摘要
将求解平面二维浅水方程组的Godunov型有限体积法扩展至求解三维浅水方程组,建立具有激波捕捉特性的三维数学模型,将扩大三维浅水方程数学模型的应用范围。模型中湍流封闭采用非线性K-ε模型,水平方向数值通量采用HLLC近似黎曼求解器计算。为改善数值格式稳定性,垂向扩散项采用隐式离散,且在局部小水深处将三维模型退化为水深平均平面二维模型,所开发的模型在形式上具有时、空二阶精度。随后采用水跃、干河床溃坝洪水演进等算例对模型进行检验,结果表明:该模型具有较好的稳定性,能保证静水平衡,在间断解处能给出高分辨率的数值解,并具有较好的干湿边界模拟能力。
The Godunov finite volume method for solving planar 2D shallow water equations is extended to solve 3D shallow water equations,so as to establish a three-dimensional mathematical model with shock capture characteristic,the application of 3D shallow water equations will be expanded.In this paper,the 3D shallow-water equations inσ-coordinates were solved based on the Godunov-type finite-volume method.The nonlinear k-?model was employed for turbulent flow closure,the HLLC approximate Riemann solver was involved to calculate the horizontal numerical fluxes.To improve the numerical stability,the vertical diffusion-term was implicitly discretized,and the 3D model was locally switched to a horizontally depth-averaged 2D model in which the water depth was sufficiently small.The developed model was form second-order form in both space and time.The model was verified by classical tests including hydraulic jump and dam-break flood propagating in a dry river bed,and the results showed that the developed model is stable,well-balanced,capable of predicting high-resolution solution around discontinuities,and simulates wetting and drying processes well.
作者
卢新华
LU Xinhua(State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan 430072,China)
出处
《人民长江》
北大核心
2018年第20期74-80,94,共8页
Yangtze River
基金
国家自然科学基金项目"基于双层深度平均模型的波浪与浮泥相互作用研究"(51409195)
湖北省自然科学基金项目"色散与非色散波作用下航道回淤数值模拟研究"(2016CFB385)
关键词
三维浅水方程
近似黎曼求解器
静水平衡
高分辨率
σ坐标系
3D shallow water equations
approximate Riemann solver
balance in calm water
high-resolution
sigma-coordinates
作者简介
卢新华,男,副教授,博士,研究方向为河流海岸动力学。E-mail:xhluhh@whu.edu.cn。
