Nonmatrix Gradient Method for the Simulation of Water Distribution Networks

Luvizotto, Edevar; Cavichia, Mario Conrado; Vatavuk, Paulo; Andrade, José Geraldo Pena de

doi:10.1061/(asce)wr.1943-5452.0000271

Cited by 4 publications

(2 citation statements)

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“…The unknown state variables of a pipe network, i.e., pipe flow rate (Q) and nodal hydraulic head (h), are determined by solving these two equations [7]. The iteration-based methods of water distribution networks can be classified as two main approaches [10]: (1) matrix-based and (2) nonmatrix-based methods. The former ones form a matrix equation comprising the governing equations and attempt to solve these equations simultaneously whereas the latter deals with solving equations separately in two steps: First, linear continuity equations are satisfied, and second, nonlinear energy equations are solved iteratively.…”

Section: Methodsmentioning

confidence: 99%

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Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis

Niazkar

Türkkan

2021

Advances in Mathematical Physics

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In this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. The performances of these new methods and Hardy Cross method were compared by solving a sample pipe network considering four different scenarios (92 cases). The results show that the one-step methods improve the rate of convergence of the Hardy Cross method in 10 out of 24 cases (41%), while this improvement was found to be 39 out of 56 cases (69.64%) and 5 out of 8 cases (62.5%) for the two-step and three-step methods, respectively. This obviously indicates that the modified schemes, particularly the three-step methods, improve the performance of the original loop corrector method by taking lower number of iterations with the compensation of relatively more computational efforts.

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Section: Methodsmentioning

confidence: 99%

“…Not only this method is adaptable with handy calculations, but also it can be easily implemented in spreadsheets [4]. Moreover, the Hardy Cross method solves water networks without forming matrix equations [10]. Nonetheless, the convergence of this method is low in comparison to some of matrix-based approaches [11,12].…”

Section: Introductionmentioning

confidence: 99%