The numerical modelling of steep waves interacting with structures
The interaction of steep waves with structures is a complex problem which is still not fully understood, and is of great importance for the design of offshore structures. A particular problem of interest is the phenomenon of ringing which is highly nonlinear. In this thesis a number of inviscid free surface flow problems are simulated using a finite element model. The free surface boundary condition is fully nonlinear, meaning nonlinear effects up to very high order can be simulated, depending on mesh resolution. The model uses a fully automatic unstructured mesh generator; this allows the mesh to change its shape and structure as the free surface deforms. Two unstructured mesh generators have been developed, one based on the advancing front method, the other on the Voronoi technique. Variations of each method are examined. Both methods give good quality meshes. The advancing front technique is found to be faster, but the Voronoi method is more robust and reliable. In addition to the standard finite element method, a sigma transformed version of the finite element formulation has been developed as an alternative. Both techniques have been used for the numerical simulations. The sigma transformation involves stretching of the mesh between the bed and free surface, and so has the advantage that remeshing is avoided. The standard finite element method is straightforward to apply to problems involving submerged arbitrary shaped bodies. Simulations have been performed of a number of test cases, such as a standing wave of large amplitude, a base excited tank and steep travelling waves. Convergence tests were carried out and results found to be in close agreement with analytical and alternative numerical solutions of Wu and Eatock Taylor (1994), Wu et al. (1998) and Chern et al. (1999). The force on a submerged horizontal cylinder due a travelling wave has been calculated. First and second order components have been obtained by Fourier analysis. The results have been compared with the theoretical predictions of Ogilvie (1963), Vada (1987) and Wu and Eatock Taylor (1990) and the experimental results of Chaplin (1984).