Dual Boundary Element Analysis of Normal Incident Wave Passing a Thin Submerged Breakwater with Rigid, Absorbing, and Permeable Boundaries

Abstract

In this paper, the dual integral formulation is derived for solving the scattering problem of normal incident wave passing a thin vertical and inclined barrier with rigid boundary condition which is descending from the water surface to a depth. Absorbing and porous boundary conditions are both considered. The breakwater thickness is assumed to be zero since it is negligible in comparison with the water depth and the wavelength of the incident wave. Although the multidomain boundary element method (BEM) can solve boundary value problems with degenerate boundaries by dividing the interesting domain into two subdomains, the hypersingular formulation provides the key to solve the problem more efficiently in a single domain. To demonstrate the effects of the breakwater with rigid, absorbing, and porous boundary conditions for the energy dissipation by the barrier, the transmission and reflection coefficients of the scattering problem are determined by the developed dual BEM program. In addition, the results are obtained for the cases of wave scattering by the barrier with zero thickness in constant water depth and are compared with the analytical solutions, the multidomain BEM solution, and the experimental data.