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Type: Journal article
Title: A robust, rapidly convergent method that solves the water distribution equations for pressure-dependent models
Author: Elhay, S.
Piller, O.
Deuerlein, J.
Simpson, A.
Citation: Journal of Water Resources Planning and Management, 2015; 142(2):04015047-1-04015047-12
Publisher: American Society of Civil Engineers
Issue Date: 2015
ISSN: 0733-9496
Statement of
Sylvan Elhay, Olivier Piller, Jochen Deuerlein, Angus R. Simpson
Abstract: In the past, pressure dependent models (PDM) have suffered from convergence diffculties. In this paper conditions are established for the existence and uniqueness of solutions to the PDM problem posed as two optimization problems, one based on weighted least squares (WLS) and the other based on the co-content function. A damping scheme based on Goldstein's algorithm is used and has been found to be both reliable and robust. A critical contribution of this paper is that the Goldstein theorem conditions guarantee convergence of our new method. The new methods have been applied to a set of eight challenging case study networks, the largest of which has nearly 20,000 pipes and 18,000 nodes, and are shown to have convergence behaviour that mirrors that of the Global Gradient Algorithm on demand dependent model problems. A line search scheme based on the WLS optimization problem is proposed as the preferred option because of its smaller computational cost. Additionally, various consumption functions, including the Regularized Wagner function, are considered and four starting value schemes for the heads are proposed and compared. The wide range of challenging case study problems which the new methods quickly solve suggests that the methods proposed in this paper are likely to be suitable for a wide range of PDM problems.
Keywords: pressure dependent models; consumption functions; water distribution systems; co- 18 content; least squares residuals; Goldstein algorithm
Rights: © 2015 American Society of Civil Engineers Read More:
RMID: 0030033268
DOI: 10.1061/(ASCE)WR.1943-5452.0000578
Appears in Collections:Civil and Environmental Engineering publications

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