Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter November 28, 2022

Numerical modeling of the dam-break flood over natural rivers on movable beds

  • Alibek Issakhov EMAIL logo , Aliya Borsikbayeva , Aizhan Abylkassymova EMAIL logo , Assylbek Issakhov EMAIL logo and Askar Khikmetov

Abstract

In the present work, a modified numerical model was developed to simulate the water flow during a dam break with the mud layer transfer of different heights, consisting of three phases (water, air, and a phase for deposition). To carry out a numerical simulation of this process, a mathematical model based on the VOF (volume of fluid) method was modified, taking into account the movement of the water-free surface, which is carried out by the movement of water flow based on the Newtonian fluid model, and the movement of mud impurities is based on the non-Newtonian fluid model. Validation of the constructed model for the influence of three-dimensional features of the flow on morphological changes is carried out by a modified mathematical model and compared with the results of calculation for two-dimensional (2D) and three-dimensional (3D) models. The proposed method for modeling is applied on a real complex terrain, which was based on the Kargalinka – a river in Almaty and the Almaty region of Kazakhstan, the right tributary of the Kaskelen River. Simulation analysis is carried out for cases with different deposit heights. All results of the numerical simulation can be visually viewed using graphs and illustrations.


Corresponding authors: Alibek Issakhov, al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan; Kazakh British Technical University, Almaty, Republic of Kazakhstan; and International Information Technology University, Almaty, Republic of Kazakhstan, E-mail: ; and Aizhan Abylkassymova and Assylbek Issakhov, Kazakh British Technical University, Almaty, Republic of Kazakhstan, E-mail: abylkassymova.aizhan@gmail.com (A. Abylkassymova), asylissakhov@gmail.com (A. Issakhov)

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work is supported by the grant from the Ministry of education and science of the Republic of Kazakhstan (AP09058406).

  3. Conflict of interest statement: The authors declare that there is no conflict of interests regarding the publication of this paper.

  4. Availability of data and materials: The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

[1] R. Marsooli and W. Wu, “Three-dimensional numerical modeling of dam-break flows with sediment transport over movable beds,” J. Hydraul. Eng., vol. 141, no. 1, p. 04014066, 2015. https://doi.org/10.1061/(asce)hy.1943-7900.0000947.Search in Google Scholar

[2] V. Naderkhanloo, M. Soudi, and M. Hemmati, “3D numerical simulation of dam-break flows with sediment transport over movable beds,” in World Environmental and Water Resources Congress 2017: International Perspectives, History and Heritage, Emerging Technologies, and Student Papers, 2017, pp. 161–170.10.1061/9780784480595.015Search in Google Scholar

[3] R. Marsooli and W. Wu, “3-D finite-volume model of dam-break flow over uneven beds based on VOF method,” Adv. Water Resour., vol. 70, pp. 104–117, 2014. https://doi.org/10.1016/j.advwatres.2014.04.020.Search in Google Scholar

[4] S. Soares-Frazao, R. Canelas, and Z. Cao, “Dam-break flows over mobile beds: experiments and benchmark tests for numerical models,” J. Hydraul. Res., vol. 50, no. 4, pp. 364–375, 2012. https://doi.org/10.1080/00221686.2012.689682.Search in Google Scholar

[5] K. M. T. Kleefsman, G. Fekken, and A. E. P. Veldman, “A Volume-of-fluid based simulation method for wave impact problems,” J. Comput. Phys., vol. 206, no. 1, pp. 363–393, 2005. https://doi.org/10.1016/j.jcp.2004.12.007.Search in Google Scholar

[6] B. Spinewine and Y. Zech, “Small-scale laboratory dam-break waves on movable beds,” J. Hydraul. Res., vol. 45, pp. 73–86, 2007. https://doi.org/10.1080/00221686.2007.9521834.Search in Google Scholar

[7] M. Zhang, Y. Xu, and Z. Hao, “Integrating 1D and 2D hydrodynamic, sediment transport model for dam-break flow using finite volume method,” Sci. China Phys. Mech. Astron., vol. 57, no. 4, pp. 774–783, 2014. https://doi.org/10.1007/s11433-013-5294-z.Search in Google Scholar

[8] W. Wu, R. Marsooli, and Z. He, “Depth-averaged two-dimensional model of unsteady flow and sediment transport due to noncohesive embankment break/breaching,” J. Hydraul. Eng., vol. 138, no. 6, pp. 503–516, 2012. https://doi.org/10.1061/(asce)hy.1943-7900.0000546.Search in Google Scholar

