Articles | Volume 23, issue 3
https://doi.org/10.5194/hess-23-1281-2019
© Author(s) 2019. 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-23-1281-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| Highlight paper
| 
07 Mar 2019
Research article | Highlight paper |
| 07 Mar 2019
| 07 Mar 2019
Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage
National Center for Infrastructure Modeling and Management, University of Texas at Austin, Austin, Texas, USA
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Cited
25 citations as recorded by crossref.
- 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
- Numerical Simulation of Saint-Venant Equations with Thermal Energy Dependency: Applications on Global Warming R. Garcia & G. Silveira https://doi.org/10.4236/ojfd.2023.134014
- Open Water Flow in a Wet/Dry Multiply-Connected Channel Network: A Robust Numerical Modeling Algorithm S. Kivva et al. https://doi.org/10.1007/s00024-020-02416-0
- An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow B. Hodges https://doi.org/10.3390/w12061727
- Saint–Venant equations simulation by finite volume method and ULTIMATE strategy S. Hasheminejad & W. Wan https://doi.org/10.1007/s40808-022-01356-z
- Enhanced physics‐informed neural networks for efficient modelling of hydrodynamics in river networks X. Luo et al. https://doi.org/10.1002/hyp.15143
- Finite difference lattice Boltzmann method for modeling dam break debris flows G. Kefayati et al. https://doi.org/10.1063/5.0130947
- Nonlinear hydrological time series modeling to forecast river level dynamics in the Rio Negro Uruguay basin J. Duque et al. https://doi.org/10.1063/5.0201784
- A new form of the Saint-Venant equations for variable topography C. Yu et al. https://doi.org/10.5194/hess-24-4001-2020
- An integrated modeling approach for mineral and metal transport in acidic rivers at high mountainous porphyry Cu systems G. Zegers et al. https://doi.org/10.1016/j.jhydrol.2021.126718
- A physics-informed neural network method for modeling one-dimensional water flow without roughness coefficient input X. Yang et al. https://doi.org/10.1063/5.0266451
- Flood risk assessment of cultural heritage sites near lakes via advanced hydrodynamic modeling and digital technologies M. Alexopoulos et al. https://doi.org/10.1016/j.rineng.2025.107977
- Dynamic texture analysis using Temporal Gray scale Pattern Image for water surface velocity measurement B. Sirenden et al. https://doi.org/10.1016/j.imavis.2023.104749
- Data assimilation-based correction of flood forecasts in a large-scale river network: A case study of the Pearl River Basin D. Miao et al. https://doi.org/10.1016/j.envsoft.2026.106966
- Integrative modeling of the spread of serious infectious diseases and corresponding wastewater dynamics N. Schmid et al. https://doi.org/10.1016/j.epidem.2025.100836
- Real-time flood forecasting using physics-informed deep operator network for solving the shallow water equations X. Qi et al. https://doi.org/10.1080/19942060.2026.2685992
- Random-walk-path solution of unsteady flow equations for general channel networks H. Tang et al. https://doi.org/10.1016/j.jhydrol.2022.128692
- Investigation of overland flow by incorporating different infiltration methods into flood routing equations S. Gülbaz et al. https://doi.org/10.1080/1573062X.2020.1748206
- Evolution and Characterization of Pressurized Flow Conditions in Stormwater Collection Networks J. Vasconcelos et al. https://doi.org/10.1061/JHEND8.HYENG-13835
- Physics-Informed Neural Network for Reconstructing Free-Surface Transient Flow Fields in Long-Distance Water-Conveyance Tunnels from Sparse Observations X. Li et al. https://doi.org/10.3390/w18172216
- Evaluating lateral flow in an experimental channel using the diffusive wave inverse problem R. Moussa & S. Majdalani https://doi.org/10.1016/j.advwatres.2019.03.009
- Modelling the future climate impacts on hydraulic infrastructure development in tropical (peri-)urban region: Case of Kigali, Rwanda P. Iradukunda et al. https://doi.org/10.1016/j.heliyon.2024.e27126
- Timescale interpolation and no-neighbour discretization for a 1D finite-volume Saint-Venant solver B. Hodges & F. Liu https://doi.org/10.1080/00221686.2019.1671510
- The development and application of improved solids modelling to enable resilient urban sewer networks M. Murali et al. https://doi.org/10.1016/j.jenvman.2019.03.120
- Development of Rainfall-Runoff Models for Sustainable Stormwater Management in Urbanized Catchments B. Szeląg et al. https://doi.org/10.3390/w14131997
25 citations as recorded by crossref.
