Upwind Conservative Scheme for the Saint Venant Equations
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 10
Abstract
An upwind conservative scheme with a weighted average water-surface-gradient approach is proposed to compute one-dimensional open channel flows. The numerical scheme is based on the control volume method. The intercell flux is computed by the one-sided upwind method. The water surface gradient is evaluated by the weighted average of both upwind and downwind gradients. The scheme is tested with various examples, including dam-break problems in channels with rectangular and triangular cross-sections, hydraulic jump, partial dam-break problem, overtopping flow, a steady flow over bump with hydraulic jump, and a dam-break flood case in a natural river valley. Comparisons between numerical and exact solutions or experimental data demonstrated that the proposed scheme is capable of accurately reproducing various open channel flows, including subcritical, supercritical, and transcritical flows. The scheme is inherently robust, stable, and monotone. The scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients or discontinuities in the solution.
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Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 130 • Issue 10 • October 2004
Pages: 977 - 987
Copyright
Copyright © 2004 ASCE.
History
Published online: Oct 1, 2004
Published in print: Oct 2004
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