[9] L. A. LaRocque, J. Imran, and M. H. Chaudhry, “Experimental and numerical investigations of two-dimensional dam-break flows,” J. Hydraul. Eng., vol. 139, no. 6, pp. 569–579, 2013. https://doi.org/10.1061/(asce)hy.1943-7900.0000705.Search in Google Scholar

[10] Y. Zech, S. Soares-Frazao, and B. Spinewine, “Dam-break induced sediment movement: experimental approaches and numerical modelling,” J. Hydraul. Res., vol. 46, no. 2, pp. 176–190, 2008. https://doi.org/10.1080/00221686.2008.9521854.Search in Google Scholar

[11] P. Costabile and E. Macchione, “One dimensional modeling of dam break flow over erodible sediment bed,” in International Conference on Fluvial Hydraulics, RIVER FLOW 2006, 2006, p. 1501.10.1201/9781439833865.ch160Search in Google Scholar

[12] Z. Yue, Z. Fu, and H. Liu, “Well-balanced 2D coupled modelling of dam-break sediment-laden flood processes in a real river channel,” in 35th World Congress of the International-Association-for-Hydro-Environment-Engineering-and-Research (IAHR), 2013.Search in Google Scholar

[13] P. Lin, Y. Wu, and J. Bai, “A Numerical study of dam-break flow and sediment transport from a quake lake,” J. Earthq. Tsunami, vol. 5, no. 5, pp. 401–428, 2011. https://doi.org/10.1142/s1793431111001169.Search in Google Scholar

[14] L. Fu and Y. C. Jin, “Improved multiphase Lagrangian method for simulating sediment transport in dam-break flows,” J. Hydraul. Eng., vol. 142, no. 6, p. 04016005, 2016. https://doi.org/10.1061/(asce)hy.1943-7900.0001132.Search in Google Scholar

[15] F. Benkhaldoun, S. Sari, and M. Seaid, “A flux-limiter method for dam-break flows over erodible sediment beds,” Appl. Math. Model., vol. 36, no. 10, pp. 4847–4861, 2012. https://doi.org/10.1016/j.apm.2011.11.088.Search in Google Scholar

[16] C. H. Yu, H. L. Wen, and Z. H. Gu, “Numerical simulation of dam-break flow impacting a stationary obstacle by a CLSVOF/IB method,” Commun. Nonlinear Sci. Numer. Simulat., vol. 79, pp. 1–39, 2019. https://doi.org/10.1016/j.cnsns.2019.104934.Search in Google Scholar

[17] Z. H. Gu, H. L. Wen, and C. H. Yu, “Interface-preserving level set method for simulating dam-break flows,” J. Comput. Phys., vol. 374, pp. 249–280, 2018. https://doi.org/10.1016/j.jcp.2018.07.057.Search in Google Scholar

[18] M. Zhang and W. M. Wu, “A two dimensional hydrodynamic and sediment transport model for dam break based on finite volume method with quadtree grid,” Appl. Ocean Res., vol. 33, no. 4, pp. 297–308, 2011. https://doi.org/10.1016/j.apor.2011.07.004.Search in Google Scholar

[19] T. R. Wu, V. Thi-Hong-Nhi, and J. W. Lin, “Three-dimensional numerical study on the interaction between dam-break wave and cylinder array,” J. Earthq. Tsunami, vol. 12, no. 2, p. 1840007, 2018. https://doi.org/10.1142/s1793431118400079.Search in Google Scholar

[20] Y. Ozeren, R. Aleixo, and M. Altinakar, “Laboratory experiments on dam-break flow of water-sediment mixtures,” in 7th International Conference on Fluvial Hydraulics (River Flow), River flow, 2014, pp. 1639–1646.10.1201/b17133-218Search in Google Scholar

[21] A. Issakhov, Y. Zhandaulet, and A. Nogaeva, “Numerical simulation of dam break flow for various forms of the obstacle by VOF method,” Int. J. Multiphas. Flow, vol. 109, pp. 191–206, 2018. https://doi.org/10.1016/j.ijmultiphaseflow.2018.08.003.Search in Google Scholar

[22] A. Issakhov and M. Imanberdiyeva, “Numerical simulation of the movement of water surface of dam break flow by VOF methods for various obstacles,” Int. J. Heat Mass Tran., vol. 136, pp. 1030–1051, 2019. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.034.Search in Google Scholar

[23] A. Issakhov and A. Borsikbayeva, “The impact of a multilevel protection column on the propagation of a water wave and pressure distribution during a dam break: numerical simulation,” J. Hydrol., vol. 598, p. 126212, 2021. https://doi.org/10.1016/j.jhydrol.2021.126212.Search in Google Scholar

