Numerical simulation of nonlinear response of moored floating structures to steep waves
This thesis presents a newly developed Quasi Arbitrary Lagrangian-Eulerian Finite Element Method (QALE-FEM) for numerically simulating wave-body interaction problems based on the fully nonlinear potential theory. The boundary value problem in this model is solved by a finite element method (FEM). The main difference between this method and the conventional FEM is that the complex mesh is generated only once at the beginning of the calculation and is moved at all other time steps in order to conform to the motion of the free surface and structures. This feature allows one to use an unstructured mesh with any degree of complexity without the need of regenerating it every time step, which is generally inevitable and very costly. Due to this feature, the QALE-FEM has high computational efficiency when applied to problems associated with the complex interaction between large steep waves and structures since the use of an unstructured mesh in such a case is likely to be necessary. In order to achieve overall high efficiency, some numerical techniques, including the method to move interior nodes, the technique to redistribute the nodes on the free surface, the scheme to calculate velocities, are developed. To overcome the difficulty associated with the force and acceleration of freeresponse floating bodies, an ISITIMFB (Iterative Semi-Implicit Time Integration Method for Floating Bodies) iterative procedure is developed. The developed QALE-FEM method is applied to simulate the waves generated by a wavemaker and their interaction with sandbars on the seabed, waves generated by a floating body in forced motion, the response of a 2D or 3D freely floating body to a steep wave. Some of the results have been validated by analytical solutions, experimental data and numerical results from other methods. Satisfactory agreements are achieved. The convergence properties of this model in cases with or without floating bodies are all investigated. The nonlinearities associated with different cases are investigated. The mesh quality is also investigated using either qualitative or quantitative methods. The results show the mesh quality during long-period simulation is retained. The efficiency of the QALE-FEM method is finally discussed and compared with other methods. It is concluded that the QALE-FEM method is 10 times faster than the conventional FEM method in case with unstructured mesh and at least 7 times faster than the fast BEM methods for the fully nonlinear waves.