Kinematic and Diffusion Waves: Analytical and Numerical Solutions to Overland and Channel Flow
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 2
Abstract
Flood wave propagation is the unifying concept in representing open channel and overland flow. Therefore, understanding flood wave routing theory and solving the governing equations accurately is an important issue in hydrology and hydraulics. In an attempt to contribute to the understanding of this subject, in this study: (1) an analytical solution is derived for diffusion waves with constant wave celerity and hydraulic diffusivity applied to overland flow problems; and (2) an algorithm is developed using the MacCormack explicit finite difference method to solve the kinematic and diffusion wave governing equations for both overland and open channel flow. The MacCormack method is particularly well suited to approximate nonlinear differential equations. The analytical solutions provide the practicing engineer with computational speed in obtaining results for overland flow problems, and a means to check the validity of the numerical models. On the other hand, for larger scale catchment-stream problems, the verified numerical methods provide efficient and accurate algorithms to obtain solutions. Both the analytical approaches and the MacCormack algorithm are used to solve the same synthetic examples. Comparison of results shows that the numerical and analytical solutions are in close agreement. Furthermore, the MacCormack algorithm is applied to a real catchment: a segment of the Duke University West Campus storm water drainage system. In order to check the accuracy of the results obtained by the MacCormack method, the results are compared to predictions of the Environmental Protection Agency storm water management model (SWMM) as calibrated with measured rainfall and surface runoff flow data. The results obtained from SWMM are in good agreement with the results obtained from applying the MacCormack algorithm.
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Acknowledgments
The writers would like to express their gratitude to Dr. Prabhakar Clement (Auburn University), to the anonymous reviewers, and the Associate Editor for their excellent suggestions, which strengthened the paper. Funding for this investigation was provided by the Facilities Management Department of Duke University, and the writers wish to acknowledge in particular Mr. Glenn Reynolds and Mr. Gary Teater (Systems/Engineering Services) and Mr. Raymond Wrenn (Construction Services) for valuable discussions on stormwater management strategies and modeling needs on campus.
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Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 133 • Issue 2 • February 2007
Pages: 217 - 228
Copyright
© 2007 ASCE.
History
Received: Jul 21, 2004
Accepted: Jun 22, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
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