References
- Aricò, C., & Tucciarelli, T. (2008). Diffusive modeling of aggradation and degradation in artificial channels. Journal of Hydraulic Engineering, 134(8), 1079–1088. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:8(1079)
- Benkhaldoun, F., Sahmim, S., & Seaid, M. (2010). A two-dimensional finite volume morphodynamic model on unstructured triangular grids. International Journal for Numerical Methods in Fluids, 63, 1296–1327. https://doi.org/10.1002/fld.2129
- Bilanceri, M., Beux, F., Elmahi, I., Guillard, H., & Salvetti, M. V. (2012). Linearized implicit time advancing and defect correction applied to sediment transport simulations. Computers & Fluids, 63, 82–104. https://doi.org/10.1016/j.compfluid.2012.04.009
- Bladé, E., Cea, L., Corestein, G., Escolano, E. P., Dolz, J., & Coll, A. (2014). Iber: Herramienta de simulación numérica del flujo en ríos. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 30(1), 1–10.
- Bomers, A., Schielen, R. M. J., & Hulscher, S. J. (2019). The influence of grid shape and grid size on hydraulic river modelling performance. Environmental fluid mechanics, 19, 1273–1294. https://doi.org/10.1007/s10652-019-09670-4
- Briganti, R., Dodd, N., Kelly, D., & Pokrajac, D. (2012). An efficient and flexible solver for the simulation of the morphodynamics of fast evolving flows on coarse sediment beaches. International Journal for Numerical Methods in Fluids, 69(4), 859–877. https://doi.org/10.1002/fld.v69.4
- Canadian Hydraulic Centre, National Research Council (1998). Reference Manual for Blue Kenue.
- Canestrelli, A., Dumbser, M., Siviglia, A., & Toro, E. F. (2010). Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed. Advances in Water Resources, 33(3), 291–303. https://doi.org/10.1016/j.advwatres.2009.12.006
- Cao, Z., Day, R., & Egashira, S. (2002). Coupled and decoupled numerical modeling of flow and morphological evolution in alluvial rivers. Journal of Hydraulic Engineering, 128(3), 306–321. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:3(306)
- Castro Díaz, M.J., Fernández-Nieto, E.D., & Ferreiro, A.M. (2008). Sediment transport models in shallow water equations and numerical approach by high order finite volume methods. Computers & Fluids, 37(3), 299–316. https://doi.org/10.1016/j.compfluid.2007.07.017
- Castro Díaz, M. J., Fernández-Nieto, E. D., Ferreiro, A. M., & Parés, C. (2009). Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes. Computer Methods in Applied Mechanics and Engineering, 198(33–36), 2520–2538. https://doi.org/10.1016/j.cma.2009.03.001
- Caviedes-Voullième, D., García-Navarro, P., & Murillo, J. (2012). Influence of mesh structure on 2D full shallow water equations and SCS Curve Number simulation of rainfall/runoff events. Journal of Hydrology, 448–449, 39–59. https://doi.org/10.1016/j.jhydrol.2012.04.006
- Caviedes-Voullième, D., Morales-Hernández, M., Juez, C., Lacasta, A., & García-Navarro, P. (2017). Two-dimensional numerical simulation of bed-load transport of a finite-depth sediment layer: Applications to channel flushing. Journal of Hydraulic Engineering, 143(9), 04017034. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001337
- Chorin, A. J. (1968). Numerical solution of the Navier-Stokes equations. Mathematics of Computation, 22(104), 745–762. https://doi.org/10.1090/S0025-5718-1968-0242392-2
- Cordier, S., Le, M. H., & De Luna, T. M. (2011). Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help. Advances in Water Resources, 34(8), 980–989. https://doi.org/10.1016/j.advwatres.2011.05.002
- De Vriend, H. J. (1987). 2DH mathematical modelling of morphological evolutions in shallow water. Coastal Engineering, 11(1), 1–27. https://doi.org/10.1016/0378-3839(87)90037-8
- De Vries, M. (1973). River bed variations: Aggradation and degradation. Proceedings of the International Seminar on Hydraulics on Alluvial Streams, New Delhi, India (pp. 1–10). Hydraulics Laboratory.
- Delis, A. I., & Papoglou, I. (2008). Relaxation approximation to bed-load sediment transport. Journal of Computational and Applied Mathematics, 213(2), 521–546. https://doi.org/10.1016/j.cam.2007.02.003
- Fernandez-Nieto, E. D., Lucas, C., Morales de Luna, T., & Cordier, S. (2014). On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems. Computers & Fluids, 91, 87–106. https://doi.org/10.1016/j.compfluid.2013.11.031
- Garegnani, G., Rosatti, G., & Bonaventura, L. (2011). Free surface flows over mobile bed: Mathematical analysis and numerical modeling of coupled and decoupled approaches. Communications in Applied and Industrial Mathematics, 2(1). https://doi.org/10.1685/journal.caim.371
- Grass, A. (1981). Sediments transport by waves and currents (Report No. FL29). SERC London Cent. Mar. Technology.
