Development of Leapfrog-Hansen Numerical Model to Simulate One-Dimensional Dam-Break Flow

Qalbi Hafiyyan; Irene Anggraini; Puspita Rahmasari; Azwa Nirmala

doi:10.31764/jtam.v10i3.38595

Development of Leapfrog-Hansen Numerical Model to Simulate One-Dimensional Dam-Break Flow

Qalbi Hafiyyan, Irene Anggraini, Puspita Rahmasari, Azwa Nirmala

Abstract

This study is a computational study aimed at developing and validating a numerical model for simulating one-dimensional dam-break flow. Dam construction, in addition to providing benefits to the community in terms of flood control, irrigation, and clean water sources, also carries the potential for disaster. Disasters can occur when dams fail or collapse. Dam failures can generate catastrophic flooding that threatens infrastructure, the environment, and human life. Therefore, numerical modeling is an important approach for understanding the characteristics of dam-break flow to support flood mitigation efforts following dam failure. The proposed model is developed using the Leapfrog finite-difference method, known for its simplicity. However, the conventional Leapfrog method is prone to numerical oscillations when handling discontinuities and shock waves in dam-break simulations. The novelty of this research lies in the development of a Leapfrog–Hansen numerical model for one-dimensional dam-break flow simulation by integrating the Hansen numerical filter into the conventional Leapfrog finite-difference scheme to improve stability while maintaining computational simplicity. The governing shallow water equations were solved using the proposed Leapfrog–Hansen model and applied to several hypothetical one-dimensional dam-break scenarios with varying downstream water depths. The performance of the developed model was evaluated by comparing its numerical simulation results with Stoker's analytical solution, which is often used as a benchmark in numerical modeling of one-dimensional dam-break flow. The comparison results show that the Leapfrog–Hansen model accurately reproduces the water surface profiles predicted by the analytical solution. The Leapfrog-Hansen model yielded relatively small Mean Absolute Error (MAE) values of 0.032 to 0.062, indicating high accuracy in reproducing dam-break flows. In addition, the developed model successfully reduces numerical oscillations in the conventional Leapfrog scheme and accurately captures flow discontinuities, shock-wave propagation, and wet-dry conditions, while maintaining simulation stability. These findings demonstrate that the proposed Leapfrog–Hansen model provides a simple, stable, and accurate alternative for simulating one-dimensional dam-break flows and has potential applications in flood-propagation analysis, preliminary dam-break hazard assessment, and other hydraulic studies related to flood risk mitigation.

Keywords

Dam-break; Finite-Difference; Hansen Filter; Leapfrog; Numerical Model.

Full Text:

DOWNLOAD [PDF]

References

Adityawan, M. B., Sandi, C., Harlan, D., Farid, M., Kuntoro, A. A., Widyaningtias, Chaidar, A. N., & Nugroho, J. (2023). Numerical modeling of dam break induced flow through multiple buildings in an idealized city. Results in Engineering, 18, 101060. https://doi.org/10.1016/j.rineng.2023.101060

Dai, S., Yang, S., Zhang, Y., He, X., Li, Z., Liu, Y., Hou, J., Wang, D., Zhang, J., Yang, J., Xue, Y., Jin, S., Liu, H., & Li, Y. (2025). Numerical study of impact pressure and force of cascading dam-break floods on the downstream dam. Journal of Hydrology, 648, 132360. https://doi.org/10.1016/j.jhydrol.2024.132360

Ferrari, A., Vacondio, R., & Mignosa, P. (2023). High-resolution 2D shallow water modelling of dam failure floods for emergency action plans. Journal of Hydrology, 618, 129192. https://doi.org/10.1016/j.jhydrol.2023.129192

Gu, L., & Lai, X. (2026). Comparative performance evaluation of DeepONet architectures for dam-break hydrodynamic simulations. Water Science and Engineering, 19(2), 302–314. https://doi.org/10.1016/j.wse.2026.01.004

Hafiyyan, Q., Adityawan, M. B., Harlan, D., Natakusumah, D. K., & Magdalena, I. (2021). Comparison of Taylor Galerkin and FTCS models for dam-break simulation. IOP Conference Series: Earth and Environmental Science, 737(1), 012050. https://doi.org/10.1088/1755-1315/737/1/012050

Hafiyyan, Q., Harlan, D., Adityawan, M. B., Natakusumah, D. K., & Magdalena, I. (2021). 2D Numerical Model of Sediment Transport Under Dam-break Flow Using Finite Element. International Journal on Advanced Science, Engineering and Information Technology, 11(6), 2476. https://doi.org/10.18517/ijaseit.11.6.14484

