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Mathematical Problems in Engineering
Volume 2015, Article ID 985731, 11 pages
http://dx.doi.org/10.1155/2015/985731
Research Article

Accurate Solutions to Water Wave Scattering by Vertical Thin Porous Barriers

Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao 266100, China

Received 1 April 2015; Revised 11 September 2015; Accepted 20 September 2015

Academic Editor: Erik Cuevas

Copyright © 2015 Ai-jun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The water wave scattering by vertical thin porous barriers is accurately solved in this study. Two typical structures of a surface-piercing barrier and a submerged bottom-standing barrier are considered. The solution procedure is based on the multi-term Galerkin method, in which the pressure jump across a porous barrier is expanded in a set of basis functions involving the Chebychev polynomials. Then, the square-root singularity of fluid velocity at the edge of the porous barrier is correctly modeled. The present solutions have the merits of very rapid convergence. Accurate results for both the reflection and the transmission coefficients and wave forces are presented. This study not only gives a promising procedure to tackle wave interaction with vertical thin porous barriers but also provides a reliable benchmark for complicated numerical solutions.