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

Majid Niazkar,Gökçen Eryılmaz Türkkan,Leopoldo Greco

doi:10.1155/2021/6692067

Majid Niazkar, Gökçen Eryılmaz Türkkan + Show 1 more

Open Access

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

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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.

Highlights

Water distribution networks (WDNs) are a critical infrastructures that affect the daily life of each and everyone who consumes purified water
Each and every algorithm was coded in MATLAB and MS Excel to solve the sample pipe networks for four different scenarios (92 cases overall), while applications of these programs were previously recommended for implementing numerical modeling [31,32,33] and in particular for pipe network analysis [2, 7, 9]
The numbers of iterations required by the two-step schemes and the original Hardy Cross method to solve the sample WDN are depicted in Figure 4 for the four scenarios

Summary

Introduction

Water distribution networks (WDNs) are a critical infrastructures that affect the daily life of each and everyone who consumes purified water. Management and design of WDNs require the knowledge of flow and pressure fields within WDNs. In essence, management and design of WDNs require the knowledge of flow and pressure fields within WDNs Such knowledge is exclusively provided through pipe network analysis. This analysis is mainly aimed at solving a set of first-order nonlinear differential algebraic equations with iterative methods. (2) It has a slow rate of convergence, and (3) coding of this method may be harder than other available methods [2]. These shortcomings confine the application of Hardy Cross method to solving WDNs [3]

Methods

Results

Conclusion