Solving Nonlinear Hydraulic Equations of Water Distribution Networks by Using a Trust-Region Method
نویسندگان
1 Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
2 Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.
3 Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
doi
10.30473/coam.2022.62968.1195چکیده
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.
