Articles | Volume 24, issue 8
https://doi.org/10.5194/hess-24-4001-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-24-4001-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
18 Aug 2020
Research article |
| 18 Aug 2020
| 18 Aug 2020
A new form of the Saint-Venant equations for variable topography
Cheng-Wei Yu
National Center for Infrastructure Modeling and Management, The University of Texas at Austin, Austin, Texas, USA
National Center for Infrastructure Modeling and Management, The University of Texas at Austin, Austin, Texas, USA
Frank Liu
Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
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Cited
17 citations as recorded by crossref.
- Development of Rainfall-Runoff Models for Sustainable Stormwater Management in Urbanized Catchments B. Szeląg et al. https://doi.org/10.3390/w14131997
- Assessment of the Relationship between Land Use and Flood Risk Based on a Coupled Hydrological–Hydraulic Model: A Case Study of Zhaojue River Basin in Southwestern China C. Xu et al. https://doi.org/10.3390/land11081182
- Low-cost, data-efficient, on-device soft sensors for sewer flow monitoring—learning from adjacent water level sensors R. Lin et al. https://doi.org/10.1016/j.wroa.2025.100415
- Enhancing dynamic flood risk assessment and zoning using a coupled hydrological-hydrodynamic model and spatiotemporal information weighting method L. Zhou & L. Liu https://doi.org/10.1016/j.jenvman.2024.121831
- Flood hazard mapping and analysis under climate change using hydro-dynamic model and RCPs emission scenario in Woybo River catchment of Ethiopia T. Ukumo et al. https://doi.org/10.1108/WJE-07-2021-0410
- Physics‐Informed Neural Networks of the Saint‐Venant Equations for Downscaling a Large‐Scale River Model D. Feng et al. https://doi.org/10.1029/2022WR033168
- Pre-trained physics-informed neural networks for one-dimensional wave propagation in coastal engineering Y. Yang et al. https://doi.org/10.1016/j.ocemod.2025.102601
- Distributed simulation of fully coupled hydrological-hydrodynamic model for predicting rainfall-induced runoff/flood in small watersheds Y. Zhu et al. https://doi.org/10.1016/j.ejrh.2025.102450
- An independent-scheduling variables LPV model integral–delay–zero representation for open-channel: Development and applicability boundary identification M. Du et al. https://doi.org/10.1016/j.envsoft.2026.106925
- A novel method for calculating distributed water depth and flow velocity of stormwater runoff during the heavy rainfall events Y. Zhu et al. https://doi.org/10.1016/j.jhydrol.2022.128064
- Topographic hydro-conditioning to resolve surface depression storage and ponding in a fully distributed hydrologic model A. Jiang et al. https://doi.org/10.1016/j.advwatres.2023.104449
- Automated Detection of Instability-Inducing Channel Geometry Transitions in Saint-Venant Simulation of Large-Scale River Networks C. Yu et al. https://doi.org/10.3390/w13162236
- One-Dimensional Shallow Water Equations Ill-Posedness T. Mahdi https://doi.org/10.3390/math13152476
- Application of Remote-Sensing-Based Hydraulic Model and Hydrological Model in Flood Simulation C. Xu et al. https://doi.org/10.3390/su14148576
- Assessing the Role of Hydrodynamics in Enhancing Height‐Above‐the‐Nearest‐Drainage Derived Synthetic Rating Curves: A Comparative Study in the Wu River Basin, Taiwan C. Yu et al. https://doi.org/10.1111/jfr3.70057
- Optimal boundary control of Saint-Venant equations with arbitrary friction and space-varying slope Y. Wang & B. Sun https://doi.org/10.1093/imamci/dnab016
- A Comparative Study of a Two-Dimensional Slope Hydrodynamic Model (TDSHM), Long Short-Term Memory (LSTM), and Convolutional Neural Network (CNN) Models for Runoff Prediction Y. Zhou et al. https://doi.org/10.3390/w17091380
17 citations as recorded by crossref.
- Development of Rainfall-Runoff Models for Sustainable Stormwater Management in Urbanized Catchments B. Szeląg et al. https://doi.org/10.3390/w14131997
- Assessment of the Relationship between Land Use and Flood Risk Based on a Coupled Hydrological–Hydraulic Model: A Case Study of Zhaojue River Basin in Southwestern China C. Xu et al. https://doi.org/10.3390/land11081182
- Low-cost, data-efficient, on-device soft sensors for sewer flow monitoring—learning from adjacent water level sensors R. Lin et al. https://doi.org/10.1016/j.wroa.2025.100415
- Enhancing dynamic flood risk assessment and zoning using a coupled hydrological-hydrodynamic model and spatiotemporal information weighting method L. Zhou & L. Liu https://doi.org/10.1016/j.jenvman.2024.121831
- Flood hazard mapping and analysis under climate change using hydro-dynamic model and RCPs emission scenario in Woybo River catchment of Ethiopia T. Ukumo et al. https://doi.org/10.1108/WJE-07-2021-0410
- Physics‐Informed Neural Networks of the Saint‐Venant Equations for Downscaling a Large‐Scale River Model D. Feng et al. https://doi.org/10.1029/2022WR033168
- Pre-trained physics-informed neural networks for one-dimensional wave propagation in coastal engineering Y. Yang et al. https://doi.org/10.1016/j.ocemod.2025.102601
- Distributed simulation of fully coupled hydrological-hydrodynamic model for predicting rainfall-induced runoff/flood in small watersheds Y. Zhu et al. https://doi.org/10.1016/j.ejrh.2025.102450
- An independent-scheduling variables LPV model integral–delay–zero representation for open-channel: Development and applicability boundary identification M. Du et al. https://doi.org/10.1016/j.envsoft.2026.106925
- A novel method for calculating distributed water depth and flow velocity of stormwater runoff during the heavy rainfall events Y. Zhu et al. https://doi.org/10.1016/j.jhydrol.2022.128064
- Topographic hydro-conditioning to resolve surface depression storage and ponding in a fully distributed hydrologic model A. Jiang et al. https://doi.org/10.1016/j.advwatres.2023.104449
- Automated Detection of Instability-Inducing Channel Geometry Transitions in Saint-Venant Simulation of Large-Scale River Networks C. Yu et al. https://doi.org/10.3390/w13162236
- One-Dimensional Shallow Water Equations Ill-Posedness T. Mahdi https://doi.org/10.3390/math13152476
- Application of Remote-Sensing-Based Hydraulic Model and Hydrological Model in Flood Simulation C. Xu et al. https://doi.org/10.3390/su14148576
- Assessing the Role of Hydrodynamics in Enhancing Height‐Above‐the‐Nearest‐Drainage Derived Synthetic Rating Curves: A Comparative Study in the Wu River Basin, Taiwan C. Yu et al. https://doi.org/10.1111/jfr3.70057
- Optimal boundary control of Saint-Venant equations with arbitrary friction and space-varying slope Y. Wang & B. Sun https://doi.org/10.1093/imamci/dnab016
- A Comparative Study of a Two-Dimensional Slope Hydrodynamic Model (TDSHM), Long Short-Term Memory (LSTM), and Convolutional Neural Network (CNN) Models for Runoff Prediction Y. Zhou et al. https://doi.org/10.3390/w17091380
Saved (final revised paper)
Latest update: 02 Aug 2026
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...
