Numerical Simulation of Flood Routing through Channels with Area Variation using Staggered Grid Method
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Keywords:
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Flood Routing, Dynamic Wave Model, Finite Volume Method on Staggered Grid, Prismatic and Non Primatic Channels
Abstract
In the event that the discharge goes to enter the channel surpasses the channel ability, than would happen floods of genuine harm to the environment around the channel. Applying the dynamic wave model, the discharge amount could be predicted in the frequent flood region if the information of discharge upstream is found out. Many numerical schemes could be utilized to discover answers to the system of differential partial equations. We proposed the usage of the staggered method to find out the solution of the system. The numerical scheme shall be used to predict the top discharge in a frequent flood region and create a flooded pocket to diminish the top discharge in the region. Based on the outcome of the numerical simulation, we may claim that a stable scheme has been created to acquire the approach resolve of the equation partial system. The staggered scheme is capable of investigating the impact of the presence of the flood pocket especially lessening the top discharge.
References
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Lai, W., & Khan, A. A. (2018). Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method. Journal of Hydrodynamics, 30(2), 189–202. https://doi.org/10.1007/s42241-018-0020-y
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Moramarco, T., Pandolfo, C., & Singh, V. P. (2008). Accuracy of Kinematic Wave Approximation for Flood Routing. II. Unsteady Analysis. Journal of Hydrologic Engineering, 13(11), 1089–1096. https://doi.org/10.1061/(asce)1084-0699(2008)13:11(1089)
Mungkasi, S. (2016). Adaptive Finite Volume Method for the Shallow Water. Advances in Mathematical Physics, 2016, 1–8.
Mungkasi, Sudi, Magdalena, I., Pudjaprasetya, S. R., Wiryanto, L. H., & Roberts, S. G. (2018). A staggered method for the shallow water equations involving varying channel width and topography. International Journal for Multiscale Computational Engineering, 16(3), 231–244. https://doi.org/10.1615/IntJMultCompEng.2018027042
Nguyen, T. S., Luong, T. A., Luong, H. D., & Tran, H. T. (2016). A finite element one-dimensional kinematic wave rainfall-runoff model. Pacific Science Review A: Natural Science and Engineering, 18(3), 233–240. https://doi.org/10.1016/j.psra.2016.11.001
Ogunlela, A. O., & Adelodun, B. (2014). Kinematic Parameters for Asa River Routing. World Academy of Science, Engineering and Technology International Journal of Environmental and Ecological Engineering, 8(5), 346–350.
Pudjaprasetya, S. R. (2018). Transport Phenomena, equations and numerical methods. https://doi.org/10.31227/osf.io/5vw73
Qureshi, A. L., Mahessar, A. A., & Baloch, A. (2014). Verification and Application of Finite Element Model Developed for Flood Routing in Rivers. 2(2), 88–91.
Retsinis, E., Daskalaki, E., & Papanicolaou, P. (2020). Dynamic flood wave routing in prismatic channels with hydraulic and hydrologic methods. Journal of Water Supply: Research and Technology - AQUA, 69(3), 276–287. https://doi.org/10.2166/aqua.2019.091
Stelling, G. S., & Duinmeijer, S. P. A. (2003). A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. International Journal for Numerical Methods in Fluids, 43(12), 1329–1354. https://doi.org/10.1002/fld.537
Sulistyono, B. A., & Wiryanto, L. H. (2017). Investigation of flood routing by a dynamic wave model in trapezoidal channels. AIP Conference Proceedings, 1867. https://doi.org/10.1063/1.4994423
Sulistyono, B. A., & Wiryanto, L. H. (2019). a Staggered Method for Numerical Flood Routing in Rectangular Channels. Advances and Applications in Fluid Mechanics, 23(2), 171–179. https://doi.org/10.17654/fm023020171
Sulistyono, B. A., Wiryanto, L. H., & Mungkasi, S. (2020). A staggered method for simulating shallow water flows along channels with irregular geometry and friction. International Journal on Advanced Science, Engineering and Information Technology, 10(3), 952–958. https://doi.org/10.18517/ijaseit.10.3.7413
Tsai, C. W. (2003). Applicability of Kinematic, Noninertia, and Quasi-Steady Dynamic Wave Models to Unsteady Flow Routing. Journal of Hydraulic Engineering, 129(8), 613–627. https://doi.org/10.1061/(ASCE)0733-9429129:8(613)
Wang, G. T., Chen, S., Boll, J., & Singh, V. P. (2003). Nonlinear Convection-Diffusion Equation with Mixing-Cell Method for Channel Flood Routing. Journal of Hydrologic Engineering, 8(5), 259–265. https://doi.org/10.1061/(ASCE)1084-0699(2003)8:5(259)
Zheng, H., Huang, E., & Luo, M. (2020). Applicability of kinematic wave model for flood routing under unsteady inflow. Water (Switzerland), 12(9). https://doi.org/10.3390/w12092528
Barati, R., Rahimi, S., & Akbari, G. H. (2012). Analysis of dynamic wave model for flood routing in natural rivers. Water Science and Engineering, 5(3), 243–258. https://doi.org/10.3882/j.issn.1674-2370.2012.03.001
Chaudhry, M. H. (2008). Open-Channel Flow. Springer Science+Business Media.
Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. Mc. Graw-Hill Book Company.
