Conservative Formulation for Natural Open Channels and Finite-Element Implementation
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 9
Abstract
This investigation considers an approximate formulation of the St. Venant equations for natural channels, in which the fully conservative form is developed by revising the boundary pressure term accounting for the topographic variation in the momentum equation. As such a formulation has the potential to enhance the performance of existing models used in practice, the accuracy implications for this approximate formulation are examined using an error analysis for a simplified case. Further, an energy calculation is performed which illustrates that an earlier formulation actually results in energy gain for some cases. A more general formula for the constant water surface elevation that corrects this is introduced and tested. It is found that the refined formulation presented here is accurate for hydraulic jumps, steep surge waves, and flood wave propagation in natural channels. The shock capturing capability of the approximate formulation is illustrated for both steady- and unsteady-flow situations using the finite-element method, for which this approximate equation formulation adapts naturally. Using the characteristic-dissipative-Galerkin finite-element scheme, good results are obtained for the case of a hydraulic jump in a diverging rectangular channel, with the maximum percent error associated with the approximate formulation determined to be only 0.34%. For the case of dam break wave propagation in a converging and diverging rectangular channel, the model performs similarly well, with the maximum error only 0.0064%. Further, the approximate formulation is used to simulate the flood routing in a natural channel, the Oldman River in southern Alberta. The computational results are in good agreement with the observed data. The arrival time of peak flow is earlier and the magnitude of peak discharge is only 3.8% lower than the observed value.
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Acknowledgments
Funding for this study was provided by the Water Research User’s Group (WRUG) at Alberta Environment as well as by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the MAGS (Mackenzie GEWEX Study) Research Network. This support is gratefully acknowledged. The writers would particularly like to thank Chandra Mahabir and Jim Choles of Alberta Environment for their support of and assistance in this research.
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© 2007 ASCE.
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Received: Nov 22, 2004
Accepted: Feb 20, 2007
Published online: Sep 1, 2007
Published in print: Sep 2007
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