在船舶与海洋工程水动力性能分析中，海浪的非线性波浪力效应及其利用正在成为科学界和工程界的研究热点，而提高浮体湿表面流体速度求解的精度成为非线性波浪力分析的关键技术。目前水动力学势流模拟常用的边界元方法，在求解带有拐角的非光滑边界处流体速度时，或者存在计算精度低的问题、或者存在稳定性和鲁棒性差的问题。这严重阻碍了非线性波浪力求解精度的提高。本项目抓住了这一关键问题，在理论创新方面，发现了边界函数及其切向导数可以联合构成第二类弗雷德霍姆边界积分方程组，独创了泰勒展开边界元（TEBEM）这一高精度新方法。本项目拟开展浮体在波浪中水动力问题求解的各类边值问题TEBEM求解方法及其精度验证研究。从而推进解决复杂外形浮体的非线性波浪力准确模拟问题。

Nonlinear wave hydrodynamics are becoming a hot research topics in ship and offshore engineering research field. For hydrodynamics analysis of free surface wave interaction with arbitrary form floating bodies, potential flow and the corresponding Laplace equation is most solved numerically through Boundary Element Method(BEM), or named panel method. Mixed distribution of sources and dipoles integral equation For lower order BEM, direct BEM which is based on mixed sources and dipoles distribution BIE is superior to the indirect BEM which is based on sources only distribution BIE from the view points of accuracy and efficiency for solving the velocity potentials on the boundary. Nevertheless, numerical differentiation have to be used to obtain tangential velocity followed from the direct BEM , where indirect BEM is more robust for obtain the induced velocity. So there are two common routines adopted for solving first order and second order wave hydrodynamics. The first way is using direct BEM for solving potentials and using indirect BEM for obtaining velocity. The second way is using indirect BEM for solving both potential and velocity. For smoothed boundary without corners like a sphere boundary both of the two ways may give satisfied numerical solutions, although the first way converge better than the second way for obtaining the potential. For no-smoothed boundary like a vertica finite draft circular cylinder or box like floating bodies, the velocity is not easy to converge near the corners by the two ways. Especially for solving the tangential velocity around the corner region, direct BEM with numerical differentiation has lower accuracy than that on other smoothed part region panels, while much bad tangential velocity in the corner region relatively to the smoothed region results from indirect BEM no matter how fine panel discretization is used. These characteristics of lower order BEM or constant panel method leads to lower convergences of prediction for second order wave forces and second order potential obtained from the results of the corresponding tangential velocity calculations..To improve the accuracy of BEM for the solution of no-smoothed boundary problem, a new numerical scheme named TEBEM is presented by Duan. TEBEM is the abbreviation of Taylor Expansion Boundary Element Method. TEBEM is shown most accurate than the general IDBEM and DBEM for simple infinite fluid flow. More detailed investigation of this method on solving nonlinear wave hydrodynamics problem for practical marine structures will be done in this project.