This master thesis presents the computation of free-surface flow phenomena with emphasis on ship hydromechanics. We perform a simulation of the heave and the pitch motion of the DTMB 5415M ship moving in head sea. To this purpose we employ an existing Arbitrary-Lagrangian-Eulerian residual-based variational multiscale method (ALE-RBVMS) to discretize the incompressible Navier-Stokes equations and use the level-set method to capture the interface. We validate the numerical results obtained from the ALE-RBVMS computation with experimental data. We show that these results significantly improve upon those acquired from other CFD codes. This demonstrates the viability of the framework for simulations in ship hydromechanics.

The case of the flow around a rotating circular cylinder is very complex. This thesis investigates the properties of a fluid flow for Reynolds numbers ranging from 50 to 400. Numerical simulations are performed using a combination of isogeometric analysis and the residual-based variational multiscale method, providing high accuracy. The results show how the lift and the drag generated by the cylinder are related to the spin rate and the Reynolds number. When comparing the lift and drag values to the required amount of torque which is needed to spin the cylinder, it is shown that at medium spin rates, a very high aerodynamic efficiency is obtained at a reasonable amount of torque. 3D simulations are performed and show at high spin rates strong vorticity and a wake that is dominated by vortex shedding. These results differ strongly from the 2D simulations, which leads to the question whether 2D simulations are still representative for real real at high spin rates, despite the low Reynolds number.

In numerical methods, correct geometry description and mesh refinement are a challenge. By using a more geometrically based Finite Element Analysis (FEA) type method called ‘Isogeometric Analysis’ (IGA), exact geometry description can be attained, even on coarse meshes. Furthermore, mesh refinement is relatively easy, since no communication with a geometry description is necessary. From a maritime perspective, this method seems to be very interesting. Therefore, a first step towards an all-inclusive IGA framework for potential flow problems of ships and offshore structures is made by using IGA to solve linear free surface waves in a bounded 2D and 3D domain. The goal of this thesis is twofold. The first goal is finding out which of three weak formulations is best suited for further development. The second goal is testing the advantages of IGA in a potential frame work. A secondary goal is testing MFEM, the C++ finite element library that was used. These goals were reached by testing the three formulations on (1) a sloshing wave, (2) an airy wave and (3) a step wave in a square tank of 1 square m and (4) a sloshing wave in a cubic tank of 1 cubic m3with a cylinder in the middle. The first two have analytical solutions that can be used for verification and validation, the last two are used to compare standard FEA with IGA. The three weak formulations are formed by transforming the strong problem definition into three different weak forms. The main difference between these three being the way the boundary conditions are implemented. The first, reduced formulation is formed by combining the free surface boundary conditions, the second, mixed formulation by implementing all three boundary conditions directly and the third decoupled formulation by decoupling the problem into a free surface and an interior part. The first formulation is the simplest, but is hard to extend towards more complicated problems and is therefore used as a reference solution. The mixed and decoupled formulations are more complicated but can be extended. The first two tests showed that the reduced and mixed formulations have identical results. These results were very accurate: the wave period could be calculated accurately for coarse meshes and, very important, energy was conserved perfectly. The results for the decoupled formulation were significantly worse: more refined meshes were needed to calculate the wave period accurately and the energy showed periodic behaviour. The last two tests demonstrated that IGA offers results comparable to FEA for less degrees of freedom. The more difficult geometry of the fourth problem was much better represented by IGA.