Spurious Numerical Oscillations in the Preissmann Slot Method: Origin and Suppression
Publication: Journal of Hydraulic Engineering
Volume 142, Issue 3
Abstract
This paper investigates the source of the spurious numerical oscillations often observed in simulations using the well-known Preissmann slot method and proposes a nonoscillatory numerical fix that can efficiently suppress the numerical oscillations. The root of these oscillations is identified by comparing the orbits calculated by a first-order Godunov type model with an ideal numerical orbit in the phase plane. It is found that in the very thin layer in the vicinity of the conduit roof the numerical model has insufficient numerical viscosity to avoid the often-observed oscillations. In order to remove these spurious oscillations, an approximate Riemann solution is proposed that automatically enhances the numerical viscosity whenever the water level is in the vicinity of the conduit roof and the pressurization of the conduit is proximate. A comparison of results from the proposed model with both experimental data and analytical solutions show that it can provide nonoscillatory solutions over a wide range of the wave velocities ranging from 10 to . Furthermore, the proposed model effectively controls data smearing.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
We would like to thank Dr. Jose Vasconcelos who generously provided both experimental and numerical data for the verification test.
References
Abbott, M. B. (1982). Engineering applications of computational hydraulics: Homage to Alexandre Preissmann, M. B. Abbott and J. A. Cunge, eds., ASME, New York.
Arai, K., and Yamamoto, K. (2003). “Transient analysis of mixed free surface pressurized flows with modified slot model (Part 1: Computational model and experiment).” Proc., ASME FEDSM’03, 4th ASME-JSME Joint Fluids Engineering Conf., Honolulu.
Arora, M., and Roe, P. L. (1997). “On postshock oscillations due to shock capturing schemes in unsteady flows.” Journal of Comput. Phys., 130(1), 25–40.
Capart, H., Sillen, X., and Zech, Y. (1997). “Numerical and experimental water transients in sewer pipes.” J. Hydraul. Res., 35(5), 659–672.
Chaudhry, M. H. (1999). Open channel flow, Prentice-Hall, Englewood Cliffs, NJ.
Cunge, J. A. (1985). “Discussion of “Transient mixed-flow models for storm sewers” by Charles C. S. Song, James A. Cardle, and Kim Sau Leung.” J. Hydraul. Eng., 557–559.
Karney, B., and Malekpour, A. (2011). Annacis Island wastewater treatment plant stage 5 expansion: Hydraulic transient analysis, HydraTek & Associate, Toronto.
Karni, S., and Čanić, S. (1997). “Computations of slowly moving shocks.” J. Comput. Phys., 136(1), 132–139.
Kerger, F., Archambeau, P., Erpicum, S., Dewals, B. J., and Pirotton, M. (2011). “An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows.” J. Comput. Appl. Math., 235(8), 2030–2040.
Leon, A. S., and Ghidaoui, M. S. (2010). “Discussion of “Numerical oscillations in pipe-filling bore predictions by shock-capturing models” by J. G. Vasconcelos, S. J. Wright, and P. L. Roe.” J. Hydraul. Eng., 392–393.
Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2009). “Application of Godunov-type schemes to transient mixed flows.” J. Hydraul. Res., 47(2), 147–156.
LeVeque, R. (2002). Finite volume methods for hyperbolic problems, Cambridge Press, Cambridge, U.K.
Sanders, B. F., and Bradford, S. F. (2010). “Network implementation of the two-component pressure approach for transient flow in storm sewers.” J. Hydraul. Eng., 158–172.
Sjöberg, A. (1982). “Sewer network models dagvl-a and dagvl-diff.” Urban stormwater hydraulics and hydrology, B. C. Yen, ed., Water Resource, Littleton, CO, 127–136.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, Chichester, U.K.
Toro, E. F., and Garcia-Navarro, P. (2007). “Godunov-type methods for free-surface shallow flows: A review.” J. Hydraul. Res., 45(6), 736–751.
Trajkovic, B., Ivetic, M., Calomino, F., and D’Ippolito, A. (1999). “Investigation of transition from free surface to pressurized flow in a circular pipe.” Water Sci. Technol., 39(9), 105–112.
Vasconcelos, J. G. (2005). “Dynamic approach to the description of flow regime transition in stormwater systems.” Ph.D. thesis., Univ. of Michigan, Ann Arbor, MI.
Vasconcelos, J. G., Wright, S. J., and Roe, P. L. (2006a). “Current issues on modeling extreme inflows in stormwater systems in intelligent modeling of urban water systems, Monograph 14.” Computational Hydraulics International (CHI), Guelph, ON.
Vasconcelos, J. G., Wright, S. J., and Roe, P. L. (2006b). “Improved simulation of flow regime transition in sewers: Two-component pressure approach.” J. Hydraul. Eng., 553–562.
Vasconcelos, J. G., Wright, S. J., and Roe, P. L. (2009). “Numerical oscillations in pipe-filling bore predictions by shock-capturing models.” J. Hydraul. Eng., 296–305.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jul 6, 2014
Accepted: Sep 15, 2015
Published online: Nov 6, 2015
Published in print: Mar 1, 2016
Discussion open until: Apr 6, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.