Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

NUMERICAL MODELING OF NON-CAPACITY MODEL FOR SEDIMENT TRANSPORT BY CENTRAL UPWIND SCHEME

  • S., JELTI (Mohamed first University) ;
  • A., CHARHABIL (Sorbone Paris Nord University) ;
  • J. EL, GHORDAF (University of Sultan Moulay Slimane)
  • Received : 2022.04.22
  • Accepted : 2022.09.27
  • Published : 2023.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

This work deals with the numerical modeling of dam-break flow over erodible bed. The mathematical model consists of the shallow water equations, the transport diffusion and the bed morphology change equations. The system is solved by central upwind scheme. The obtained results of the resolution of dam-beak problem is presented in order to show the performance of the numerical scheme. Also a comparison of central upwind and Roe schemes is presented.

Keywords

References

  1. F. Benkhaldoun, S. Sari and M. Seaid, A flux-limiter method for dam-break flows over erodible sediment beds, Applied Mathematical Modelling 36 (2012), 4847-4861.  https://doi.org/10.1016/j.apm.2011.11.088
  2. Z. Cao, G. Pender, S. Wallis and P.A. Carling, Computational dam-break hydraulics over erodible sediment bed, Journal of Hydraulic Engineering 130 (2004), 389-703.  https://doi.org/10.1061/(asce)0733-9429(2004)130:5(389)
  3. H. Capart and D.L. Young, Formation of a jum by the dam-break wave over a granular bed, Journal of Fluid Mechanics 372 (1998), 165-187.  https://doi.org/10.1017/S0022112098002250
  4. A. Chertock, S. Cui, A. Kurganov, T. Wu, Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms, International Journal for numerical methods in Fluids 78 (2015), 355-383.  https://doi.org/10.1002/fld.4023
  5. Z. Cao, R. Day and S. Egashira, Coupled and decoupled numerical modelling of flow and morphological evolution in alluvial rivers, Journal of Hydraulic Engineering 128 (2002), 306-321.  https://doi.org/10.1061/(asce)0733-9429(2002)128:3(306)
  6. R. Ferreira and J. Leal, Mathematical modeling of the instantaneous dam-break flood wave over mobile bed:application of TVD and flux-splitting schemes, Proceedings of European Concerted Action on Dam-break Modeling, Munich, Germany, 175-222, 1998. 
  7. L. Fraccarollo and H. Capart, Riemann wave description of erosional dam-break flows, Journal of Fluid Mechanics 461 (2002), 183-228.  https://doi.org/10.1017/S0022112002008455
  8. L. Fraccarollo and A. Armanini, A semi-analytical solution for the dam-break problem over a movable bed, Proceedings of European Concerted Action on Dam-Break Modeling, Munich, Germany, 145-152, 1998. 
  9. S. Gottlieb and S. Chi-Wang, Total variation diminishing Runge-Kutta schemes, Mathematics of computation 67 (1998), 73-85.  https://doi.org/10.1090/S0025-5718-98-00913-2
  10. S. Jelti, M. Mezouari and M. Boulerhcha, Numerical modeling of dam-break flow over erodible bed by Roe scheme with an original discretization of source term, International Journal of Fluid Mechanics Research 45 (2018), 21-36.  https://doi.org/10.1615/interjfluidmechres.2018019183
  11. S. Jelti and M. Boulerhcha, Numerical modeling of two dimensional non-capacity model for sediment transport by an unstructured finite volume method with a new discretization of the source term, Mathematics and Computers in Simulation 197 (2022), 253-276.  https://doi.org/10.1016/j.matcom.2022.02.012
  12. G. Kesserwani, A. Shamkhalchian and M.J. Zadeh, Fully coupled discontinuous galerkin modeling of dam-break flows over movable bed with sediment transport, Journal of Hydraulic Engineering, Technical Notes 140 (2014). DOI:10.1061/(ASCE)HY.1943-7900.0000860 
  13. A. Kurganov, E. Tadmor, New high resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000), 241-282.  https://doi.org/10.1006/jcph.2000.6459
  14. A. Kurganov, S. Noelle, G. Petrova, Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM Journal on Scientific Computing 23 (2001), 707-740.  https://doi.org/10.1137/S1064827500373413
  15. A. Kurganov, D. Levy, Central-upwind schemes for the saint-venant system, ESAIM: Mathematical Modelling and Numerical Analysis 32 (2002), 397-425.  https://doi.org/10.1051/m2an:2002019
  16. A. Kurganov, G. Petrova, A second-order well-balanced positivity preserving central-upwind scheme for the saintvenant system, Communications in Mathematical Sciences 5 (2007), 133-160.  https://doi.org/10.4310/CMS.2007.v5.n1.a6
  17. A. Kurganov, C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes, Communications in Computational Physics 2 (2007), 141-163. 
  18. A. Kurganov, E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numerical Methods for Partial Differential Equations 18 (2002), 584-608.  https://doi.org/10.1002/num.10025
  19. A. Kurganov, G. Petrova, Central-upwind schemes for two-layer shallow equations, SIAM Journal on Scientific Computing 31 (2009), 1742-1773.  https://doi.org/10.1137/080719091
  20. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002. 
  21. S. Li and C.J. Duffy, Fully coupled approach to modeling shallow water flow, sediment transport and bed evolution in rivers, Water Resources Research 47 (2011), 1-20.  https://doi.org/10.1029/2010WR009138
  22. H.A. Peng, L.A. Yunlong, H.A. Jianjian, C.B. Zhixian, L.C. Huaihan and H.A. Zhiguo, Computationally efficient modeling of hydro-sediment-morphodynamic processes using a hybrid local time step/global maximum time step, Advances in Water Resources 127 (2019), 26-38.  https://doi.org/10.1016/j.advwatres.2019.03.006
  23. G. Simpson and S. Castelltort, Coupled model of surface water flow, sediment transport and morphological evolution, Computers and geosciences 32 (2006), 1600-1614.  https://doi.org/10.1016/j.cageo.2006.02.020
  24. W. Wu, Computational River Dynamics, Taylor and Francis, London, 2008. 
  25. W. Wu and S.S. Wang, One-dimensional modeling of dam-break flow over movable beds, Journal of Hydraulic Engineering 133 (2007), 48-58.  https://doi.org/10.1061/(asce)0733-9429(2007)133:1(48)
  26. C.T. Yang and B.P. Greimann, Dam-break unsteady flow and sediment transport, Proceedings of European Concerted Action on Dam-Break Modeling, Zaragoza, Spain, 327-365, 1999. 
  27. Z. Yue, H. Liu, Y. Li, P. Hu and Y. Zhang, A Well-Balanced and Fully Coupled Noncapacity Model for Dam-Break Flooding, Mathematical Problems in Engineering 2015 (2015), Article ID 613853, 13 pages.