Abstract
The scaled boundary finite-element method is developed for second-order wave scattering by a rectangular surface obstacle in water of finite depth. The major advantage of this method lies in its ability to model the velocity field near singularity points and at infinity, which is not possible in other numerical techniques for wave-structure interaction problems. With the help of the analytical representation of the first-order velocity values along the surface of structure, the secondorder wave loading component induced by the first-order dynamic pressure is evaluated analytically in the radial co-ordinate direction. Since both the first and second-order velocity potential fields are determined explicitly in the scaled boundary finite-element solution, the second-order component of the wave loading can therefore be calculated very accurately. In this paper, the derivation and solution process of the scaled boundary finite-element equations for second-order wave scattering problems are presented in detail. The computed scaled boundary finite-element solutions are compared with analytical solutions. The accuracy and efficiency of the method are demonstrated by studying the convergence.