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An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches

1
Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
2
Department of Civil and Mineral Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada
*
Authors to whom correspondence should be addressed.
Academic Editor: Inmaculada Pulido-Calvo
Water 2021, 13(11), 1597; https://doi.org/10.3390/w13111597
Received: 14 May 2021 / Accepted: 1 June 2021 / Published: 5 June 2021
(This article belongs to the Section Hydraulics and Hydrodynamics)
Here, recent developments in the key numerical approaches to water hammer modelling are summarized and critiqued. This paper summarizes one-dimensional modelling using the finite difference method (FDM), the method of characteristics (MOC), and especially the more recent finite volume method (FVM). The discussion is briefly extended to two-dimensional modelling, as well as to computational fluid dynamics (CFD) approaches. Finite volume methods are of particular note, since they approximate the governing partial differential equations (PDEs) in a volume integral form, thus intrinsically conserving mass and momentum fluxes. Accuracy in transient modelling is particularly important in certain (typically more nuanced) applications, including fault (leakage and blockage) detection. The FVM, first advanced using Godunov’s scheme, is preferred in cases where wave celerity evolves over time (e.g., due to the release of air) or due to spatial changes (e.g., due to changes in wall thickness). Both numerical and experimental studies demonstrate that the first-order Godunov’s scheme compares favourably with the MOC in terms of accuracy and computational speed; with further advances in the FVM schemes, it progressively achieves faster and more accurate codes. The current range of numerical methods is discussed and illustrated, including highlighting both their limitations and their advantages. View Full-Text
Keywords: water hammer; computational fluid dynamics; MOC; FDM; FVM; pipe network water hammer; computational fluid dynamics; MOC; FDM; FVM; pipe network
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MDPI and ACS Style

Pal, S.; Hanmaiahgari, P.R.; Karney, B.W. An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches. Water 2021, 13, 1597. https://doi.org/10.3390/w13111597

AMA Style

Pal S, Hanmaiahgari PR, Karney BW. An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches. Water. 2021; 13(11):1597. https://doi.org/10.3390/w13111597

Chicago/Turabian Style

Pal, Susovan, Prashanth R. Hanmaiahgari, and Bryan W. Karney 2021. "An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches" Water 13, no. 11: 1597. https://doi.org/10.3390/w13111597

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