Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis
In this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in s...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6692067 |
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| _version_ | 1832555011525050368 |
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| author | Majid Niazkar Gökçen Eryılmaz Türkkan |
| author_facet | Majid Niazkar Gökçen Eryılmaz Türkkan |
| author_sort | Majid Niazkar |
| collection | DOAJ |
| description | In this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. The performances of these new methods and Hardy Cross method were compared by solving a sample pipe network considering four different scenarios (92 cases). The results show that the one-step methods improve the rate of convergence of the Hardy Cross method in 10 out of 24 cases (41%), while this improvement was found to be 39 out of 56 cases (69.64%) and 5 out of 8 cases (62.5%) for the two-step and three-step methods, respectively. This obviously indicates that the modified schemes, particularly the three-step methods, improve the performance of the original loop corrector method by taking lower number of iterations with the compensation of relatively more computational efforts. |
| format | Article |
| id | doaj-art-be938c9c6de34a799c2f3f4efdf6eea1 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-be938c9c6de34a799c2f3f4efdf6eea12025-02-03T05:49:49ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66920676692067Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network AnalysisMajid Niazkar0Gökçen Eryılmaz Türkkan1Department of Civil and Environmental Engineering, Shiraz University, Shiraz, IranDepartment of Civil Engineering, Bayburt University, Bayburt, TurkeyIn this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. The performances of these new methods and Hardy Cross method were compared by solving a sample pipe network considering four different scenarios (92 cases). The results show that the one-step methods improve the rate of convergence of the Hardy Cross method in 10 out of 24 cases (41%), while this improvement was found to be 39 out of 56 cases (69.64%) and 5 out of 8 cases (62.5%) for the two-step and three-step methods, respectively. This obviously indicates that the modified schemes, particularly the three-step methods, improve the performance of the original loop corrector method by taking lower number of iterations with the compensation of relatively more computational efforts.http://dx.doi.org/10.1155/2021/6692067 |
| spellingShingle | Majid Niazkar Gökçen Eryılmaz Türkkan Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis Advances in Mathematical Physics |
| title | Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis |
| title_full | Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis |
| title_fullStr | Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis |
| title_full_unstemmed | Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis |
| title_short | Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis |
| title_sort | application of third order schemes to improve the convergence of the hardy cross method in pipe network analysis |
| url | http://dx.doi.org/10.1155/2021/6692067 |
| work_keys_str_mv | AT majidniazkar applicationofthirdorderschemestoimprovetheconvergenceofthehardycrossmethodinpipenetworkanalysis AT gokceneryılmazturkkan applicationofthirdorderschemestoimprovetheconvergenceofthehardycrossmethodinpipenetworkanalysis |