Research On Hydraulic Calculation Of Water Pipe Network Based On Preconditioned Conjugate Gradient Method

With the development of the national economy and the acceleration of the urbaniza-tion process, the problem of water supply has become one of the most prominent problemsin the sustainable social and economic development in China. Scientific and modern wa-ter management provides an efective way to solve the current problem of water supply.Digital modeling and dynamic simulation of the Water Distribution Network(WDN) toachieve urban WDN of scientific management decision-support tools, hydraulic calculationand analysis of WDN, especially with multi-reservoirs or multi-lakes has become the kerneltechnology of digital modeling and dynamic simulation of it.Unconstrained optimization problems have always been the hot topics of optimiza-tion field, conjugate gradient method and its improved algorithms are one solution ofunconstrained optimization problems. WDN modeling can be formed as the WDN hy-draulic characteristics of equations when combined with hydraulic characteristics. Solutionmethod with node flow continuity equations is one of the most suitable and implementedhydraulic calculation method with computers.In this paper, node flow continuity equations have been re-designed and constructedso that the coefcient matrix of equations has symmetric positive definiteness and diag-onally dominant matrix. To solve it with preconditioned conjugate gradient method, themodified Cholesky decomposition method is used to triangularly decompose the recon-structed matrix. The indexed triples structure is designed to compress and store the largesparse matrix due to its high dimensions in the practical application and in accordancewith the fast calculation for the preconditioned conjugate gradient method.Numerical calculation examples show that the proposed algorithm in this paper canbe used to real-time solve large-scale urban WDN system. Based on the method proposedin this paper, one of the important applications in the WDN hydraulic calculation, WDNplanning calculation and analysis, is also demonstrated the proposed calculation methodis less time-consuming diverse computing model. The proposed method is also suitable for a wide range of other application scenarios, such as reconstruction and optimization ofWDN.