Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis. (10th March 2021)

• Record Type: Journal Article
• Authors: Niazkar, Majid; Eryılmaz Türkkan, Gökçen
• Other Names: Greco Leopoldo Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2021(2021)
• Publication Date: 2021-03-10
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2021/6692067
• Languages: English
• ISSNs: 1687-9120

Abstract

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.