Cunge, F. P., Verwey, F. M., & Holly, F. M. (1980). Practical Aspects of Computational River Hydraulics. Pitman Advanced Publishing Program.
Jufriansah, A., Pramudya, Y., Hermanto, A., & Khusnani, A. (2020). Surface Wave Topography using The 4 Point FDM Simulator. Science and Technology Indonesia, 5(4), 117. https://doi.org/10.26554/sti.2020.5.4.117-120
Keskin, M. E., & Aǧiralioǧlu, N. (1997). A simplified dynamic model for flood routing in rectangular channels. Journal of Hydrology, 202(1–4), 302–314. https://doi.org/10.1016/S0022-1694(97)00072-3
Lai, W., & Khan, A. A. (2018). Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method. Journal of Hydrodynamics, 30(2), 189–202. https://doi.org/10.1007/s42241-018-0020-y
Mandailing, P. M., Mardiansyah, W., Irfan, M., Arsali, A., & Iskandar, I. (2020). Characteristics of Diurnal Rainfall over Peatland Area of South Sumatra, Indonesia. Science and Technology Indonesia, 5(4), 136.
https://doi.org/10.26554/sti.2020.5.4.136-141
Moramarco, T., Pandolfo, C., & Singh, V. P. (2008). Accuracy of Kinematic Wave Approximation for Flood Routing. II. Unsteady Analysis. Journal of Hydrologic Engineering, 13(11), 1089–1096. https://doi.org/10.1061/(asce)1084-0699(2008)13:11(1089)
Mungkasi, S. (2016). Adaptive Finite Volume Method for the Shallow Water. Advances in Mathematical Physics, 2016, 1–8.
Mungkasi, Sudi, Magdalena, I., Pudjaprasetya, S. R., Wiryanto, L. H., & Roberts, S. G. (2018). A staggered method for the shallow water equations involving varying channel width and topography. International Journal for Multiscale Computational Engineering, 16(3), 231–244. https://doi.org/10.1615/IntJMultCompEng.2018027042
Nguyen, T. S., Luong, T. A., Luong, H. D., & Tran, H. T. (2016). A finite element one-dimensional kinematic wave rainfall-runoff model. Pacific Science Review A: Natural Science and Engineering, 18(3), 233–240. https://doi.org/10.1016/j.psra.2016.11.001
Ogunlela, A. O., & Adelodun, B. (2014). Kinematic Parameters for Asa River Routing. World Academy of Science, Engineering and Technology International Journal of Environmental and Ecological Engineering, 8(5), 346–350.
Pudjaprasetya, S. R. (2018). Transport Phenomena, equations and numerical methods. https://doi.org/10.31227/osf.io/5vw73
Qureshi, A. L., Mahessar, A. A., & Baloch, A. (2014). Verification and Application of Finite Element Model Developed for Flood Routing in Rivers. 2(2), 88–91.
Retsinis, E., Daskalaki, E., & Papanicolaou, P. (2020). Dynamic flood wave routing in prismatic channels with hydraulic and hydrologic methods. Journal of Water Supply: Research and Technology - AQUA, 69(3), 276–287. https://doi.org/10.2166/aqua.2019.091
Stelling, G. S., & Duinmeijer, S. P. A. (2003). A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. International Journal for Numerical Methods in Fluids, 43(12), 1329–1354. https://doi.org/10.1002/fld.537
Sulistyono, B. A., & Wiryanto, L. H. (2017). Investigation of flood routing by a dynamic wave model in trapezoidal channels. AIP Conference Proceedings, 1867. https://doi.org/10.1063/1.4994423
Sulistyono, B. A., & Wiryanto, L. H. (2019). a Staggered Method for Numerical Flood Routing in Rectangular Channels. Advances and Applications in Fluid Mechanics, 23(2), 171–179. https://doi.org/10.17654/fm023020171
Sulistyono, B. A., Wiryanto, L. H., & Mungkasi, S. (2020). A staggered method for simulating shallow water flows along channels with irregular geometry and friction. International Journal on Advanced Science, Engineering and Information Technology, 10(3), 952–958. https://doi.org/10.18517/ijaseit.10.3.7413
Tsai, C. W. (2003). Applicability of Kinematic, Noninertia, and Quasi-Steady Dynamic Wave Models to Unsteady Flow Routing. Journal of Hydraulic Engineering, 129(8), 613–627. https://doi.org/10.1061/(ASCE)0733-9429129:8(613)
Wang, G. T., Chen, S., Boll, J., & Singh, V. P. (2003). Nonlinear Convection-Diffusion Equation with Mixing-Cell Method for Channel Flood Routing. Journal of Hydrologic Engineering, 8(5), 259–265. https://doi.org/10.1061/(ASCE)1084-0699(2003)8:5(259)
Zheng, H., Huang, E., & Luo, M. (2020). Applicability of kinematic wave model for flood routing under unsteady inflow. Water (Switzerland), 12(9). https://doi.org/10.3390/w12092528
Authors
Sulistyono, B. A. ., Samijo, Nurfahrudianto, A. ., Yohanie, D. D. ., & Handayani, A. D. . (2021). Numerical Simulation of Flood Routing through Channels with Area Variation using Staggered Grid Method. Science and Technology Indonesia, 6(4), 261–266. https://doi.org/10.26554/sti.2021.6.4.261-266
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