数值模拟在钱塘江涌潮分析中的应用──Ⅰ.数值计算方法

THE APPLICATION OF NUMERICAL SIMULATION IN ANALYSIS OF QIANTANGJIANG TIDE──Ⅰ. NUMERICAL METHOD

利用数值模拟的方法对钱塘江涌潮从杭州湾口开始形成、发展直至消失的全过程进行了深入全面的描写．从杭州湾口到钱塘江出口，采用二维圣维南浅水波方程描述水波的运动，而在钱塘江河内采用一维圣维南浅水波方程描写涌潮的发展过程．详细描述用于一维和二维圣维南方程计算钱塘江涌潮的数值计算方法，首次把无结构网格上的NND格式应用于求解二维圣维南方程，并给出了详细的推导过程．对上下游水边界分别采用无反射边界条件和特征线方法，而对于动边界问题本文也给出了相应的处理方法．

The full description of the formation, development and disappear of Qiantangjiangtide by numerical method is presented in this paper in details. In Hangzhou Gulf(near Ganpu),the water region is very wide and the water wave movement are two dimensional, then the two dimensional Saint--Venant equations are used to discribe the movement of waterwave from HangzhouGulf to estuary of Qiantangjiang River (Yanguan). In the Qiantangjiang River (before Yanguan),the water region is narrow and the river is very long, the water wave movement can be consideredas one dimensional, then one dimensional Saint-Venant equations are used. This paper is the firstpart. In this paper we describe the numerical method to solve iD and 2D Saint-Venant equationsin details. It is the first time that NND scheme is used to solve 2D Saint-Venant equations in theunstructured mesh. In order to use NND scheme the equations must be conservation and satisfyU=F. But the 2D Saint-Venant equations don't satisfy U = F, so derived equation ofmechanical energy is added to 2D Saint--Venant equations and the equations are written in conservative forms. Therefore the equations satisfy U = F and the NND scheme can be used.However the equation of mechanical energy is not independent and is derived from momentumequation. It is not necessary to solve this equation. The calculations of the first derivative ofvariables are very important in the unstructured mesh computations. The least square method areadopted here and the results show that it is much better than Gauss method. The finite volumemethod is used in spatial discretization and explicit time stepping scheme is used in temporaldiscretization. On the upstream water boundary, the nonreflect boundary condition are used. Onthe downstream water boundary, the coordinate is rotated until one of coordinate axises is parallelto the normal direction of the boundary, then one dimensional characteristic method can be used.And on the moving boundary, a special dealing method is given in this paper.