Hafiyyan, Q., Nirmala, A., Ms, M., Sumiyattinah, S., Bachtiar, V., & Yusuf, M. Y. (2023). Application of Finite Difference Method in Simulating 2D Partial Dam-break Flow with an Obstacle. Indonesian Journal of Multidisciplinary Science, 2(12), 4181–4190. https://doi.org/10.55324/ijoms.v2i12.609

Harlan, D., Adityawan, M. B., Natakusumah, D. K., & Zendrato, N. L. H. (2019). Application Of Numerical Filter To A Taylor Galerkin Finite Element Model For Movable Bed Dam Break Flows. International Journal of GEOMATE, 16(57). https://doi.org/10.21660/2019.57.70809

Holzbecher, E. (2022). Adaptive Mesh Refinement for Dam-Break Models using the Shallow Water Equations. Journal of the Civil Engineering Forum, 79–90. https://doi.org/10.22146/jcef.4260

Huang, D., Yu, Z., Li, Y., Han, D., Zhao, L., & Chu, Q. (2017). Calculation method and application of loss of life caused by dam break in China. Natural Hazards, 85(1), 39–57. https://doi.org/10.1007/s11069-016-2557-9

Iserles, A. (1986). Generalized Leapfrog Methods. IMA Journal of Numerical Analysis, 6(4), 381–392. https://doi.org/10.1093/imanum/6.4.381

Issakhov, A., & Imanberdiyeva, M. (2019). Numerical simulation of the movement of water surface of dam break flow by VOF methods for various obstacles. International Journal of Heat and Mass Transfer, 136, 1030–1051. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.034

Latrubesse, E. M., Park, E., Sieh, K., Dang, T., Lin, Y. N., & Yun, S.-H. (2020). Dam failure and a catastrophic flood in the Mekong basin (Bolaven Plateau), southern Laos, 2018. Geomorphology, 362, 107221. https://doi.org/10.1016/j.geomorph.2020.107221

Liu, R., Wang, D., Zhang, X., Li, W., & Yu, B. (2013). Comparison Study on the Performances of Finite Volume Method and Finite Difference Method. Journal of Applied Mathematics, 2013, 1–10. https://doi.org/10.1155/2013/596218

Magdalena, I., Adityawan, M. B., & Jonathan, C. (2020). Numerical Model for Dam Break Over a Movable Bed Using Finite Volume Method. International Journal of GEOMATE, 19(71). https://doi.org/10.21660/2020.71.27074

Magdalena, I., & Eka Pebriansyah, M. F. (2022). Numerical treatment of finite difference method for solving dam break model on a wet-dry bed with an obstacle. Results in Engineering, 14, 100382. https://doi.org/10.1016/j.rineng.2022.100382

Magdalena, I., Haloho, D. N., & Adityawan, M. B. (2024). Numerical approaches for Boussinesq type equations with its application in Kampar River, Indonesia. Mathematics and Computers in Simulation, 225, 820–834. https://doi.org/10.1016/j.matcom.2023.05.002

Magdalena, I., Hariz, A. A. A., Farid, M., & Kusuma, M. S. B. (2021). Numerical studies using staggered finite volume for dam break flow with an obstacle through different geometries. Results in Applied Mathematics, 12, 100193. https://doi.org/10.1016/j.rinam.2021.100193

Maitsa, T. R., Hafiyyan, Q., Adityawan, M. B., Magdalena, I., & Kuntoro, A. A. (2021). Development of A 2D Numerical Model for Pollutant Transport using FTCS Scheme and Numerical Filter. Makara Journal of Technology, 25(3). https://doi.org/10.7454/mst.v25i3.3966

Mao, J., Zhao, L., Bai, X., Guo, B., Liu, Z., & Li, T. (2016). A novel well-balanced scheme for modeling of dam break flow in drying-wetting areas. Computers & Fluids, 136, 324–330. https://doi.org/10.1016/j.compfluid.2016.06.022

Mellivera, A., Zain, K., Adityawan, M. B., Harlan, D., Farid, M., & Yakti, B. P. (2020). Development of FTCS Artificial Dissipation for Dam Break 2D Modelling. Jurnal Teknik Sipil, 27(1), 1–8. https://doi.org/10.5614/jts.2020.27.1.1

