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

This study mathematically formulates the fluid field of a water-wave intera ction with a porous structure as a two-dimensional, non-linear boundary val ue problem (bvp) in terms of a generalized velocity potential. The non-line ar bvp is reformulated into an infinite set of linear bvps of ascending ord er by Stokes perturbation technique, with wave steepness as the perturbatio n parameter. Only the first- and second-order linear bvps are retained in t his study. Each linear bvp is transformed into a boundary integral equation . In addition, the boundary element method (BEM) with linear elements is de veloped and applied to solve the first- and second-order integral equations . The first- and second-order wave profiles, reflection and transmission co efficients, and the amplitude ratio of the second-order components are comp uted as well. The numerical results correlate well with previous analytical and experimental results. Numerical results demonstrate that the second-or der component can be neglected for a deep water-wave and may become signifi cant for an intermediate depth wave. Copyright (C) 1999 John Wiley & Sons, Ltd.