A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media
Considering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/15/6/1030 |
| _version_ | 1797608628753006592 |
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| author | Qianfeng Yuan Dong Yin Yuting Chen |
| author_facet | Qianfeng Yuan Dong Yin Yuting Chen |
| author_sort | Qianfeng Yuan |
| collection | DOAJ |
| description | Considering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic conductivity and continuity equation equivalent to the continuum model are formulated based on the principle of flow balance. Subsequently, the unified form for flow velocity and continuity equation is established based on the local coordinate system, and a finite line-element method is developed, in which three-dimensional steady free surface flow is reduced to one-dimensional form, and the numerical difficulty is greatly decreased. The proposed line-element model is validated by the good agreements of free surface locations with other methods through steady flow in a rectangular dam and a right trapezoidal dam, respectively. It is found that the proposed line-element model is not heavily dependent on the mesh size and penalty parameter. Steady free surface flow on the left bank abutment slope of the Kajiwa Dam in Southwestern China is further evaluated, and a parabolic variational inequality algorithm based on the continuum model is also employed for comparison. The consistent results indicate that the proposed line-element model can capture the steady free surface flow behavior as well as the continuum-based method. Moreover, the proposed line-element model can rapidly achieve accurate solutions whether for simple examples or for complicated engineering applications. |
| first_indexed | 2024-03-11T05:45:54Z |
| format | Article |
| id | doaj.art-88120075908e40979545daebff89d523 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-11T05:45:54Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-88120075908e40979545daebff89d5232023-11-17T14:25:25ZengMDPI AGWater2073-44412023-03-01156103010.3390/w15061030A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous MediaQianfeng Yuan0Dong Yin1Yuting Chen2School of Resource and Environmental Engineering, Wuhan University of Science and Technology, Wuhan 430081, ChinaSchool of Resource and Environmental Engineering, Wuhan University of Science and Technology, Wuhan 430081, ChinaChangjiang Survey, Planning, Design and Research Co., Ltd., Wuhan 430010, ChinaConsidering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic conductivity and continuity equation equivalent to the continuum model are formulated based on the principle of flow balance. Subsequently, the unified form for flow velocity and continuity equation is established based on the local coordinate system, and a finite line-element method is developed, in which three-dimensional steady free surface flow is reduced to one-dimensional form, and the numerical difficulty is greatly decreased. The proposed line-element model is validated by the good agreements of free surface locations with other methods through steady flow in a rectangular dam and a right trapezoidal dam, respectively. It is found that the proposed line-element model is not heavily dependent on the mesh size and penalty parameter. Steady free surface flow on the left bank abutment slope of the Kajiwa Dam in Southwestern China is further evaluated, and a parabolic variational inequality algorithm based on the continuum model is also employed for comparison. The consistent results indicate that the proposed line-element model can capture the steady free surface flow behavior as well as the continuum-based method. Moreover, the proposed line-element model can rapidly achieve accurate solutions whether for simple examples or for complicated engineering applications.https://www.mdpi.com/2073-4441/15/6/1030three-dimensional flowfree surfaceline-element modelporous media |
| spellingShingle | Qianfeng Yuan Dong Yin Yuting Chen A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media Water three-dimensional flow free surface line-element model porous media |
| title | A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media |
| title_full | A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media |
| title_fullStr | A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media |
| title_full_unstemmed | A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media |
| title_short | A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media |
| title_sort | simple line element model for three dimensional analysis of steady free surface flow through porous media |
| topic | three-dimensional flow free surface line-element model porous media |
| url | https://www.mdpi.com/2073-4441/15/6/1030 |
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