[Ancey, C., Iverson, R.M., Rentschler, M., Denlinger, R.P., 2008. An exact solution for ideal dam-break floods on steep slopes. Water Resour. Res., 44, 1, W01430.10.1029/2007WR006353]Open DOISearch in Google Scholar
[Barré de Saint-Venant, A.J.C., 1871. Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l’introduction des marées dans leur lits. Comptes Rendus des séances de l’Académie des Sciences, 73, 1871, 237–240. (In French.)]Search in Google Scholar
[Bouchut, F., Mangeney-Castelnau, A., Perthame, B., Vilotte, J., 2003. A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows. C. R. Acad. Sci. Paris, 336, 6, 531–536.10.1016/S1631-073X(03)00117-1]Search in Google Scholar
[Bussing, T.R.A., Murmant, E.M., 1988. Finite-volume method for the calculation of compressible chemically reacting flows. AIAA J., 26, 9, 1070–1078.10.2514/3.10013]Open DOISearch in Google Scholar
[Cantero-Chinchilla, F.N., Castro-Orgaz, O., Khan, A.A., 2017. Depth-integrated non-hydrostatic free-surface flow modelling using weighted-averaged equations. Int. J. Numer. Mech. Fluids, 87, 1. DOI: 10.1002/fld.4481.10.1002/fld.4481]Open DOISearch in Google Scholar
[Cao, Z.X, Yue, Z., Li, X., Che, T., 2007. Two-dimensional mathematical modeling of flooding over erodible sediment bed. Proceedings of the 32nd IAHR Congress, Venice, Italy. CD-ROM, IAHR, Madrid.]Search in Google Scholar
[Cao, Z.X, Hu, P., Hu, K., Pender G., Liu, Q.Q., 2015. Modelling roll waves with shallow water equations and turbulent closure. J. Hydraul. Res., 53, 2, 161–177.10.1080/00221686.2014.950350]Search in Google Scholar
[Cao, Z.X, Xia, C.C., Pender, G., Liu, Q.Q., 2017. Shallow water hydro-sediment-morphodynamics equations for fluvial processes. J. Hydraul. Eng., 143, 5, 02517001.10.1061/(ASCE)HY.1943-7900.0001281]Search in Google Scholar
[Castro-Orgaz, O., Hager, W.H., 2017. Non-Hydrostatic Free Surface Flows. Springer International Publishing AG, Cham, Switzerland.10.1007/978-3-319-47971-2]Search in Google Scholar
[Castro-Orgaz, O., Hutter, K., Giraldez, J.V., Hager, W.H., 2015. Nonhydrostatic granular flow over 3-D terrain: New Boussinesq-type gravity waves? J. Geophys. Res., 120, 1–28.10.1002/2014JF003279]Search in Google Scholar
[Denlinger, R.P., Iverson, R.M., 2004. Granular avalanches across irregular three-dimensional terrain: I. Theory and computation. J. Geophys. Res., 109, F01014.10.1029/2003JF000085]Search in Google Scholar
[Denlinger, R.P., O’Connell, D.R.H., 2008. Computing nonhydrostatic shallow-water flow over steep terrain. J. Hydraul. Eng., 134, 11, 1590–1602.10.1061/(ASCE)0733-9429(2008)134:11(1590)]Search in Google Scholar
[Fernandez-Feria, R., 2006. Dam-break flow for arbitrary slopes of the bottom. J. Eng. Math., 54, 4, 319–331.10.1007/s10665-006-9034-5]Open DOISearch in Google Scholar
[Gray, J.M.N.T., Wieland, M., Hutter, K., 1999. Gravity-driven free surface flow of granular avalanches over complex basal topography. Proc. R. Soc. Lond. A, 455, 1841–1874.10.1098/rspa.1999.0383]Search in Google Scholar
[Greve, R., Koch, T., Hutter, K., 1994. Unconfined flow of granular avalanches along a partly curved surface. I. Theory. Proc. R. Soc. Lond. A, 445, 399–413.10.1098/rspa.1994.0068]Search in Google Scholar
[Hou, J., Liang, Q., Simons, F., Hinkelmann, R., 2013a. A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment. Adv. Water Resour., 52, 107–131.10.1016/j.advwatres.2012.08.003]Open DOISearch in Google Scholar
[Hou, J., Liang, Q., Simons, F., Hinkelmann, R., 2013b. A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains. Comput. Fluids, 82, 132–147.10.1016/j.compfluid.2013.04.015]Search in Google Scholar
[Huang, W., Cao, Z.X, Carling, P., Pender, G., 2014. Coupled 2D hydrodynamic and sediment transport modeling of mega-flood due to glacier dam-break in Altai Mountain, Southern Siberia. J. Mt. Sci., 11, 6, 1442–1453.10.1007/s11629-014-3032-2]Open DOISearch in Google Scholar
[Huang, W., Cao, Z.X, Qi, W., Pender, G., Zhao, K., 2015. Full 2D hydrodynamic modelling of rainfall-induced flash floods. J. Mt. Sci., 12, 5, 1203–1218.10.1007/s11629-015-3466-1]Search in Google Scholar
