Application of Finite Difference Method in Simulating 2D Partial Dam-break Flow with an Obstacle
DOI:
https://doi.org/10.55324/ijoms.v2i12.609Keywords:
dam-break, FTCS, Hansen filter, obstacle, shallow water equationsAbstract
A numerical model capable of simulating the dam-break flow is required to reduce the detrimental impact on the downstream area of the dam. This study aims to see how the characteristics and patterns of flow due to partial dam failure and the presence of an obstacle in the floodplain. In real life, the obstacle can be considered as a building. In this research, a model based on the FTCS method was developed with the addition of a Hansen numerical filter. This model is known as the FTCS-Hansen model. The Hansen filter in this study is used to enhance the numerical of the model and reduce oscillations due to shock waves. The FTCS-Hansen model simulates a 2D partial dam break with an obstacle. The simulation results are compared with other simulation results from previous studies. This comparison intends to see the performance of the FTCS-Hansen model. The results show good agreement between the FTCS-Hansen model and other numerical models. In addition, the complicated dam-break flow characteristics due to the presence of an obstacle (reflection and diffraction) can also be well captured by the FTCS-Hansen model.
References
Adityawan, M. B., & Tanaka, H. (2012). Bed stress assessment under solitary wave run-up. Earth, Planets and Space, 64(10). https://doi.org/10.5047/eps.2011.02.012
Baghlani, A. (2011). Simulation of dam-break problem by a robust flux-vector splitting approach in Cartesian grid. Scientia Iranica, 18(5). https://doi.org/10.1016/j.scient.2011.09.004
Glotov, V. E., Chlachula, J., Glotova, L. P., & Little, E. (2018). Causes and environmental impact of the gold-tailings dam failure at Karamken, the Russian Far East. Engineering Geology, 245. https://doi.org/10.1016/j.enggeo.2018.08.012
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). 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). https://doi.org/10.18517/ijaseit.11.6.14484
Huang, Y., Zhang, N., & Pei, Y. (2013). Well-balanced finite volume scheme for shallow water flooding and drying over arbitrary topography. Engineering Applications of Computational Fluid Mechanics, 7(1). https://doi.org/10.1080/19942060.2013.11015452
Lakhlifi, Y., Daoudi, S., & Boushaba, F. (2018). Dam-Break computations by a dynamical adaptive finite volume method. Journal of Applied Fluid Mechanics, 11(6). https://doi.org/10.29252/jafm.11.06.28564
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. https://doi.org/10.1016/j.geomorph.2020.107221
Lee, H. (2014). Application of Runge-Kutta Discontinuous Galerkin finite element method to shallow water flow. KSCE Journal of Civil Engineering, 18(5). https://doi.org/10.1007/s12205-014-0068-3
Liang, D., Lin, B., & Falconer, R. A. (2007). Simulation of rapidly varying flow using an efficient TVD-MacCormack scheme. International Journal for Numerical Methods in Fluids, 53(5). https://doi.org/10.1002/fld.1305
Liang, S. J., & Hsu, T. W. (2009). Least-squares finite-element method for Shallow-water equations with source terms. Acta Mechanica Sinica/Lixue Xuebao, 25(5). https://doi.org/10.1007/s10409-009-0250-x
Lumbroso, D., Davison, M., Body, R., & Petkovšek, G. (2021). Modelling the Brumadinho tailings dam failure, the subsequent loss of life and how it could have been reduced. Natural Hazards and Earth System Sciences, 21(1). https://doi.org/10.5194/nhess-21-21-2021
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. https://doi.org/10.1016/j.rineng.2022.100382
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. https://doi.org/10.1016/j.rinam.2021.100193
Maitsa, T. R., 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. https://doi.org/10.1051/e3sconf/202015604003
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). https://doi.org/10.5614/jts.2020.27.1.1
Ouyang, C., He, S., Xu, Q., Luo, Y., & Zhang, W. (2013). A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain. Computers and Geosciences, 52. https://doi.org/10.1016/j.cageo.2012.08.024
Peng, S. H. (2012). 1D and 2D numerical modeling for solving dam-break flow problems using finite volume method. Journal of Applied Mathematics, 2012. https://doi.org/10.1155/2012/489269
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). https://doi.org/10.1007/s40430-017-0776-y
Silva Rotta, L. H., Alcântara, E., Park, E., Negri, R. G., Lin, Y. N., Bernardo, N., Mendes, T. S. G., & Souza Filho, C. R. (2020). The 2019 Brumadinho tailings dam collapse: Possible cause and impacts of the worst human and environmental disaster in Brazil. International Journal of Applied Earth Observation and Geoinformation, 90. https://doi.org/10.1016/j.jag.2020.102119
Wang, J. S., Ni, H. G., & He, Y. S. (2000). Finite-Difference TVD Scheme for Computation of Dam-Break Problems. Journal of Hydraulic Engineering, 126(4). https://doi.org/10.1061/(asce)0733-9429(2000)126:4(253)
Xing, Y., & Shu, C. W. (2005). High order finite difference WENO schemes with the exact conservation property for the shallow water equations. Journal of Computational Physics, 208(1). https://doi.org/10.1016/j.jcp.2005.02.006
Zendrato, N. L. H., Harlan, D., Adityawan, M. B., & Natakusumah, D. K. (2019). 1D Numerical modelling of dam break using finite element method. MATEC Web of Conferences, 270. https://doi.org/10.1051/matecconf/201927004022
Zhao, L., Guo, B., Li, T., Avital, E. J., & Williams, J. J. R. (2014). A well-balanced explicit/semi-implicit finite element scheme for shallow water equations in drying-wetting areas. International Journal for Numerical Methods in Fluids, 75(12). https://doi.org/10.1002/fld.3919
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Qalbi Hafiyyan, Azwa Nirmala, Murad MS, Sumiyattinah Sumiyattinah, Vivi Bachtiar, Muhammad Yusuf Yusuf

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-ShareAlike 4.0 International (CC-BY-SA). that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.






