A boundary‐type finite element model for water surface wave problems

SUMMARY A new combinative method of boundary-type finite elements and boundary solutions is presented to study wave diffraction-refraction and harbour oscillation problems. The numerical model is based on the mild-slope equation. The key feature of this method is that the discretized matrix equation can be formulated only by the calculation of a line integral, since the interpolation equation which satisfies the governing equation in each element is used. The numerical solutions are compared with existing analytical, experimental, observed and other numerical results. The present method is shown to be an effective and accurate method for water surface wave problems. The demands of the planning and construction of various offshore and coastal structures have increased in recent years. Consequently, the analysis of wave diffraction-refraction problems and harbour oscillation problems is becoming more important from the point of view of the planning of offshore and coastal structures. Various numerical methods have been presented to analyse water surface wave problems. The eigen function expansion method,',' the finite difference meth~d,~ the finite element method4 and the boundary element meth~d~-~ have been developed. However, the finite difference method and the finite element method have difficulty in considering the Sommerfeld radiation condition. Recently, some combinative methods based on the finite element method have also been developed to overcome this difficulty, since the finite element method can easily treat the arbitrary shape and variable water depth. These combinative methods are roughly classified into three types with respect to the treatment of the radiation condition. Chen and Mei," Zienkiewicz et aZ.," Houston," Tsay and LiuI3 and Skovgaard et ~1.'~ presented the combinative method of finite elements and boundary solutions. This method is called the hybrid finite element method. Berkhoff l5*I6 and Zienkiewicz et a1.I7 presented thecombinative method using boundary elements. Battess and Zienkiewicz,18 Bettess et al.' 9,20 and Zienkiewicz et al." presented the combinative method using infinite elements. However, the principal objective of these methods was