Refraction and Diffraction of Surface Water Waves Using a Coupled FEM-BEM Model

Abstract

The aim of this research work was the calculation of the wave calmness in arbitrary-shaped port basins. The governing differential equation was firstly devised by Berkhoff (1972) and Schoenfeld (1972). This is the so-called mild slope equation and can be used only in case of gently bottomed or gradually-varied depths. So far several methods have been proposed to find out solutions to the aforementioned equation. The domain of the equation is the fundamental difficulty of this problem since this extends to infinity. In this paper an adaptation of a coupled FEM-BEM model developed by He Yinnian and Li Katai (1987) is presented that leads to the obtention of useful solutions when very simple elements are used in the domain discretization and allows an a-priori estimation of the error involved in the approximation. Results obtained with this method are checked against theoretical solutions and other numerical methods and the order of convergence is empirically established.