短峰波与圆弧型贯底式多孔介质防波堤相互作用研究

将比例边界有限元法(SBFEM)推广到短峰波与圆弧型贯底式多孔介质防波堤相互作用研究中.将圆弧延伸构建一个虚拟圆柱面,对于圆弧段与圆弧延伸段,分别采用不同的孔隙影响系数.该圆将整个流场划分成一个无限子域和一个有限子域,并利用变分原理在各个子域上推导了SBFEM的基本方程.然后,SBFEM针对无限域和有限域分别采用汉开尔函数和贝塞尔函数作为基函数来求解对应域的解,并在公共圆边界处加以匹配.数值计算验证了该方法是一种利用很少单元离散虚拟圆便能得到精确结果的高效方法.进一步给出了不同波向入射、相对波数、防波堤不同孔隙影响系数、不同张角等参数对防波堤波浪荷载、波浪爬升的影响,这为该类防波堤水动力分析和结构设计提供了有价值的参考.

Study of interaction of short-crested waves with arc-shaped bottom-mounted porous breakwater

The scaled boundary finite element method (SBFEM) is applied to the solution of short-crested wave interaction with arc-shaped bottom-mounted porous breakwater. The fluid domain is divided into two sub-domains by introducing an imaginary circular interface. The outer one is an unbounded sub-domain and the inner one is a bounded sub-domain. Various porous coefficients for the arc and the imaginary arc are considered. A new variational principle formulation to derive the SBFEM equations for the two sub-domains is developed. Hankel function and Bessel function are chosen as the basis functions for the solution of the unbounded and bounded domains, respectively and matched at public circle boundary. Numerical examples show that the presented method yields excellent results with quite few nodes discretized on the imaginary circle. The effects of the wave parameters and structure configuration including porosity of the arc, the relative wave number and the annular spacing on the wave forces, wave run-up are examined. The experimental results provide valuable reference for the hydrodynamic analyses and structure design of arc-shaped bottom-mounted porous breakwater.