具有守恒特性的二维溃坝洪水演进数值模型  

A well-balanced two-dimensional numerical model for dam-break flood simulation

作　　者：吴钢锋[1] 贺治国[2] 刘国华[1] 

机构地区：[1]浙江大学水工结构与水环境研究所,浙江杭州310058 [2]浙江大学海洋科学与工程学系,浙江杭州310058

出　　处：《水科学进展》2013年第5期683-691,共9页Advances in Water Science

基　　金：国家重点基础研究发展计划(973计划)资助项目(2013CB035900);国家自然科学基金资助项目(51009120)~~

摘　　要：基于结构网格,采用有限体积法建立了二维水动力学模型,模拟溃坝洪水在复杂实际地形条件下的流动过程。该模型采用中心迎风格式求解界面通量,并结合对界面变量的线性重构,使其具有空间上的二阶精度。分别采用中心差分方法和半隐式方法对底床坡度项和摩擦阻力项进行离散,保证了模型的和谐性和稳定性。对于复杂地形条件下溃坝洪水的模拟,负水深的产生是影响模型稳定的关键因素。当库朗特数小于0.25时,模型能够保证任何时刻的计算水深都是非负的,而无需对负水深单元进行特殊处理。因此,相比于现有的大部分溃坝洪水模型,该模型具有更强的鲁棒性和稳定性。A two-dimensional hydrodynamic model is developed to simulate the dam-break flood wave propagation o- ver complex topography. A structured grid and the finite volume method are used for the model development. A cen- tral upwind scheme is used to calculate the flux at the interface of computational meshes and the linear reconstruction of flow variables is adopted to achieve the second-order accuracy in space. The bed slope source term and friction term are respectively discretized using a central difference scheme and a semi-implicit method, which can ensure a well- balanced property and the stability of the model. The negative water depth is the key factor affecting the model stability when a dam-break flood simulation is performed on irregular terrains. The new model is able to avoid negative water depths when the Courant number remains less than 0.25. Therefore, the new model is more robust and stable compared to most existing models. The numerical result shows that the model is stable and robust, and has a wide range of application potentials.

关 键 词：溃坝 结构网格 二维浅水方程 有限体积法 中心迎风格式 数值和谐性 

分 类 号：TV131.2[水利工程—水力学及河流动力学]