Preissmann Four-Point Methods for Solution of Simplified Saint-Venant Equations Applied to Flood Routing in Prismatic Open Channels
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Keywords:
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Prismatic Channel Flow, Simplified Saint-Venant Equations, Preissmann Four-Point Scheme, Flow Properties
Abstract
This research goal to compare the flow properties in the rectangular and trapezoidal open channels by examining the influence of the channel side slope is depicted by simplified Saint Venant Equations. The solution of these equations has been completed numerically by using Preissmann four-point scheme. The model is simulated using the Matlab application to point out the flow properties. The proposed model is validated by the model without simplification which was selected from the literature. The validation outcomes indicate that in common, the simulation outcomes of the two models have a good agreement. The simulation results show that the greater the slope of the channel side, the greater the peak discharge and the greater the time shift. The analysis emphasizes how channel geometry influences flow behavior, indicating that trapezoidal channels, with inclined side slopes z, yield slightly higher peak discharges compared to rectangular ones. For z = 0, discharge of peak Q = 7.38 m3/s and t = 18 s. For z = 2, discharge of peak Q = 7.39 m3/s and t = 21 s. For z = 4, discharge of peak Q = 7.45 m3/s and t = 23 s. For z = 6, discharge of peak Q = 7.51 m3/s and t = 24 s.
References
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Jahanbazi, M., I. Özgen, R. Aleixo, and R. Hinkelmann (2017). Development of a Diffusive Wave Shallow Water Model with a Novel Stability Condition and Other New Features. Journal of Hydroinformatics, 19(3); 405–425
Kandpal, S. and S. N. Bora (2023). Analytical Solution for Linearized Saint-Venant Equations with a Uniformly Distributed Lateral Inflow in a Finite Rectangular Channel. Water Resources Management, 37(14); 5655–5676
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Moramarco, T., C. Pandolfo, and V. P. Singh (2008). Accuracy of Kinematic Wave Approximation for Flood Routing. II. Unsteady Analysis. Journal of Hydrologic Engineering, 13(11); 1089–1096
Moussa, R. and S. Majdalani (2021). Use of the Hayami Diffusive Wave Equation to Model the Relationship Infected–Recoveries–Deaths of Covid-19 Pandemic. Epidemiology & Infection, 149; 1–13
Neira, J. M. T., G. Tallec, V. Andréassian, and J. Mouchel (2020). A Combined Mixing Model for High-Frequency Concentration–Discharge Relationships. Journal of Hydrology, 591; 125559
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Paprotny, D., H. Kreibich, O. Morales-Nápoles, A. Castellarin, F. Carisi, and K. Schröter (2020). Exposure and Vulnerability Estimation for Modelling Flood Losses to Commercial Assets in Europe. Science of the Total Environment, 737; 140011
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Sulistyono, B. A., S. Samijo, and D. D. Yohanie (2021b). Numerical Simulation of Flood Routing using the Simplified Saint Venant Equations in Rectangular Channels. Indonesian Journal of Pure and Applied Mathematics, 3(2); 63–74
Sulistyono, B. A. and L. Wiryanto (2017). Investigation of Flood Routing by a Dynamic Wave Model in Trapezoidal Channels. In AIP Conference Proceedings, volume 1867. AIP Publishing
Sulistyono, B. A. and L. Wiryanto (2018). An Analysis of the Influence of Variability Rainfall on Flow Rate Based on the Watershed Characteristics. In IOP Conference Series: Earth and Environmental Science, volume 124. IOP Publishing, page 012001
Sulistyono, B. A. and L. H. Wiryanto (2019). A Staggered Method for Numerical Flood Routing in Rectangular Channels. Advances and Applications in Fluid Mechanics, 23(2); 171–179
Wang, G., S. Chen, J. Boll, and V. Singh (2003). Nonlinear Convection-Diffusion Equation with Mixing-Cell Method for Channel Flood Routing. Journal of Hydrologic Engineering, 8(5); 259–265
Wu, H., P. Fu, J. P. Morris, R. R. Settgast, and F. J. Ryerson (2019). ICAT: A Numerical Scheme to Minimize Numerical Diffusion in Advection-Dispersion Modeling and Its Application in Identifying Flow Channeling. Advances in Water Resources, 134; 103434
Zheng, H., E. Huang, and M. Luo (2020). Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow. Water, 12(9); 2528
Chaudhry, M. H. (2008). Open-Channel Flow, volume 523. Springer
Cozzolino, L., L. Cimorelli, R. Della Morte, G. Pugliano, V. Piscopo, and D. Pianese (2019). Flood Propagation Modeling with the Local Inertia Approximation: Theoretical and Numerical Analysis of Its Physical Limitations. Advances in Water Resources, 133(2); 103422
Ficchì, A., C. Perrin, and V. Andréassian (2019). Hydrological Modelling at Multiple Sub-Daily Time Steps: Model Improvement Via Flux-Matching. Journal of Hydrology, 575; 1308–1327
Geravand, F., S. M. Hosseini, and B. Ataie-Ashtiani (2020). Influence of River Cross-Section Data Resolution on Flood Inundation Modeling: Case Study of Kashkan River Basin in Western Iran. Journal of Hydrology, 584(2); 124743
