Development of a Cell-Centered Godunov-Type Finite Volume Model for Shallow Water Flow Based on Unstructured Mesh
Development of a Cell-Centered Godunov-Type Finite Volume Model for Shallow Water Flow Based on Unstructured Mesh
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基于非结构网格的浅水流单元中心Godunov型有限体积模型的建立
DOI：
10.1155/2014/257915
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发表时间：
2014-05
影响因子：
--
通讯作者：
Liu Guohua
中科院分区：
文献类型：
--
作者：
Wu Gangfeng;He Zhiguo;Liu Guohua
基于godunov型胞心有限体积法，提出了一种二维良好平衡浅水模型，用于模拟任意地形上的干湿流动。采用中心迎风格式计算界面上的质量通量和动量通量。该模型的新颖之处在于在非结构化网格中实现鲁棒、精确的非负水深重建方法，以实现空间上的二阶精度，并跟踪不规则地形上流动的干湿锋。通过在非交错网格系统中定义床层高程和细胞中心的一次流动变量，所有计算细胞要么是完全湿的，要么是干燥的，以避免部分湿润的问题。所建立的模型具有良好的平衡性，在一定的CFL约束下保持计算水深不为负，具有鲁棒性和稳定性。通过三个基准试验和两个实验室溃坝实例验证了该模型的有效性。最后，马尔帕塞特溃坝事件1/400比例尺物理模型的数值计算结果与实测数据吻合较好，说明该模型具有较好的实际应用价值。
Based on the Godunov-type cell-centered finite volume method, this paper presents a two-dimensional well-balanced shallow water model for simulating flows over arbitrary topography with wetting and drying. The central upwind scheme is used for the computation of mass and momentum fluxes on interface. The novel aspect of the present model is a robust and accurate nonnegative water depth reconstruction method which is implemented in the unstructured mesh to achieve second-order accuracy in space and to track the moving wet/dry fronts of the flow over irregular terrain. By defining the bed elevation and primary flow variables at the cell center in the nonstaggered grid system, all computational cells are either fully wet or dry to avoid the problem of being partially wetted. The developed model is capable of being well balanced and preserving the computed water depth to be nonnegative under a certain CFL restriction, which makes it robust and stable. The present model is validated against three benchmark tests and two laboratory dam-break cases. Finally, the good agreement between the numerical results by the established model and measured data of the Malpasset dam break event on a 1/400 scale physical model demonstrates the capability of the model for the real-life applications.
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DOI：
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发表时间：
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影响因子：
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