References
- 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
- 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)
- 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
- 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
- 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)
- 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.
- 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
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- A. Kurganov, C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes, Communications in Computational Physics 2 (2007), 141-163.
- 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
- 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
- R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002.
- 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
- 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
- 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
- W. Wu, Computational River Dynamics, Taylor and Francis, London, 2008.
- 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)
- 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.
- 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.