Maple software code for study of linear waves interaction with a vertical permeable cylinder of arbitrary cross-section based on perturbation theory

Vertical permeable cylinders are interesting structures with broad applications in the marine industry, such as breakwaters, and marine fish farming. This Maple Software code studies linear waves incident to a vertical permeable cylinder with arbitrary cross-section based on the boundary element method and perturbation theory. Considering a near-zero thickness for the permeable media, and using Darcy's law, the governing equation for the wave incident to a porous circular cylinder is derived based on the boundary element method. Then using perturbation theory and considering a small parameter epsilon denoting the variation of cylinder radius from circular ones, the corresponding equations were expanded for non-circular cylinders. The developed method was applied to ellipse-shaped and rectangular cylinders. The wave forces and the wave strength inside the cylinder under a variety of parameters such as wavenumber, and porosity parameter were studied. One application of these research results is a better understanding of the behavior of non-circular aquaculture cages in sea waves.垂直透水圆柱是一类极具研究价值的结构，在海洋工程领域拥有广泛应用场景，例如防波堤建设与海水养殖。本Maple软件代码基于边界元法（boundary element method）与摄动理论（perturbation theory），针对任意截面垂直透水圆柱的入射线性波浪开展研究。考虑透水介质厚度近似为零的前提，并结合达西定律（Darcy's law），基于边界元法推导得到入射波浪作用下透水圆柱的控制方程。随后借助摄动理论，引入表征圆柱半径与标准圆形圆柱偏差的小参数ε（epsilon），将上述控制方程推广至非圆形截面圆柱的情形。将所开发的方法应用于椭圆截面与矩形截面圆柱的分析验证，研究了波数、孔隙率参数等多种参数条件下，圆柱所受的波浪荷载以及圆柱内部的波浪强度。本研究成果的一项重要应用价值在于，可深化对非圆形海水养殖网箱在海浪中运动特性的认知。