应用SBFEM研究波浪与薄板的相互作用问题

Research on the wave interaction with thin barriers by a scaled boundary finite element method

应用比例边界有限元法(SBFEM)求解了频域下波浪与刚性薄板防波堤相互作用问题。求解中将整个计算区域分为薄板周围的有限子域和直到无限远处的无限子域。有限子域的比例中心设置在薄板的下端,这时薄板的两侧为侧边面,而无限子域的比例中心设置在无限子域与有限子域的交界上,同时将水底和自由水面做为平行侧边面。应用加权余量法在每个子域内推导出比例边界有限元方程,然后在有限子域与无限子域交界上匹配求解。通过与解析解的对比,证明了这种方法的精确性,而后对不同类型的薄板防波堤进行了计算,并给出了反射和透射系数的变化规律。

In this paper, the wave interaction with rigid thin barrier breakwaters is studied in the fiequent domain by the scaled boundary finite element method （SBFEM）. The whole computational domain is divided into two kinds of sub-domain, one is the bounded domain which is next to the structures, and the other is the unbounded domain which is out of the bounded domain and expanded to the far field. The scaled center is set at the lower end of the barrier in the bounded domain, and two surfaces of the barrier are the side-faces. For the unbounded, the scaled center is set at the interface of the two do- mains, and the free surface and the sea bed are the parallel side-faces. The SBFEM equations are de- duced in every sub-domain using the weighted residual approach, and then these equations are matched on the interface of two adjacent sub-domains. Through comparing with the analytical solution, the accu- racy of the SBEFM has been testified. Then, some other kinds of thin barriers are simulated using this method, and the reflection coefficient and the transmission coefficient are given.