Well-Balanced Scheme for Modeling Open-Channel and Surcharged Flows in Steep-Slope Closed Conduit Systems
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 4
Abstract
The model presented in this paper preserves lake at rest conditions in sloped prismatic conduits. These schemes are based on the two-governing equation model in which open-channel flows are simulated using the Saint-Venant equations and pressurized flows using the compressible water hammer equations. The model in this paper preserves lake at rest conditions (horizontal still water) regardless of the conduit slope, resolves moving jump discontinuities over dry beds in sloped conduits, and resolves small perturbations from steady states, even when adjacent to dry regions. The preserving steady-state capability of this model is of particular importance in continuous long simulations when the conduits are relatively steep (. Two main contributions are presented in this paper, namely, (1) a new method for water stage reconstruction is presented that preserves lake at rest conditions regardless of the pipe slope, and (2) a horizontal system of coordinates, instead of the commonly used inclined coordinate system, is used for facilitating the implementation of the proposed well-balanced scheme to complex systems. In the horizontal coordinate system, the cross section of a circular pipe becomes an ellipse. The hydraulic characteristics of an ellipse are presented. Good results are achieved in the test cases.
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Acknowledgments
The authors gratefully acknowledge the financial support of the School of Civil and Construction Engineering at Oregon State University (OSU) and Northwest Hydraulic Consultants (NHC), Pasadena, CA. The authors also gratefully acknowledge Drs. David Axworthy, Mohamed Ghidaoui, and Arthur Schmidt for providing insightful comments and suggestions during the preparation of the manuscript. Last but not least, the authors are indebted to the anonymous reviewers for their insight, constructive criticisms and suggestions on an earlier version of the manuscript.
References
Begnudelli, L., and Sanders, B. F. (2006). “Unstructured grid finite volume algorithm for shallow-water flow and transport with wetting and drying.” J. Hydraul. Eng., 132(4), 371–384.
Bourdarias, C., and Gerbi, S. (2007). “A finite volume scheme for a model coupling free surface and pressurised flows in pipes.” J. Comput. Appl. Math., 209(1), 109–131.
Canestrelli, A., Siviglia, A., Dumbser, M., and Toro, E. F. (2009). “Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed.” Adv. Water Res., 32(6), 834–844.
Capart, H., Eldho, T. I., Huang, S. Y., Young, D. L., and Zech, Y. (2003). “Treatment of natural geometry in finite volume river flow computations.” J. Hydraul. Eng., 129(5), 385–393.
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. (1987). Applied hydraulic transients, Van Nostrand Reinhold, New York.
Chaudhry, M. H. (2008). Open-channel flow, 2nd Ed., Springer-Verlag, New York.
George, D. L. (2006). “Finite volume methods and adaptive refinement for tsunami propagation and inundation.” Ph.D. thesis, Dept. of Applied Mathematics, Univ. of Washington, Seattle.
Leon, A. S., and Ghidaoui, M. S. (2010). “Discussion of ‘Numerical oscillations in pipe-filling bore predictions by shock-capturing models’ by Jose G. Vasconcelos, Steven J. Wright and Philip L. Roe.” J. Hydraul. Eng., 136(6), 392–393.
Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2006). “Godunov-type solutions for transient flows in sewers.” J. Hydraul. Eng., 132(8), 800–813.
Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2007). “An efficient finite-volume scheme for modeling water hammer flows.” Contemporary modeling of urban water systems, Monograph 15, W. James, ed., Computational Hydraulics International (CHI), Toronto, ON, Canada.
Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2008). “An efficient second-order accurate shock capturing scheme for modeling one and two-phase water hammer flows.” J. Hydraul. Eng., 134(7), 970–983.
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.
Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2010a). “A robust two-equation model for transient mixed flows.” J. Hydraul. Res., 48(1), 44–56.
Leon, A. S., Liu, X., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2010b). “Junction and drop-shaft boundary conditions for modeling free-surface, pressurized, and mixed free-surface pressurized transient flows.” J. Hydraul. Eng., 136(10), 705–715.
LeVeque, R. J. (1998). “Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm.” J. Comput. Phys., 146(1), 346–365.
LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems, Cambridge University Press, Cambridge, UK.
Sanders, B. F., and Bradford, S. F. (2011). “A network implementation of the two-component pressure approach for transient flow in storm sewers.” J. Hydraul. Eng. 137(2), 158–172.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, Chichester, U.K.
Vasconcelos, J. G., Wright, S. J., and Roe, P. L. (2006). “Improved simulation of flow regime transition in sewers: Two-component pressure approach.” J. Hydraul. Eng., 132(6), 553–562.
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Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 4 • April 2013
Pages: 374 - 384
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Oct 9, 2011
Accepted: Oct 9, 2012
Published online: Oct 11, 2012
Published in print: Apr 1, 2013
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