[24] E. Lakzian and A. Estiri, “Entropy generation analysis as design criteria in dam-break flows for non-Newtonian fluids,” Eur. Phys. J. Plus, vol. 133, no. 11, p. 454, 2018. https://doi.org/10.1140/epjp/i2018-12259-7.Search in Google Scholar

[25] G. Wu, Z. Yang, and K. Zhang, “A non-equilibrium sediment transport model for dam break flow over moveable bed based on non-uniform rectangular mesh,” Water, vol. 10, no. 5, p. 616, 2018. https://doi.org/10.3390/w10050616.Search in Google Scholar

[26] W. Lai and A. A. Khan, “Modeling dam-break flood over natural rivers using discontinuous Galerkin method,” J. Hydrodyn., vol. 24, no. 4, pp. 467–478, 2012. https://doi.org/10.1016/s1001-6058(11)60268-0.Search in Google Scholar

[27] B. Yu-chuan, D. Xu, and L. Dong-qiang, “Numerical simulation of two-dimensional dam-break flows in curved channels,” J. Hydrodyn., vol. 19, no. 6, pp. 726–735, 2007. https://doi.org/10.1016/s1001-6058(08)60010-4.Search in Google Scholar

[28] S. K. Biswal, M. K. Moharana, and A. K. Agrawal, “Effects of initial stage of dam-break flows on sediment transport,” Sadhana Acad. Proc. Eng. Sci., vol. 43, no. 12, p. 203, 2018. https://doi.org/10.1007/s12046-018-0968-x.Search in Google Scholar

[29] H. Capart and D. L. Young, “Formation of a jump by the dam-break wave over a granular bed,” J. Fluid Mech., vol. 372, pp. 165–187, 1998. https://doi.org/10.1017/s0022112098002250.Search in Google Scholar

[30] H. Capart, D. L. Young, and Y. Zech, “Dam-break induced debris flow,” Particulate Gravity Currents, vol. 31, pp. 149–156, 2001. https://doi.org/10.1002/9781444304275.ch11.Search in Google Scholar

[31] L. Guertault, B. Camenen, and C. Peteuil, “One-dimensional modeling of suspended sediment dynamics in dam reservoirs,” J. Hydraul. Eng., vol. 142, no. 10, p. 04016033, 2016. https://doi.org/10.1061/(asce)hy.1943-7900.0001157.Search in Google Scholar

[32] l. Fraccarollo and H. Capart, “Riemann wave description of erosional dam-break flows,” J. Fluid Mech., vol. 461, pp. 183–228, 2002. https://doi.org/10.1017/s0022112002008455.Search in Google Scholar

[33] P. Z. Lin and P. L. F. Liu, “A numerical study of breaking waves in the surf zone,” J. Fluid Mech., vol. 359, pp. 239–264, 1998. https://doi.org/10.1017/s002211209700846x.Search in Google Scholar

[34] P. Z. Lin and P. L. F. Liu, “Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone,” J. Geophys. Res., vol. 103, no. C8, pp. 15677–15694, 1998. https://doi.org/10.1029/98jc01360.Search in Google Scholar

[35] H.-C. Hsu, A. Torres-Freyermuth, T.-J. Hsu, H.-H. Hwung, and P.-C. Kuo, “On dam-break wave propagation and its implication to sediment erosion,” J. Hydraul. Res., vol. 52, no. 2, pp. 205–218, 2014. https://doi.org/10.1080/00221686.2013.857365.Search in Google Scholar

[36] Z. Cao, G. Pender, S. Wallis, and P. Carling, “Computational dam-break hydraulics over erodible sediment bed,” J. Hydraul. Eng., vol. 130, no. 7, pp. 689–703, 2004. https://doi.org/10.1061/(asce)0733-9429(2004)130:7(689).10.1061/(ASCE)0733-9429(2004)130:7(689)Search in Google Scholar

[37] J. J. Monaghan, “Smoothed particle hydrodynamics and its diverse applications,” Annu. Rev. Fluid Mech., vol. 44, pp. 323–346, 2012. https://doi.org/10.1146/annurev-fluid-120710-101220.Search in Google Scholar

[38] X. Xu, “An improved SPH approach for simulating 3D dam-break flows with breaking waves,” Comput. Methods Appl. Mech. Eng., vol. 311, pp. 723–742, 2016. https://doi.org/10.1016/j.cma.2016.09.002.Search in Google Scholar