Jahanbazi, M., I. Özgen, R. Aleixo, and R. Hinkelmann (2017). Development of a Diffusive Wave Shallow Water Model with a Novel Stability Condition and Other New Features. Journal of Hydroinformatics, 19(3); 405–425
Kandpal, S. and S. N. Bora (2023). Analytical Solution for Linearized Saint-Venant Equations with a Uniformly Distributed Lateral Inflow in a Finite Rectangular Channel. Water Resources Management, 37(14); 5655–5676
Keskin, M. (1970). A Model of Free Surface Flow for Prismatic Channels. WIT Transactions on Modelling and Simulation, 24; 121–127
Komi, K., J. Neal, M. A. Trigg, and B. Diekkrüger (2017). Modelling of Flood Hazard Extent in Data Sparse Areas: A Case Study of the Oti River Basin, West Africa. Journal of Hydrology: Regional Studies, 10; 122–132
Koussis, A. (1976). An Approximate Dynamic Flood Routing Method. In Int. Symposium on Unsteady Flow in Open Channel. Univ. of Newcastle-upon-Tyne
Krutov, A., R. Choriev, B. Norkulov, D. Mavlyanova, and A. Shomurodov (2021). Mathematical Modelling of Bottom Deformations in the Kinematic Wave Approximation. In IOP Conference Series: Materials Science and Engineering, volume 1030. IOP Publishing, page 012147
Lamberti, P. and S. Pilati (1996). Flood Propagation Models for Real-Time Forecasting. Journal of Hydrology, 175(1-4); 239–265
Mandailing, P. M., W. Mardiansyah, M. Irfan, A. Arsali, and I. Iskandar (2020). Characteristics of Diurnal Rainfall Over Peatland Area of South Sumatra, Indonesia. Science and Technology Indonesia, 5(4); 136–141
Mirzazadeh, P. and G. H. Akbari (2023). Flood Wave Simulation Case Study for Natural Water Stream by Numerical Solutions of Unsteady Equations. Journal of Hydrosciences and Environment, 6(11); 1–8
Moramarco, T., C. Pandolfo, and V. P. Singh (2008). Accuracy of Kinematic Wave Approximation for Flood Routing. II. Unsteady Analysis. Journal of Hydrologic Engineering, 13(11); 1089–1096
Moussa, R. and S. Majdalani (2021). Use of the Hayami Diffusive Wave Equation to Model the Relationship Infected–Recoveries–Deaths of Covid-19 Pandemic. Epidemiology & Infection, 149; 1–13
Neira, J. M. T., G. Tallec, V. Andréassian, and J. Mouchel (2020). A Combined Mixing Model for High-Frequency Concentration–Discharge Relationships. Journal of Hydrology, 591; 125559
Ogunlela, A. and B. Adelodun (2014). Kinematic Parameters for Asa River Routing. International Journal of Environmental and Ecological Engineering, 8(5); 346–350
Paprotny, D., H. Kreibich, O. Morales-Nápoles, A. Castellarin, F. Carisi, and K. Schröter (2020). Exposure and Vulnerability Estimation for Modelling Flood Losses to Commercial Assets in Europe. Science of the Total Environment, 737; 140011
Piadeh, F., K. Behzadian, and A. M. Alani (2022). A Critical Review of Real-Time Modelling of Flood Forecasting in Urban Drainage Systems. Journal of Hydrology, 607(12); 1–16
Pu, J. H., M. Pandey, and P. R. Hanmaiahgari (2020). Analytical Modelling of Sidewall Turbulence Effect on Streamwise Velocity Profile Using 2D Approach: A Comparison of Rectangular and Trapezoidal Open Channel Flows. Journal of Hydro-Environment Research, 32; 17–25
Pudjaprasetya, S. R. (2018). Transport Phenomena, Equations and Numerical Methods. INA-Rxiv Sulistyono, B. A., S. Samijo, N. Aan, D. D. Yohanie, and A. D. Handayani (2021a). Numerical Simulation of Flood Routing through Channels with Area Variation using Staggered Grid Method. Science and Technology Indonesia, 6(4); 261–266
Sulistyono, B. A., S. Samijo, and D. D. Yohanie (2021b). Numerical Simulation of Flood Routing using the Simplified Saint Venant Equations in Rectangular Channels. Indonesian Journal of Pure and Applied Mathematics, 3(2); 63–74
Sulistyono, B. A. and L. Wiryanto (2017). Investigation of Flood Routing by a Dynamic Wave Model in Trapezoidal Channels. In AIP Conference Proceedings, volume 1867. AIP Publishing
Sulistyono, B. A. and L. Wiryanto (2018). An Analysis of the Influence of Variability Rainfall on Flow Rate Based on the Watershed Characteristics. In IOP Conference Series: Earth and Environmental Science, volume 124. IOP Publishing, page 012001
Sulistyono, B. A. and L. H. Wiryanto (2019). A Staggered Method for Numerical Flood Routing in Rectangular Channels. Advances and Applications in Fluid Mechanics, 23(2); 171–179
Wang, G., S. Chen, J. Boll, and V. Singh (2003). Nonlinear Convection-Diffusion Equation with Mixing-Cell Method for Channel Flood Routing. Journal of Hydrologic Engineering, 8(5); 259–265
Wu, H., P. Fu, J. P. Morris, R. R. Settgast, and F. J. Ryerson (2019). ICAT: A Numerical Scheme to Minimize Numerical Diffusion in Advection-Dispersion Modeling and Its Application in Identifying Flow Channeling. Advances in Water Resources, 134; 103434
Zheng, H., E. Huang, and M. Luo (2020). Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow. Water, 12(9); 2528
Authors
Bambang Agus Sulistyono, & Widodo, S. . (2024). Preissmann Four-Point Methods for Solution of Simplified Saint-Venant Equations Applied to Flood Routing in Prismatic Open Channels. Science and Technology Indonesia, 9(1), 183–188. https://doi.org/10.26554/sti.2024.9.1.183-188
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