基于黎曼近似解的溃堤洪水一维-二维耦合数学模型

Coupled one-and two-dimensional numerical modeling of levee-breach flows using the Godunov method

采用一维-二维耦合数学模型对溃堤洪水进行模拟,可以发挥两者优势,提高计算效率。将基于黎曼近似解Godunov格式的一维、二维水流数学模型通过堰流公式进行耦合,实现交界面的水力要素交互;一维、二维模型均采用中心形式的有限体积法求解,分别采用HLL格式和Roe格式计算界面通量,具有一致的空间同步性。通过经典算例验证了模型的可靠性和稳定性,应用耦合模型对1998年松花江干流胖头泡溃堤洪水进行了模拟计算,较好地模拟了溃堤洪水的演进过程与淹没范围,对200年一遇洪水的分洪效果进行了分析,为此区域的分洪利用及松花江中上游防洪调度提供参考依据。

A coupled one-and two-dimensional（1D and 2D） numerical model is used to simulate levee-breach flows.The model uses the Godunov method and can take full advantage of both 1D and 2D modules.The modules can enhance the computational efficiency and improve the simulation accuracy of the coupled model.The exchange of important hydraulic information among the two modules is achieved through the use of a weir flow equation.The approximate Riemann solver of Roe is used in the 2D module for flow computation,while the 1D module uses the HLL（Harten-Lax-van Leer） Riemann solver.Both solvers can ensure the spatial synchronization.The coupled model is tested against a classic data set.The model is also applied to simulate the 1998 levee-breach case occurred in the Songhuajiang River.An analysis is done on the use of Pangtoupao as a flood detention area for accommodating 200-year flood events.The result shows that the coupled model is able to simulate the flood wave propagation through the breaches.The Pangtoupao study provides the valuable information for the levee-breach flood management in the area.