[39] X. Xu, Y. L. Jiang, and P. Yu, “SPH simulations of 3D dam-break flow against various forms of the obstacle: toward an optimal design,” Ocean Eng., vol. 229, p. 108978, 2021. https://doi.org/10.1016/j.oceaneng.2021.108978.Search in Google Scholar

[40] I. K. Nikolos and A. I. Delis, “An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography,” Comput. Methods Appl. Mech. Eng., vol. 198, nos. 47–48, pp. 3723–3750, 2009. https://doi.org/10.1016/j.cma.2009.08.006.Search in Google Scholar

[41] C. Di Cristo, S. Evangelista, M. Greco, M. Iervolino, A. Leopardi, and A. Vacca, “Dam-break waves over an erodible embankment: experiments and simulations,” J. Hydraul. Res., vol. 56, no. 2, pp. 196–210, 2018. https://doi.org/10.1080/00221686.2017.1313322.Search in Google Scholar

[42] S. Evangelista, M. S. Altinakar, C. Di Cristo, and A. Leopardi, “Simulation of dam-break waves on movable beds using a multi-stage centered scheme,” Int. J. Sediment Res., vol. 28, no. 3, pp. 269–284, 2013. https://doi.org/10.1016/s1001-6279(13)60039-6.Search in Google Scholar

[43] Y. Cui, G. Parker, J. Pizzuto, and T. E. Lisle, “Sediment pulses in mountain rivers: 2. Comparison between experiments and numerical predictions,” Water Resour. Res., vol. 39, no. 9, pp. 1240–1251, 2003. https://doi.org/10.1029/2002wr001805.Search in Google Scholar

[44] W. Wu, D. A. Vieira, and S. S. Wang, “One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks,” J. Hydraul. Eng., vol. 130, no. 9, pp. 914–923, 2004. https://doi.org/10.1061/(asce)0733-9429(2004)130:9(914).10.1061/(ASCE)0733-9429(2004)130:9(914)Search in Google Scholar

[45] L. Goutière, S. Soares-Frazão, C. Savary, T. Laraichi, and Y. Zech, “One-dimensional model for transient flows involving bed-load sediment transport and changes in flow regimes,” J. Hydraul. Eng., vol. 134, no. 6, pp. 726–735, 2008. https://doi.org/10.1061/(asce)0733-9429(2008)134:6(726).10.1061/(ASCE)0733-9429(2008)134:6(726)Search in Google Scholar

[46] R. I. Ferguson, M. Church, C. D. Rennie, and J. G. Venditti, “Reconstructing a sediment pulse: modeling the effect of placer mining on Fraser river, Canada,” J. Geophys. Res. Solid Earth, vol. 120, no. 7, pp. 1436–1454, 2015. https://doi.org/10.1002/2015jf003491.Search in Google Scholar

[47] F. Carraro, A. Valiani, and V. Caleffi, “Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant–Exner morphodynamic model,” Adv. Water Resour., vol. 113, pp. 189–201, 2018. https://doi.org/10.1016/j.advwatres.2018.01.011.Search in Google Scholar

[48] W. Wu and S. S. Wang, “One-dimensional modeling of dam-break flow over movable beds,” J. Hydraul. Eng., vol. 133, no. 1, pp. 48–58, 2007. https://doi.org/10.1061/(asce)0733-9429(2007)133:1(48).10.1061/(ASCE)0733-9429(2007)133:1(48)Search in Google Scholar

[49] L. Liang, X. Yu, and F. Bombardelli, “A general mixture model for sediment laden flows,” Adv. Water Resour., vol. 107, pp. 108–125, 2017. https://doi.org/10.1016/j.advwatres.2017.06.012.Search in Google Scholar

[50] C. Juez, J. Murillo, and P. García-Navarro, “A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed,” Adv. Water Resour., vol. 71, pp. 93–109, 2014. https://doi.org/10.1016/j.advwatres.2014.05.014.Search in Google Scholar

[51] F. N. Cantero-Chinchilla, O. Castro-Orgaz, S. Dey, and J. L. Ayuso-Muñoz, “Nonhydrostatic dam break flows. II: one-dimensional depth-averaged modeling for mov- able bed flows,” J. Hydraul. Eng., vol. 142, no. 12, p. 04016069, 2016. https://doi.org/10.1061/(asce)hy.1943-7900.0001206.Search in Google Scholar

