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Solving Nonlinear Hydraulic Equations of Water Distribution Networks by Using a Trust-Region Method | ||
Control and Optimization in Applied Mathematics | ||
مقاله 3، دوره 7، شماره 2، اسفند 2022، صفحه 53-75 اصل مقاله (1.03 M) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.30473/coam.2022.62968.1195 | ||
نویسندگان | ||
Mahdi Ahmadnia1؛ Reza Ghanbari* 1؛ Khatere Ghorbani-Moghadam2 | ||
1Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. | ||
2Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran. | ||
چکیده | ||
In a water distribution network, in order to analyze and determine its parameters such as head and flow rate, we have to solve nonlinear hydraulic equations in each component of the network. Contrary to most of the water distribution network simulation software, solving these equations by using the gradient method, we propose a trust-region method to solve them, as the trust-region method is newer than the gradient method and has well worked in mathematical problems. To prove the effectiveness of our method, we made a comparison between our proposed method and the well-known gradient method. The results show that the trust-region method is convergent in all instances, but the gradient method diverges when the dimension of nonlinear hydraulic equations of water distribution networks increases. In addition, our results convince the solution obtained from the trust-region method is more accurate compared to the gradient method. Thus, using the trust-region method in solving the network equations can lead to a better hydraulic analysis of the network. | ||
کلیدواژهها | ||
Water distribution network؛ Hydraulic equations؛ Nonlinear equation؛ Trust-Region method | ||
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