| A new model for the grid size optimization of the finite element method --Based on its application to the water quality modeling of the topographically complicated river |
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| 作者姓名： | ZENG Guangming SU Xiaokang HUANG Guohe XIE Gengxin |
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| 作者单位： | Department of Environment Science and Engineering, Hunan University, Changsha 410082, China,Department of Environment Science and Engineering, Hunan University, Changsha 410082, China,Department of Environment Science and Engineering, Hunan University, Changsha 410082, China,Department of Environment Science and Engineering, Hunan University, Changsha 410082, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (Grant Nos.70171055, 50179011), the National Foud for Distinguished Young Scholars (Grant No.50225926), the Doctoral Foundation of Ministry of Education of China (20020532017), the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China (TRAPOYT) in 2000 and the National 863 High Technology Research Program of China (2001AA644020). |
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| 摘 要： | The finite element method is one of the typical methods that are used for numerical water quality modeling of the topographically complicated river. In this paper, based on the principle of probability theory the probability density of pollutants is introduced. A new model for the grid size optimization based on the finite element method is developed with the incorporation of the maximum information entropy theory when the length of the grid is given. Combined with the experiential evaluation approach of the flow discharge per unit river width, this model can be used to determine the grid size of the finite element method applied to water quality modeling of the topographically complicated river when the velocity field of the river is not given. The calculating results of the application of the model to an ideal river testified the correctness of the model. In a practical case-the application of the model to the Xingjian River (the Hengyang section of the Xiangjiang River), the optimized width of the grid of the finite element method was gained and the influence of parameters was studied, which demonstrated that the model reflected the real situation of the pollutants in the river, and that the model had many excellent characteristics such as stabilization, credibility and high applicability in practical applications.
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| 关 键 词： | finite element method probability density grid maximum information entropy water quality |
A new model for the grid size optimization of the finite element method --Based on its application to the water quality modeling of the topographically complicated river |
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| ZENG Guangming,SU Xiaokang,HUANG Guohe,XIE Gengxin.A new model for the grid size optimization of the finite element method --Based on its application to the water quality modeling of the topographically complicated river[J].Progress in Natural Science,2003,13(12):920-926. |
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| Authors: | ZENG Guangming SU Xiaokang HUANG Guohe XIE Gengxin |
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| Institution: | Department of Environment Science and Engineering, Hunan University, Changsha 410082, China |
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| Abstract: | The finite element method is one of the typical methods that are used for numerical water quality modeling of the topographically complicated river. In this paper, based on the principle of probability theory the probability density of pollutants is introduced. A new model for the grid size optimization based on the finite element method is developed with the incorporation of the maximum information entropy theory when the length of the grid is given. Combined with the experiential evaluation approach of the flow discharge per unit river width, this model can be used to determine the grid size of the finite element method applied to water quality modeling of the topographically complicated river when the velocity field of the river is not given. The calculating results of the application of the model to an ideal river testified the correctness of the model. In a practical case-the application of the model to the Xingjian River (the Hengyang section of the Xiangjiang River), the optimized width of the grid of the finite element method was gained and the influence of parameters was studied, which demonstrated that the model reflected the real situation of the pollutants in the river, and that the model had many excellent characteristics such as stabilization, credibility and high applicability in practical applications. |
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| Keywords: | finite element method probability density grid maximum information entropy water quality |
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