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

Journal Article · · Hydrology and Earth System Sciences (Online)
 [1];  [1];  [2]
  1. Univ. of Texas, Austin, TX (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
+ Show Author Affiliations
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 slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section 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 Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.
Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1665967
Journal Information:
Hydrology and Earth System Sciences (Online), Journal Name: Hydrology and Earth System Sciences (Online) Journal Issue: 8 Vol. 24; ISSN 1607-7938
Publisher:
European Geosciences Union (EGU)Copyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (26)

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