Singular boundary method for water wave problems

Abstract

This article presents the singular boundary method (SBM) for water wave-structure interaction analysis. The SBM is a novel recent boundary meshless collocation method, which uses the singular fundamental solutions of governing equation as basis function in the interpolation formulation and introduces the concept of source intensity factors to avoid the singularities of the fundamental solutions at origin. It is a strong-form meshless boundary collocation technique with the merits being easy-to-implement and integration-free. In this study, two types of water wave-structure interactions, water wave interaction of multiple-cylinder-array structure and semicircular harbor, are considered. Numerical results show the efficiency and accuracy of the present SBM scheme in comparison with the analytical solutions, the method of fundamental solutions and the null field boundary integral element method. Then the near trapped mode phenomenon of ten-cylinder structure and the focusing effect of the semicircular harbor are revisited by using the present SBM.