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

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.