不规则地形上浅水模拟平衡性的实现

Method for keeping balance in shallow-water simulation over irregular topography

天然河道地形复杂而无规律,采用守恒型浅水方程进行水流运动数值模拟时往往会出现不平衡现象。本文在任意四边形网格的基础上采用Roe方法对守恒型浅水方程进行离散,针对连续方程离散后所出现的不平衡性,从原方程及离散方法的物理实质出发提出了局部水位法,使该问题得以解决;参照数值通量构造方法采用有限体积法构造了底坡项的离散方式,消除了动量方程底坡项离散后可能出现的虚假流动现象,同时保证了物理量的守恒性。将模型应用于松花江佳木斯河段的水流模拟中,其计算结果表现出了良好的守恒性、收敛性和平衡性。

Numerical imbalance may arise when a numerical simulation of water movement using shallow- water equations （SWEs） is performed on an irregular natural riverbed form. A mathematical model is es- tablished directly by applying Rocks method in FVM pattern based upon irregular quadri-lateral grids and some imbalance emerges. Based on analyzing the essential meaning of this numerical discretization method,partial surface method （PSM） is brought forward to eradicate the imbalance in continuity equa- tion; as to the motion equations,a new method is firstly proposed in this paper which imitates the con- struction of numerical flux of Roe＇s method. Finally, we adopt the revised mathematical model in simu- lating flow in Jiamusi Reach of the Songhuajiang River and the result shows perfect performance in con- servation, convergence and balance.