基于Godunov格式的一维明渠水流运动数值模拟  

Numerical Simulation of One-Dimensional Open Channel Flows Based on Godunov Scheme

作　　者：梁鑫 侯精明 李东来 吕佳豪 荆海晓[1] 王添[1] 王明宇 LIANG Xin;HOU Jingming;LI Donglai;LYU Jiahao;JING Haixiao;WANG Tian;WANG Mingyu(State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China,Xi’an University of Technology,Xi’an 710048,China;CAUPD Beijing Planning&Design Consultants Ltd.,Beijing 100044,China)

机构地区：[1]西安理工大学西北旱区生态水利国家重点实验室,陕西西安710048 [2]中规院(北京)规划设计有限公司,北京100044

出　　处：《人民黄河》2025年第4期58-63,共6页Yellow River

基　　金：国家自然科学基金资助项目(52079106,52009104)。

摘　　要：针对复杂地形上存在急流、激波或急缓流交替等问题的一维明渠水动力模拟,基于Godunov格式的有限体积法离散Saint-Venant方程组,建立了复杂明渠水动力模型。采用HLL近似Riemann解计算界面通量,通过MUSCL格式和Runge-Kutta方法将时空精度提高至二阶,同时将流量替换为连续性方程中的通量形式以保证流量守恒。采用水面梯度整体作为源项的方程形式,并引入底坡通量法对其求解,摩阻源项则使用无须迭代的显隐式方法进行处理。通过4个典型算例验证了该模型可很好地模拟溃坝、激波和急缓流交替等复杂水流运动过程,具有良好的守恒性和适应性。For the simulation of one-dimensional open channel hydrodynamics on complex terrain with supercritical flow,shockwave or transient mixed super-subcritical flow,a complex open channel hydrodynamic model was developed based on the Saint-Venant equations in Godunov format by using the finite volume method.First of all,the HLL approximate Riemann solution was applied to calculate the interface fluxes,meantime the spatial-temporal accuracy was improved to the second order by MUSCL scheme and Runge-Kutta method,while the flux results were replaced by the flux form in the continuity equations to ensure flux conservation.Besides,the water surface gradient was taken as the source term in equation then the bottom slope flux method was introduced to solve it.Last but not least,the frictional source term was treated by an explicit-implicit method that requires no iterations.The model was validated by four typical examples and the comparison results show that the model can simulate complex processes such as dam break and transient mixed super-subcritical flow very well,having good conservation and adaptability.

关 键 词：明渠水流 GODUNOV 有限体积法 数值模拟 

分 类 号：TV122.1[水利工程—水文学及水资源]