- 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
- Numerical Simulation of Saint-Venant Equations with Thermal Energy Dependency: Applications on Global Warming R. Garcia & G. Silveira https://doi.org/10.4236/ojfd.2023.134014
- Open Water Flow in a Wet/Dry Multiply-Connected Channel Network: A Robust Numerical Modeling Algorithm S. Kivva et al. https://doi.org/10.1007/s00024-020-02416-0
- An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow B. Hodges https://doi.org/10.3390/w12061727
- Saint–Venant equations simulation by finite volume method and ULTIMATE strategy S. Hasheminejad & W. Wan https://doi.org/10.1007/s40808-022-01356-z
- Enhanced physics‐informed neural networks for efficient modelling of hydrodynamics in river networks X. Luo et al. https://doi.org/10.1002/hyp.15143
- Finite difference lattice Boltzmann method for modeling dam break debris flows G. Kefayati et al. https://doi.org/10.1063/5.0130947
- Nonlinear hydrological time series modeling to forecast river level dynamics in the Rio Negro Uruguay basin J. Duque et al. https://doi.org/10.1063/5.0201784
- A new form of the Saint-Venant equations for variable topography C. Yu et al. https://doi.org/10.5194/hess-24-4001-2020
- An integrated modeling approach for mineral and metal transport in acidic rivers at high mountainous porphyry Cu systems G. Zegers et al. https://doi.org/10.1016/j.jhydrol.2021.126718
- A physics-informed neural network method for modeling one-dimensional water flow without roughness coefficient input X. Yang et al. https://doi.org/10.1063/5.0266451
- Flood risk assessment of cultural heritage sites near lakes via advanced hydrodynamic modeling and digital technologies M. Alexopoulos et al. https://doi.org/10.1016/j.rineng.2025.107977
- Dynamic texture analysis using Temporal Gray scale Pattern Image for water surface velocity measurement B. Sirenden et al. https://doi.org/10.1016/j.imavis.2023.104749
- Data assimilation-based correction of flood forecasts in a large-scale river network: A case study of the Pearl River Basin D. Miao et al. https://doi.org/10.1016/j.envsoft.2026.106966
- Integrative modeling of the spread of serious infectious diseases and corresponding wastewater dynamics N. Schmid et al. https://doi.org/10.1016/j.epidem.2025.100836
- Real-time flood forecasting using physics-informed deep operator network for solving the shallow water equations X. Qi et al. https://doi.org/10.1080/19942060.2026.2685992
- Random-walk-path solution of unsteady flow equations for general channel networks H. Tang et al. https://doi.org/10.1016/j.jhydrol.2022.128692
- Investigation of overland flow by incorporating different infiltration methods into flood routing equations S. Gülbaz et al. https://doi.org/10.1080/1573062X.2020.1748206
- Evolution and Characterization of Pressurized Flow Conditions in Stormwater Collection Networks J. Vasconcelos et al. https://doi.org/10.1061/JHEND8.HYENG-13835
- Physics-Informed Neural Network for Reconstructing Free-Surface Transient Flow Fields in Long-Distance Water-Conveyance Tunnels from Sparse Observations X. Li et al. https://doi.org/10.3390/w18172216
- Evaluating lateral flow in an experimental channel using the diffusive wave inverse problem R. Moussa & S. Majdalani https://doi.org/10.1016/j.advwatres.2019.03.009
- Modelling the future climate impacts on hydraulic infrastructure development in tropical (peri-)urban region: Case of Kigali, Rwanda P. Iradukunda et al. https://doi.org/10.1016/j.heliyon.2024.e27126
- Timescale interpolation and no-neighbour discretization for a 1D finite-volume Saint-Venant solver B. Hodges & F. Liu https://doi.org/10.1080/00221686.2019.1671510
- The development and application of improved solids modelling to enable resilient urban sewer networks M. Murali et al. https://doi.org/10.1016/j.jenvman.2019.03.120
- Development of Rainfall-Runoff Models for Sustainable Stormwater Management in Urbanized Catchments B. Szeląg et al. https://doi.org/10.3390/w14131997
Saved (final revised paper)
Latest update: 05 Oct 2026
Short summary
A new derivation of the equations for one-dimensional open-channel flow in rivers and storm drainage systems has been developed. The new approach solves some long-standing problems for obtaining well-behaved solutions with conservation forms of the equations. This research was motivated by the need for highly accurate models of large-scale river networks and the storm drainage systems in megacities. Such models are difficult to create with existing equation forms.
A new derivation of the equations for one-dimensional open-channel flow in rivers and storm...
