Numerical solution for the second-order wave interaction with porous structures

Abstract

This study mathematically formulates the fluid field of a water-wave interaction with a porous structure as a two-dimensional, non-linear boundary value problem (bvp) in terms of a generalized velocity potential. The non-linear bvp is reformulated into an infinite set of linear bvps of ascending order by Stokes perturbation technique, with wave steepness as the perturbation parameter. Only the first- and second-order linear bvps are retained in this study. Each linear bvp is transformed into a boundary integral equation. In addition, the boundary element method (BEM) with linear elements is developed and applied to solve the first- and second-order integral equations. The first- and second-order wave profiles, reflection and transmission coefficients, and the amplitude ratio of the second-order components are computed as well. The numerical results correlate well with previous analytical and experimental results. Numerical results demonstrate that the second-order component can be neglected for a deep water-wave and may become significant for an intermediate depth wave. Copyright (C) 1999 John Wiley & Sons, Ltd.