Generalized Flexible Method for Simulating Transient Pipe Network Hydraulics J. D. Nault 1 ; B. W. Karney, M.ASCE 2 ; and B.-S. Jung 3 Abstract: Characteristic solution methods, namely the method of characteristics (MOC) and wave characteristics method (WCM), are widely used for simulating transient pipe network flows. Because the MOC computes solutions at interior nodes, it features higher spatial resolution, whereas the WCM makes simplifications that yield more efficient computations. Practical analyses require numerical methods that are both accurate and computationally efficient. To benefit from the advantages of the two approaches, a generalized characteristic method (GCM) is developed in this paper by combining a flexible friction approximation with a variable reach scheme. Significantly, computational savings are realized by selectively providing greater accuracy and higher resolution solutions only where needed via more interior reaches and higher order solutions; further, the new method reduces to either of the MOC and WCM, thereby showing their intrinsic similarities. Multiple examples compare and contrast the numerical methods. From these, unsteady friction effects and, more importantly, spatial resolution are shown to be directly affected by the interior reach treatment, thus exposing a limitation for solution methods with too few interior reaches. Overall, the key contribution of this work is a methodology featuring a similar degree of accuracy to the MOC, but with a computational cost better than that of the WCM. DOI: 10.1061/(ASCE)HY.1943-7900.0001432. © 2018 American Society of Civil Engineers. Author keywords: Water hammer; Method of characteristics; Wave characteristics method; Hydraulic models; Transient flow; Pipe networks; Water distribution systems. Introduction Water pipe systems are designed and operated to meet specific hy- draulic requirements for pressure and flow. One particular challenge concerns these properties under transient flow conditions, which arise due to changes at the boundaries of a system (e.g., pump and valve operations). The extreme pressures resulting from rapid changes can lead to pipe breaks, component failure, and contaminant intrusion (Boyd et al. 2004; Friedman et al. 2004), so there is an ever- present need for hydraulic transient analysis via numerical modeling. Though important, models are computationally demanding. Fundamental to unsteady flow modeling and thus efficient analysis is the numerical solution of the governing water hammer equations. Various approaches have been developed for pipe net- works, including Eulerian time domain (Chaudhry and Hussaini 1985; Zhao and Ghidaoui 2004; Le´ on et al. 2008; Chaudhry 2014), Lagrangian time domain (Ferrante et al. 2009; Huang et al. 2017), and frequency domain schemes (Wylie and Streeter 1993; Kim 2007; Zecchin et al. 2010; Vítkovský et al. 2011). Among these, the Eulerian method of characteristics (MOC) (Wylie and Streeter 1978) and the Lagrangian wave characteristics method (WCM) (Wood et al. 1966) remain the preferred time-domain alternatives due to their ease of implementation, accurate resolution of shock fronts, and ability to handle complex boundary conditions. By considering interior pipe hydraulics, the MOC yields higher reso- lution solutions; in contrast, the WCM is more efficient because of its underlying simplifications, a key advantage for large pipe net- works. Algebraic water hammer (AWH) (Wylie and Streeter 1993; Nault et al. 2016), a meshless variant of the MOC, represents an even further simplification. Each characteristic approach has a dis- tinct advantage and disadvantage. Central to modeling are numerical accuracy and computational efficiency. The former is necessary to obtain representative solu- tions. Computational efficiency pertains more to practical applica- tions, such as problems involving large networks, optimization (Jung et al. 2011), and model calibration (Ebacher et al. 2011). Water distribution system (WDS) analyses, for instance, concern models having thousands to tens-of-thousands of elements. With- out efficient solution methods, analyses must compromise on accuracy or performing fewer simulations. For this reason, many studies emphasize the more efficient WCM as a superior alternative to the MOC (Wood 2005; Wood et al. 2005b; Ramalingam et al. 2009), but its efficiency comes at the expense of lower solution resolution. Moreover, there is a trade-off between numerical accu- racy and computational efficiency. To improve model efficiency while balancing the need for nu- merically accurate solutions, this work generalizes the advantages of the MOC, WCM, and AWH into a flexible unified fixed grid characteristic approach for simulating transient pipe network hy- draulics. Central to the generalized characteristic method (GCM) are a flexible friction treatment and a variable reach fixed grid scheme; together, these permit individual pipes to be modeled ac- cording to the required solution accuracy. More interior reaches and higher order friction treatments are only provided where needed, maintaining numerical accuracy while yielding efficient computa- tions. Multiple networks of varying complexity demonstrate the 1 Hydraulic Specialist, HydraTek & Associates, Vaughan, ON, Canada L4L 8S5; formerly, Ph.D. Candidate, Dept. of Civil Engineering, Univ. of Toronto, Toronto, ON, Canada M5S 1A4 (corresponding author). E-mail: j.nault@hydratek.com 2 Professor, Dept. of Civil Engineering, Univ. of Toronto, Toronto, ON, Canada M5S 1A4. E-mail: karney@ecf.utoronto.ca 3 Discipline Specialist, Tebodin, P.O. Box 2652, Abu Dhabi, United Arab Emirates. E-mail: paul.jung@tebodin.com Note. This manuscript was submitted on April 3, 2017; approved on September 18, 2017; published online on April 19, 2018. Discussion period open until September 19, 2018; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydraulic Engineering, © ASCE, ISSN 0733-9429. © ASCE 04018031-1 J. Hydraul. Eng. J. Hydraul. Eng., 2018, 144(7): 04018031 Downloaded from ascelibrary.org by Johnathan Nault on 04/19/18. Copyright ASCE. 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