[52] G. Chambon, A. Ghemmour, and D. Laigle, “Gravity-driven surges of a viscoplastic fluid: an experimental study,” J. Non-Newtonian Fluid Mech., vol. 158, nos. 1–3, pp. 54–62, 2009. https://doi.org/10.1016/j.jnnfm.2008.08.006.Search in Google Scholar

[53] C. Ancey and S. Cochard, “The dam-break problem for Herschel-Bulkley viscoplastic fluids down steep flumes,” J. Non-Newtonian Fluid Mech., vol. 158, nos. 1–3, pp. 18–35, 2009. https://doi.org/10.1016/j.jnnfm.2008.08.008.Search in Google Scholar

[54] X. Li and J. Zhao, “Dam-break of mixtures consisting of non-Newtonian liquids and granular particles,” Powder Technol., vol. 338, pp. 493–505, 2018. https://doi.org/10.1016/j.powtec.2018.07.021.Search in Google Scholar

[55] C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys., vol. 39, no. 1, pp. 201–225, 1981. https://doi.org/10.1016/0021-9991(81)90145-5.Search in Google Scholar

[56] A. Liu, A. Xiong, and X. Liu, “Numerical simulations of dam-break flow on complicated terrain using VOF method,” in International Conference on Mechanical and Automation Engineering, 2013, pp. 229–232.Search in Google Scholar

[57] R. I. Issa, “Solution of the implicitly discretized fluid flow equations by operator splitting,” J. Comput. Phys., vol. 62, no. 1, pp. 40–65, 1986. https://doi.org/10.1016/0021-9991(86)90099-9.Search in Google Scholar

[58] A. Issakhov, A. Alimbek, and Y. Zhandaulet, “The assessment of water pollution by chemical reaction products from the activities of industrial facilities: numerical study,” J. Clean. Prod., vol. 282, p. 125239, 2021. https://doi.org/10.1016/j.jclepro.2020.125239.Search in Google Scholar

[59] A. Issakhov and P. Omarova, “Modeling and analysis of the effects of barrier height on automobiles emission dispersion,” J. Clean. Prod., vol. 296, p. 126450, 2021. https://doi.org/10.1016/j.jclepro.2021.126450.Search in Google Scholar

[60] A. Issakhov, A. Alimbek, and A. Issakhov, “A numerical study for the assessment of air pollutant dispersion with chemical reactions from a thermal power plant,” Eng. Appl. Comp. Fluid Mech., vol. 14, no. 1, pp. 1035–1061, 2020. https://doi.org/10.1080/19942060.2020.1800515.Search in Google Scholar

[61] A. Issakhov, A. Abylkassymova, and A. Issakhov, “Assessment of the influence of the barriers height and trees with porosity properties on the dispersion of emissions from vehicles in a residential area with various types of building developments,” J. Cleaner Prod., vol. 366, p. 132581, 2022. https://doi.org/10.1016/j.jclepro.2022.132581.Search in Google Scholar

[62] A. Issakhov, A. Tursynzhanova, and A. Abylkassymova, “Numerical study of air pollution exposure in idealized urban street canyons: Porous and solid barriers,” Urban Climate, vol. 43, p. 101112, 2022. https://doi.org/10.1016/j.uclim.2022.101112.Search in Google Scholar

[63] A. Issakhov and P. Omarova, “Numerical simulation of pollutant dispersion in the residential areas with continuous grass barriers,” Int. J. Environ. Sci. Technol., vol. 17, no. 1, pp. 525–540, 2020.10.1007/s13762-019-02517-xSearch in Google Scholar

[64] A. Issakhov,A. Alimbek, and A. Abylkassymova, “Numerical modeling of water pollution by products of chemical reactions from the activities of industrial facilities at variable and constant temperatures of the environment,” J. Cont.  Hydrol., vol. 104116, p. 104116, 2022. https://doi.org/10.1016/j.jconhyd.2022.104116.Search in Google Scholar

[65] I. E. Barton, “Comparison of SIMPLE and PISO type algorithms for transient flows,” Int. J. Numer. Methods Fluid., vol. 26, no. 4, pp. 459–483, 1998. https://doi.org/10.1002/(sici)1097-0363(19980228)26:4<459::aid-fld645>3.0.co;2-u.10.1002/(SICI)1097-0363(19980228)26:4<459::AID-FLD645>3.0.CO;2-USearch in Google Scholar

Received: 2021-07-05
Revised: 2022-09-03
Accepted: 2022-09-18
Published Online: 2022-11-28

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 2.5.2024 from https://www.degruyter.com/document/doi/10.1515/ijnsns-2021-0273/html
Scroll to top button