| 基于非结构混合网格求解二维浅水方程的一种数值方法 |
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| 引用本文： | 董炳江,卢新华,袁晶.基于非结构混合网格求解二维浅水方程的一种数值方法[J].水科学进展,2013,24(1):103-110. |
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| 作者姓名： | 董炳江 卢新华 袁晶 |
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| 作者单位： | 1.长江水利委员会水文局, 湖北武汉 430010; |
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| 基金项目： | 国家重点基础研究发展计划(973)资助项目(2012CB417001);中央高校基本科研业务费专项资金资助项目(206275798)~~ |
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| 摘 要： | 复杂边界下的流场数值模拟常基于非结构化网格进行求解,建立一种在非结构混合网格上求解水深平均的二维浅水方程的模型,以便精确模拟复杂边界、提高计算效率。该模型时间项离散采用隐格式使得模型具有较好的稳定性,对流项和扩散项分别采用总变差减小(Total Variation Diminishing,TVD)格式和构造辅助点的方法来离散,同时采用水深平均的标准k-ε模型来封闭湍流模型。选用两个经典验证算例检验模型,计算结果表明,基于非结构混合网格开发的模型具有较高的精度,且收敛性能较好。
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| 关 键 词： | 非结构网格 混合网格 TVD格式 浅水方程 |
| 收稿时间： | 2012-02-13 |
A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids |
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| DONG Bingjiang,LU Xinhua,YUAN Jing.A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids[J].Advances in Water Science,2013,24(1):103-110. |
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| Authors: | DONG Bingjiang LU Xinhua YUAN Jing |
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| Affiliation: | 1.Bureau of Hydrology Changjiang Water Resources Commission, Wuhan 430010, China;2.State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China |
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| Abstract: | Unstructured grids are usually adopted in the solution of complex boundary flows. In this study, a depth-averaged two-dimensional (2-D) flow model is developed for mixed unstructured grids. The model uses both triangular cells and quadrilaterals, which ensures an accurate representation of irregular boundaries and at the same time, achieving a high computational efficiency. The unsteady term in the 2-D shallow water equations is treated implicitly. While the convection and diffusion terms are respectively approximated using the TVD (Total Variation Diminishing) algorithm and the auxiliary-point method. The depth-averaged standard k-ε model is used for turbulent closure. Two classical test cases are chosen for model verification. The first one is a 2-D diversion flow case, and the second is a 90 degree bend-flow case. Results show that the proposed model performs well in terms of accuracy and presents good convergence characteristics. |
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| Keywords: | unstructured grid mixed grid total variation diminishing shallow water equations |
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