任意曲线边界条件下缓变水深水域波浪传播的数值模拟  

Numerical simulation of wave propagation in water of slowly varying topography with complicated boundary

作　　者：张洪生[1] 洪广文[2] 丁平兴[1] 

机构地区：[1]华东师范大学河口海岸国家重点实验室,上海200062 [2]河海大学港口航道及海岸工程学院,江苏南京210024

出　　处：《海洋学报》2002年第1期108-116,共9页

基　　金：国家杰出青年基金资助项目 (4 982 5 16 1)

摘　　要：缓坡方程被广泛地应用于描述波浪的传播变形计算 ,目前一般采用矩形网格求解 .将计算域剖分为任意四边形网格 ,以格林公式为基础 ,在变量沿单元边界线性变化的假定下 ,对双曲型的波能守恒方程、波数矢无旋性方程进行离散 ,同时通过等参单元变换推求节点偏导数值以离散椭圆型光程函数方程 ,从而建立了任意曲线边界条件下缓变水深水域波浪传播的数值模拟模型 .将模型应用于平行直线型等深线地形 ,并将计算域剖分为不规则四边形网格 ,对不同入射角、底坡、波高等多种组合情况比较了数值解与解析解 ,结果表明两者一致 .应用于复杂边界的实例 ,数值模拟结果与物模实验值基本吻合 .The mild slope equation is widely applied to the calculation of wave transformation with the computation region being divided into rectangular meshes. While the computation region is divided into irregular quadrilateral, the wave action conservation equation and wave number vector irrotational equation are discretized based on Greens formula, and the eikonal equation is done with deriving partial differential values by transformation of isoparametric element.Thereby the numerical simulation model of wave propagation for waters of slowly varying topography is presented. In the case of different incident wave angles, slope angles of bottom and incident wave heights, the systematic numerical simulation has been made for the straight contour condition and the computation region being divided into irregular quadrilateral, and the calculations show that the results of numerical modeling agree with those of theoretical solution. When the present mathematical model is applied to an example with complicated boundary, the results of numerical solution are basically consistent with those of physical models.

关 键 词：任意四边形 格林公式 等参单元 数值模拟 深水域 波浪 缓坡方程 

分 类 号：P731.22[天文地球—海洋科学]