适用于曲边界的浅水非线性波浪数值模型  

A numerical model applied to curved boundaries for nonlinear waves in shallow water

作　　者：张俊生[1] 滕斌[1] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《海洋工程》2015年第3期1-9,共9页The Ocean Engineering

基　　金：国家自然科学基金资助项目(51379032;51221961);国家重点基础研究发展(973)计划资助项目(2013CB036101)

摘　　要：实际工程中存在大量的曲边界,因此在曲边界上的计算准确性可以考察出一个数值模型的实用价值。利用Beji的改进型Boussinesq方程建立了一个有限元方法的数值波浪模型。造波方面采用Fenton提出的非线性规则波浪解;在墙边界处,以求解法线方向和切线方向的速度和导数代替求解x、y方向的速度和导数,从而使边界条件直接适用、严格满足,保证了对曲边界计算的准确性。"重开始广义极小残量法"的使用保证了求解方程组的效率和精度,使造波和边界处理方法的有效性和准确性得到了合理地诠释。通过与试验数据、他人数值结果、解析解的比对,显示出该模型计算稳定、结果准确,真正体现出了有限元方法对曲边界适用的优势。It is important for a numerical wave model to calculate accurately curved boundaries because there are a lot of curved boundaries in coastal engineering. The authors of this paper build a numerical wave model based on the improved Boussinesq-type Equations derived by Beji and Nadaoka using the finite element method. The solutions for nonlinear regular waves derived by Fenton are used to create waves. On wall boundaries, solving velocities and derivatives in the normal and tangential directions substitutes for doing it in the x and y directions, which makes boundary conditions be directly applied to curved boundaries and ensures the accuracy of treating the curved boundaries. The generalized minimal residual method （GMRES） used to solve equations can give accurate solutions efficiently, which ensures that the methods of wave generation and treating curved boundaries in the present model can be verified without the distraction of the errors in solving the equations. Through the comparison of present results, experimental data and analytical resolutions, the present numerical model proves to be accurate and stable. The advantage of the finite element method over the finite difference method for dealing with curved boundaries is exactly embodied in the present paper.

关 键 词：浅水非线性波浪 曲边界 有限元方法 造波与波浪传播 BOUSSINESQ方程 

分 类 号：P731.22[天文地球—海洋科学]