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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/hess-2020-75
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-75
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 19 Mar 2020

Submitted as: research article | 19 Mar 2020

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This preprint is currently under review for the journal HESS.

A new form of the Saint–Venant equations for variable topography

Cheng-Wei Yu1, Ben R. Hodges1, and Frank Liu2 Cheng-Wei Yu et al.
  • 1National Center for Infrastructure Modeling and Management, The University of Texas at Austin
  • 2Oak Ridge National Laboratory

Abstract. The solution stability of river models using the one-dimensional (1D) Saint–Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint–Venant equations to ensure smooth source terms and eliminate potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-sectional flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz-continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source SPRNT model in a series of artificial test cases and simulation of a small urban creek. Validation comparisons are made with analytical solutions and the HEC-RAS model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

Cheng-Wei Yu et al.

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Cheng-Wei Yu et al.

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Test case data for Reference Slope study with HEC-RAS and SPRNT-RS Cheng-W. Yu, B. Hodges, and F. Liu https://doi.org/10.18738/T8/BXJBF5

Cheng-Wei Yu et al.

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Latest update: 03 Apr 2020
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Short summary
This study investigates the effects of bottom-slope discontinuity on the stability of numerical solutions for the Saint–Venant equations. A new reference slope concept is proposed to ensure smooth source terms and eliminate potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-sectional flow area and the piezometric pressure gradient that drives the flow.
This study investigates the effects of bottom-slope discontinuity on the stability of numerical...
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