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Solving Nonlinear Hydraulic Equations of Water Distribution Networks by Using a Trust-Region Method

Publish Year: 1401
Type: Journal paper
Language: English
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JR_COAM-7-2_003

Index date: 19 February 2023

Solving Nonlinear Hydraulic Equations of Water Distribution Networks by Using a Trust-Region Method abstract

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.

Solving Nonlinear Hydraulic Equations of Water Distribution Networks by Using a Trust-Region Method Keywords:

Solving Nonlinear Hydraulic Equations of Water Distribution Networks by Using a Trust-Region Method authors

Mahdi Ahmadnia

Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran.

Reza Ghanbari

Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran.

Khatere Ghorbani-Moghadam

Mosaheb Institute of Mathematics‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran‎.

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