[Juez, C., Murillo, J., García-Navarro, P., 2013. 2D simulation of granular flow over irregular steep slopes using global and local coordinates. J. Comput. Phys., 255, 166–204.10.1016/j.jcp.2013.08.002]Search in Google Scholar
[Juez, C., Soares-Frazao, S., Murillo, J., García-Navarro, P., 2017. Experimental and numerical simulation of bed load transport over steep slopes. J. Hydraul. Res., 55, 4, 455–469.10.1080/00221686.2017.1288417]Open DOISearch in Google Scholar
[Keller, J.B., 2003. Shallow-water theory for arbitrary slopes of the bottom. J. Fluid Mech., 489, 345–348.10.1017/S0022112003005342]Search in Google Scholar
[Li, J., Cao, Z.X., Qian, H.L., Liu, Q.Q., Pender, G., 2017. A depth-averaged two-phase model for fluvial sediment-laden flows over erodible beds. Adv. Water Resour., in press. https://doi.org/10.1016/j.advwatres.2017.08.01410.1016/j.advwatres.2017.08.014]Open DOISearch in Google Scholar
[Li, J., Cao, Z.X, Hu, K., Pender, G., Liu, Q.Q., 2018a. A depth-averaged two-phase model for debris flows over fixed beds. Int. J. Sediment Res., 33, 4, 462–477.10.1016/j.ijsrc.2017.06.003]Open DOISearch in Google Scholar
[Li, J., Cao, Z.X, Hu, K., Pender, G., Liu, Q.Q., 2018b. A depth-averaged two-phase model for debris flows over erodible beds. Earth Surf. Process. Landforms, 43, 817–839.10.1002/esp.4283]Open DOISearch in Google Scholar
[Liang, Q., Marche, F., 2009. Numerical resolution of well-balanced shallow water equations with complex source terms. Adv. Water Resour., 32, 873–884.10.1016/j.advwatres.2009.02.010]Open DOISearch in Google Scholar
[Mangeney-Castelnau, A., Bouchut, F., Vilotte, J. P., Lajeunesse, E., Aubertin, A., Pirulli, M., 2005. On the use of Saint Venant equations to simulate the spreading of a granular mass. J. Geophys. Res., 110, B09103.10.1029/2004JB003161]Search in Google Scholar
[Qian, H.L., Cao, Z.X, Pender, G., Liu, H.H., Hu, P., 2015. Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers. Int. J. Sediment Res., 30, 2, 117–130.10.1016/j.ijsrc.2015.03.002]Search in Google Scholar
[Qian, H.L., Cao, Z.X, Liu, H.H., Pender, G., 2017. Numerical modeling of alternate bar formation, development and sediment sorting in straight channels. Earth Surf. Process. Land-forms, 42, 4, 555–574.10.1002/esp.3988]Open DOISearch in Google Scholar
[Savage, S.B., Hutter, K., 1989. The motion of a finite mass of granular material down a rough incline. J. Fluid Mech., 199, 177–215.10.1017/S0022112089000340]Search in Google Scholar
[Savage, S.B., Hutter, K., 1991. The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis. Acta Mechanica, 86, 1, 201–223.10.1007/BF01175958]Search in Google Scholar
[Toro, E.., 2001. Shock-Capturing Methods for Free-Surface Shallow Flows. Chichester, U. K.: Wiley.]Search in Google Scholar
[Toro, E.F., 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. 3rd Ed. Springer-Verlag, Berlin.10.1007/b79761]Search in Google Scholar
[Van Emelen, S., 2014. Breaching processes of river dikes: effects on sediment transport and bed morphology, (Doctoral dissertation). Retrieved from DIAL. (http://hdl/handle.net/2078.1/151925). Université catholique de Louvain, Leuven, Belgium.]Search in Google Scholar
[Van Emelen, S., Zech, Y., Soares-Frazao, S., 2014. Limitations of the shallow water assumptions for problems involving steep slopes: Application to a dike overtopping test case. In: River Flow 2014, Lausanne, pp. 1669–1677.10.1201/b17133-222]Search in Google Scholar
[Wang, X., Cao, Z.X, Pender, G., Neelz, S., 2010. Numerical modeling of flood flows over irregular topography. Proc. ICE – Water Manage., 163, WM5, 255–265.10.1680/wama.2010.163.5.255]Search in Google Scholar
[Wu, W., 2007. Computational River Dynamics. Taylor & Francis, London, UK.10.4324/9780203938485]Search in Google Scholar
[Xue, Y., Xu, W., Luo, S., Chen, H., Li, N., 2011. Experimental study of dam-break flow in cascade reservoirs with steep bottom slope. J. Hydrod. B, 23, 4, 491–497.10.1016/S1001-6058(10)60140-0]Search in Google Scholar
[Yue, Z., Cao, Z., Li, X., Tao, C., 2008. Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution. Sci. China Ser. G-Phys. Mech. Astron., 51, 9, 1427–1438.10.1007/s11433-008-0135-1]Open DOISearch in Google Scholar