Dual boundary element analysis of oblique incident wave passing a thin submerged breakwater

Abstract

In this paper, the dual integral formulation for the modified Helmholtz equation in solving the propagation of oblique incident wave passing a thin barrier (a degenerate boundary) is derived. All the improper integrals for the kernel functions in the dual integral equations are reformulated into regular integrals by integrating by parts and are calculated by means of the Gaussian quadrature rule. The jump properties for the single layer potential, double layer potential and their directional derivatives are examined and the potential distributions are shown. To demonstrate the validity of the present formulation, the transmission and reflection coefficients of oblique incident wave passing a thin rigid barrier are determined by the developed dual boundary element method program. Also, the results are obtained for the cases of wave scattering by a rigid barrier with a finite or zero thickness in a constant water depth and compared with those of experiment and analytical solution using eigenfunction expansion method. Good agreement is observed.