Numerical simulation of nonlinear interaction between structures and steep waves

Abstract

Responding to great concerns about the interaction between steep waves and structures in naval architecture and offshore engineering, a methodology and corresponding numerical algorithm for computing three-dimensional inviscid flow with a free surface are developed based on a fully nonlinear theory in this thesis. The associated boundary value problem is solved using a finite element method. In order to chose an efficient solver for algebraic equations, a direct method and an iterative method with two different preconditioners are compared to each other, which leads to the suggestion that the conjugate gradient method with an SSOR preconditioner is the most suitable for the problem of concern. Furthermore, the radiation condition at a truncated boundary is imposed with an associated damping coefficient optimised to reduce the reflection of waves. In addition, an analytical solution for transient standing waves in a circular tank is derived using second order theory, which provides a tool to validate the numerical method. The developed numerical method is first utilised in simulating the sloshing wave in a tank generated by initial disturbance on the free surface and by the translational motion of the tank. Numerical results are compared with analytical solutions in several cases, which show that the numerical method can be very accurate. The features of the steep sloshing waves are then examined. In the second application, the interaction between vertical cylinders and waves generated by a wave maker is investigated. The motion of the wavemaker can be specified accordingly, in order to generate monochromatic, bichromatic or irregular progressive waves. The forces on one and two cylinders are obtained and compared with published data. The steep waves and their effects on hydrodynamic loads are analysed. It is concluded that the developed methodology based on the finite element method is a good alternative to the existing techniques for the simulation of steep waves. Its accuracy, flexibility and efficiency demonstrated by various numerical examples appear to be quite favourable