Quasi-Conservative Formulation of the One-Dimensional Saint-Venant–Exner Model
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 10
Abstract
Coupling the Saint-Venant equations with the Exner equation a morphodynamic model is produced, which can be used to describe flow and bed evolution in natural rivers. The system of governing equations is hyperbolic and is expressed in nonconservative form. For this reason, fully primitive formulations of the model are often adopted for the solution, which however are known to incorrectly compute strength and celerity of shock waves (bores). In the present work a quasi-conservative formulation of the differential system is proposed, which aims at reducing these errors to a minimum. The performances of the model are assessed by comparison with primitive formulations applied to some schematic cases and with experimental observations obtained on a physical model of a river reach. Results are satisfactory and overcome predictions based on fully primitive formulations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research has been partially supported by the Fondazione Cassa di Risparmio di Verona, Vicenza, Belluno ed Ancona (Project MODITE).
References
Bellal, M., Spinewine, C., and Zech, Y. (2003). “Morphological evolution of steep-sloped river beds in the presence of a hydraulic jump.” Proc., XXX IAHR Congress, International Association for Hydraulic Research (IAHR), 133–140.
Cao, Z., Day, R., and Egashira, A. (2002). “Coupled and decoupled numerical modeling of flow and morphological evolution in alluvial rivers.” J. Hydraul. Eng., 128(3), 306–321.
Colombini, M., and Stocchino, A. (2005). “Coupling or decoupling bed and flow dynamics: Fast and slow sediment waves at high Froude numbers.” Phys. Fluids, 17(3), 1–9.
Correia, L., Krishnappan, B., and Graf, W. (1992). “Fully coupled unsteady mobile boundary flow model.” J. Hydraul. Eng., 118(3), 476–494.
Cui, Y., Parker, G., and Paola, C. (1996). “Numerical simulation of aggradation and downstream fining.” J. Hydraul. Res., 34(2), 195–204.
Cunge, J. A., Holly, F. M., and Verwey, A. (1994). Practical aspects of computational river hydraulics, Pitman, reprinted by the Univ. of Iowa.
Engelund, F. (1964). “Book of abstracts.” Rep. No. 6, Univ. of Denmark.
Garcia-Navarro, P., Fras, A., and Villanueva, I. (1999). “Dam-break flow simulation: Some results for one-dimensional models of real cases.” J. Hydrol., 216, 227–247.
Holly, F., and Rahuel, J. (1990). “New numerical/physical framework for mobile bed modelling. Part 1: Numerical and physical principles.” J. Hydraul. Res., 28(4), 401–416.
Hou, T., and LeFloch, P. (1994). “Why non-conservative schemes converge to the wrong solutions: Error analysis.” Math. Comput., 62, 497–530.
Lanzoni, S., Siviglia, A., Frascati A., and Seminara, G. (2006). “Long waves in erodible channels and morphodynamic influence.” Water Resour. Res., 42, W06D17.
Lax, P., and Wendroff, B. (1960). “Systems of conservation laws.” Commun. Pure Appl. Math., 13, 217–237.
Lyn, D., and Altinakar, M. (2002). “St. Venant exner equations for near-critical and transcritical flows.” J. Hydraul. Eng., 128(6), 579–587.
Parker, G. (1990). “Surface-based bedload transport relation for gravel rivers.” J. Hydraul. Res., 28(4), 417–436.
Sieben, J. (1999). “A theoretical analysis of discontinuous flows with mobile bed.” J. Hydraul. Res., 37(2), 199–212.
Singh, A., Kothyari, U., and Ranga Raju, K. (2004). “Rapidly varying transient flows in alluvial rivers.” J. Hydraul. Res., 42(5), 473–486.
Toro, E. (1999). Riemann solvers and numerical methods for fluid dynamics, 2nd Ed., Springer, New York.
Toro, E. (2006). “Riemann solvers with evolved initial conditions.” Int. J. Numer. Methods Fluids, 52(4), 433–453, ⟨http://www3.interscience.wiley.com/journal/112769978/issue⟩.
Toro, E., and Siviglia, A. (2003). “Price: Primitive centered schemes for hyperbolic system of equations.” Int. J. Numer. Methods Fluids, 42, 1263–1291.
Tseng, M. (2003). “The improved surface gradient method for flow simulation in variable bed topography channel using tvd-maccormack scheme.” Int. J. Numer. Methods Fluids, 43, 71–91.
Wu, W., Vieira, D., and Wang, S. (2004). “One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks.” J. Hydraul. Eng., 130(9), 914–923.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: Aug 2, 2006
Accepted: Dec 23, 2007
Published online: Oct 1, 2008
Published in print: Oct 2008
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.