Mirauda, D., Albano, R., Sole, A., & Adamowski, J. (2020). Smoothed Particle Hydrodynamics Modeling with Advanced Boundary Conditions for Two-Dimensional Dam-Break Floods. Water, 12(4), 1142. https://doi.org/10.3390/w12041142

Pratama, M. I., Hafiyyan, Q., & Mardika, M. G. I. (2025). 2D numerical simulation of the impact of formation and shape of column on shallow water behavior. 030004. https://doi.org/10.1063/5.0282208

Putri, P. I. D., Iskandar, R. F., Adityawan, M. B., Kardhana, H., & Indrawati, D. (2020). 2D Shallow Water Model for Dam Break and Column Interactions. Journal of the Civil Engineering Forum, 6(3), 237. https://doi.org/10.22146/jcef.54307

Qian, H., Cao, Z., Liu, H., & Pender, G. (2018). New experimental dataset for partial dam-break floods over mobile beds. Journal of Hydraulic Research, 56(1), 124–135. https://doi.org/10.1080/00221686.2017.1289264

Ravena Maitsa, T., Indra Mardika, M. G., Bagus Adityawan, M., Harlan, D., Kusumastuti, D., & Adi Kuntoro, A. (2020). 2D numerical simulation of urban dam break and its effect to building using lax scheme with numerical filter. E3S Web of Conferences, 156, 04003. https://doi.org/10.1051/e3sconf/202015604003

Rehman, K., & Cho, Y.-S. (2019). A novel well-balanced scheme for spatial and temporal bed evolution in rapidly varying flow. Journal of Hydro-Environment Research, 27, 87–101. https://doi.org/10.1016/j.jher.2019.10.001

Salamttalab, M. M., Parmas, B., Mustafa Alee, H., Hooshyaripor, F., Danandeh Mehr, A., Vosoughifar, H., Hosseini, S. A., Maghrebi, M., & Noori, R. (2023). A Finite Volume Method for a 2D Dam-Break Simulation on a Wet Bed Using a Modified HLLC Scheme. Water, 15(21), 3841. https://doi.org/10.3390/w15213841

Seyedashraf, O., & Akhtari, A. A. (2017). Two-dimensional numerical modeling of dam-break flow using a new TVD finite-element scheme. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(11), 4393–4401. https://doi.org/10.1007/s40430-017-0776-y

Simsek, O., & Islek, H. (2023). 2D and 3D numerical simulations of dam-break flow problem with RANS, DES, and LES. Ocean Engineering, 276, 114298. https://doi.org/10.1016/j.oceaneng.2023.114298

Sukhinov, A., Chistyakov, A., Kuznetsova, I., Protsenko, E., & Belova, Y. (2020). Modified Upwind Leapfrog difference scheme. Computational Mathematics and Information Technologies, 1(1), 56–70. https://doi.org/10.23947/2587-8999-2020-1-1-56-70

Tseng, M. H., & Chu, C. R. (2000). The simulation of dam-break flows by an improved predictor±corrector TVD scheme. Advances in Water Resources, 23(6), 637–643. https://doi.org/10.1016/S0309-1708(99)00051-2

Wang, Y., Liang, Q., Kesserwani, G., & Hall, J. W. (2011). A 2D shallow flow model for practical dam-break simulations. Journal of Hydraulic Research, 49(3), 307–316. https://doi.org/10.1080/00221686.2011.566248

Yakti, B. P., Adityawan, M. B., Farid, M., Suryadi, Y., Nugroho, J., & Hadihardaja, I. K. (2018). 2D Modeling of Flood Propagation due to the Failure of Way Ela Natural Dam. MATEC Web of Conferences, 147, 03009. https://doi.org/10.1051/matecconf/201814703009

Zendrato, N. L. H., Harlan, D., Bagus Adityawan, M., & Kardana Natakusumah, D. (2019). 1D Numerical modelling of dam break using finite element method. MATEC Web of Conferences, 270, 04022. https://doi.org/10.1051/matecconf/201927004022

Zhang, M., & Wu, W. M. (2011). A two dimensional hydrodynamic and sediment transport model for dam break based on finite volume method with quadtree grid. Applied Ocean Research, 33(4), 297–308. https://doi.org/10.1016/j.apor.2011.07.004

Zhang, Y., Li, Z., Wang, J., Ge, W., & Chen, X. (2022). Environmental impact assessment of dam-break floods considering multiple influencing factors. Science of The Total Environment, 837, 155853. https://doi.org/10.1016/j.scitotenv.2022.155853

DOI: https://doi.org/10.31764/jtam.v10i3.38595