Singular Boundary Method: Three Regularization Approaches and Exterior Wave Applications

Abstract

This study investigates the singular boundary method (SBM) with three regularization approaches for solving 2D and 3D exterior wave problems. The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three approaches, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of Helmholtz fundamental solutions at origin. This study compares numerical accuracy and stability of these three approaches on some benchmark examples under 2D and 3D exterior wave radiation and scattering problems. Numerical investigations show that SAT1>IIT>SAT2 in numercial accuracy and SAT2>SAT1>IIT in numerical stability. Then the SBM with SAT1 is applied to water wave-structure interaction and SH wave scattering problem. For water wave-structure interaction, numerical results show that both the porosity of the cylinder sidewall and the disorder arrangement have a great effect on the free-surface elevations in the vicinity of the wave structure. For SH wave scattering by a semi-circular hill, the focusing phenomenon is revisited.