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

Majid Niazkar and Gökçen Eryılmaz Türkkan

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: 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.

Date: 2021
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https://doi.org/10.1155/2021/6692067

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6692067

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