; 3. The extention of the last application to 3-D and forward speed. The resulting configuration is a hull undergoing a coupled roll, pitch, sway and heave motion at high speed until reaching a planing condition.

This work has been partially supported by the DFG "Deutsche Forschungsgemeinschaft" within the Graduate Research Programme "Ocean Engineering" at the Technical University Hamburg-Harburg.