| 自适应网格在复杂地形浅水方程求解中的应用 |
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| 引用本文： | 周建中,张华杰,毕胜,严凡,赵越.自适应网格在复杂地形浅水方程求解中的应用[J].水科学进展,2013,24(6):861-868. |
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| 作者姓名： | 周建中 张华杰 毕胜 严凡 赵越 |
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| 作者单位： | 1.华中科技大学水电与数字化工程学院, 湖北武汉 430074; |
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| 基金项目： | 国家自然科学基金资助项目（51239004）；水利部公益性行业科研专项经费资助项目（201001080） |
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| 摘 要： | 计算域内地形的概化精度对模拟结果有较大影响，针对实际地形中同时存在狭长河谷与广阔泛洪区的问题，在层次自适应网格模型的基础上，研究了网格快速加密与合并的步骤，并以水位梯度与局部弗劳德数为基础设计了网格自适应准则，当水流运动情势变化时网格密度自动调整，实现计算精度与效率的平衡。在此网格模型基础上，采用有限体积法求解二维浅水方程，利用梯度限制器技术及龙格-库塔法提高模型的空间、时间计算精度。算例表明，层次自适应网格模型既能实现随水流运动动态变化并捕获水位计算敏感区，也能对局部区域进行静态固定加密，自适应性良好，具有较好的推广应用价值。
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| 关 键 词： | 洪水 二维浅水方程 自适应网格 Godunov格式 复杂地形 |
| 收稿时间： | 2013-01-23 |
An application of adaptive grid method to shallow water equations on complex topography |
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| ZHOU Jianzhong,ZHANG Huajie,BI Sheng,YAN Fan,ZHAO Yue.An application of adaptive grid method to shallow water equations on complex topography[J].Advances in Water Science,2013,24(6):861-868. |
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| Authors: | ZHOU Jianzhong ZHANG Huajie BI Sheng YAN Fan ZHAO Yue |
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| Institution: | 1.School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2.Hubei Key Laboratory of Digital Valley Science and Technology, Wuhan 430074, China |
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| Abstract: | The quality of terrain generalization has an important impact on the result of numerical simulations. Aiming at the practical issue associated with the coexistence of long narrow valleys and vast floodplain, an adaptive grid method with hierarchical structures (HAGM) is introduced. The adaptive criterion is made on the basis of the gradient of free surface elevation and the local Froude number. The local grid density can be adjusted automatically in response to a changing flow regime, which makes it possible to achieve a balance between accuracy and computational efficiency in numerical simulations. The finite volume method is used to solve the two-dimensional shallow water equations based on the HAGM. Gradient limiters and the two-step Runge-Kutta scheme are employed to improve the accuracy in space resolution and time marching, respectively. Results of numerical experiments show that the HAGM has good performance in adapting to a changing flow regime, in capturing sensitive zones for water level calculation, and in achieving local grid refinement. The proposed HAGM is thus suitable for a wide range of applications. |
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| Keywords: | flood two-dimensional shallow water equations adaptive grid Godunov scheme complex topography |
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