Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems
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VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 139, Issue 4
Abstract
This paper presents and discusses a simple method to deal with zero flows in Newton solvers for water distribution systems, in particular in a previously published global gradient algorithm. The method consists in replacing the Hazen-Williams head loss–flow relationship for flows below a certain threshold with a linear relationship, which coincides with Hazen-Williams’ at zero, but has a nonzero derivative at that point, thus avoiding computational troubles associated with zero flows. Manual and automatic random testing of example networks shows that the proposed method compares well with both the algorithm adopted in water distribution modeling software and the recently proposed regularization method in convergence rate while outperforming them in computational veracity and applicability range.
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Acknowledgments
This work was supported by the National Council of Science and Technology (CONACYT) of Mexico.
References
Boulos, P. F., and Altman, T. (1993). “An explicit approach to modeling closed pipes in water networks.” Appl. Math. Model, 17(8), 437–443.
Boulos, P. F., Lansey, K. E., and Karney, B. W. (2006). Comprehensive water distribution systems analysis handbook for engineers and planners, 2nd Ed., MWH Soft Press, Bloomfield, CO.
Campos, A. (1993). “Steady-state fluid network analysis.” J. Hydraul. Eng., 119(3), 431–436.
Elhay, S., and Simpson, A. R. (2011). “Dealing with zero flows in solving the nonlinear equations for water distribution systems.” J. Hydraul. Eng., 137(10), 1216–1224.
Estrada, S., González, C., Aloid, R., and Paño, J. (2009). “Improved pressurized pipe network hydraulic solver for applications in irrigation systems.” J. Irrig. Drain. Eng., 135(4), 421–430.
Gorev, N. B., and Kodzhespirova, I. F. (2013). “Discussion of ‘Dealing with zero flows in solving the nonlinear equations for water distribution systems’ by Sylvan Elhay and Angus R. Simpson.” J. Hydraul. Eng., 139(5), in press.
Gorev, N. B., Kodzhespirova, I. F., Kovalenko, Yu., Álvarez, R., Prokhorov, E., and Ramos, A. (2011). “Evolutionary testing of hydraulic simulator functionality.” Water Resour. Manage., 25(8), 1935–1947.
Rivera, J. J., et al. (2010). “Hydraulic simulator testing: Methods, tools, and results.” Water Distribution Systems Analysis 2010: Proc., 12th Int. Conf., ASCE, Reston, VA, 263–279.
Rossman, L. (2000). EPANET 2 user’s manual, U.S. Environmental Protection Agency, Cincinnati.
Todini, E., and Pilati, S. (1988). “A gradient algorithm for the analysis of pipe networks.” Computer applications in water supply, Vol. 1, system analysis and simulation, B. Coulbeck and O. Chun-Hou, eds., Wiley, London, 1–20.
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Information
Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 4 • April 2013
Pages: 456 - 459
Copyright
© 2013 American Society of Civil Engineers.
History
Received: May 29, 2012
Accepted: Oct 23, 2012
Published online: Oct 25, 2012
Published in print: Apr 1, 2013
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