一种求解时间关联型缓坡方程的数值方法  

A Numerical Scheme of the Time-Dependent Mild-Slope Equation

作　　者：赵红军[1] 张洪生[1] 丁平兴[2] 

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200030 [2]华东师范大学河口海岸国家重点实验室,上海200062

出　　处：《上海交通大学学报》2006年第6期1050-1054,共5页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金资助项目(40106008);国家重点基础研究发展规划(973)项目(2002CB412403);华东师范大学河口海岸国家重点实验室开放基金项目

摘　　要：以含底摩阻能量耗散项的时间关联型缓坡方程为控制方程,建立了一种具有二阶精度的数值离散格式.该格式对时间导数使用Euler预测-校正格式离散;对空间导数使用中心差分格式离散.基于统一边界条件表达式,对边界条件进行处理.数值解与物理模型实验值吻合较好,表明数值模拟模型可以有效地模拟波面随时间和空间的变化以及波高的空间分布.A numerical model was proposed with the time-dependent mild-slope equation including the bottom dissipation term used as the governing equations. In the model, the Euler predictor-corrector scheme is used to discretize the time derivatives, and the central difference scheme is used to discretize the spatial derivatives, thus leading to both time and spatial derivatives to second-order accuracy. Based on the general boundary conditions, the boundary conditions for the present model are treated. The calculated results are in good agreement with the experimental ones, which indicates that the numerical model can be used to simulate the time and spatial variation of surface elevation and the distribution of wave heights.

关 键 词：时间关联型 缓坡方程 数值方法 边界条件 

分 类 号：P731.22[天文地球—海洋科学] O353.2[理学—流体力学]