- Guillou, S., & Nguyen, K. D. (1999). An improved technique for solving two-dimensional shallow water problems. Intnational Journal for Numerical Methods in Fluids, 29, 465–483. https://doi.org/10.1002/(ISSN)1097-0363
- Hervouet, J. M. (2003). Hydrodynamique des écoulements a surface libre: Modélisation numérique avec la méthode des élements finis. Edition Presses de l'Ecole Nationale des Ponts et Chaussées, Paris, 312.
- Hou, J., Simons, F., Mahgoub, M., & Hinkelmann, R. (2013). A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography. Computer Methods in Applied Mechanics and Engineering, 257(257), 126–149. https://doi.org/10.1016/j.cma.2013.01.015
- Hudson, J. (2001). Numerical technics for morphodynamic modelling [PhD thesis]. University of Whiteknights.
- Hudson, J., Damgaard, J., Dodd, N., Chesher, T., & Cooper, A. (2005). Numerical approaches for 1D morphodynamic modelling. Coastal Engineering, 52(8), 691–707. https://doi.org/10.1016/j.coastaleng.2005.04.004
- Hudson, J., & Sweby, P. K. (2003). Formulations for numerically approximating hyperbolic systems governing sediment transport. Journal of Scientific Computing, 19, 225–252. https://doi.org/10.1023/A:1025304008907
- Jiang, Y., Li, R., & Wu, S. (2016). A second order time homogenized model for sediment transport. Multiscale Modeling & Simulation, 14(3), 965–996. https://doi.org/10.1137/15M1041778
- Juez, C., Ferrer-Boix, C., Murillo, J., Hassan, M.A., & García-Navarro, P. (2016). A model based on Hirano-Exner equations for two-dimensional transient flows over heterogeneous erodible beds. Advances in Water Resources, 87, 1–18. https://doi.org/10.1016/j.advwatres.2015.10.013
- Juez, C., Murillo, J., & García-Navarro, P. (2014). A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed. Advances in Water Resources, 71, 93–109. https://doi.org/10.1016/j.advwatres.2014.05.014
- Kassem, A. A., & Chaudhry, M. H. (1998). Comparison of coupled and semicoupled numerical models for alluvial channels. Journal of Hydraulic Engineering, 124(8), 794–802. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:8(794)
- Kobayashi, M. H., Pereira, J. M. C., & Pereira, J. C. F. (1999). A conservative finite-volume second-order accurate projection method on hybrid unstructured grids. Journal of Computational Physics, 150(1), 40–75. https://doi.org/10.1006/jcph.1998.6163
- Kozyrakis, G. V., Delis, A. I., Alexandrakis, G., & Kampanis, N. A. (2016). Numerical modeling of sediment transport applied to coastal morphodynamics. Applied Numerical Mathematics, 104, 30–46. https://doi.org/10.1016/j.apnum.2014.09.007
- Liang, Q. (2011). A coupled morphodynamic model for applications involving wetting and drying. Journal of Hydrodynamics, 23(3), 273–281. https://doi.org/10.1016/S1001-6058(10)60113-8
- Liu, X., & Beljadid, A. (2017). A coupled numerical model for water flow, sediment transport and bed erosion. Computers & Fluids, 154, 273–284. https://doi.org/10.1016/j.compfluid.2017.06.013
- Liu, X., Infante Sedano, J. Á., & Mohammadian, A. (2015). A coupled two-dimensional numerical model for rapidly varying flow, sediment transport and bed morphology. Journal of Hydraulic Research, 53(5), 609–621. https://doi.org/10.1080/00221686.2015.1085919
- Liu, X., Landry, B. J., & García, M. H. (2008). Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes. Coastal Engineering, 55(10), 800–810. https://doi.org/10.1016/j.coastaleng.2008.02.012
- Martínez-Aranda, S., Murillo, J., & García-Navarro, P. (2019). A 1D numerical model for the simulation of unsteady and highly erosive flows in rivers. Computers & Fluids, 181, 8–34. https://doi.org/10.1016/j.compfluid.2019.01.011
- Meyer-Peter, E., & Müller, R. (1948). Formulas for bed-load transport. Proceedings of the 2nd Meeting of the IAHSR, Stockholm (pp. 39–64).
- Morales de Luna, T., Castro Díaz, M., & Madronal, C. P. (2011). A duality method for sediment transport based on a modified Meyer-Peter & Müller model. Journal of Scientific Computing, 48(1–3), 258–273. https://doi.org/10.1007/s10915-010-9447-1
- Murillo, J., & García-Navarro, P. (2010). An Exner-based coupled model for two-dimensional transient flow over erodible bed. Journal of Computational Physics, 229(23), 8704–8732. https://doi.org/10.1016/j.jcp.2010.08.006
- Nguyen, D. K., Shi, Y. E., Wang, S. S., & Nguyen, T. H. (2006). 2-D Shallow-Water Models using unstructured finite-volumes methods. Journal of Hydraulic Engineering, 132(3), 258–269. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:3(258)
- Peña González, E., Marqués, J. F., F. Sánchez-Tembleque Díaz-Pache, Puertas Agudo, J., & Gómez, L. C. (2008). Experimental validation of a sediment transport two-dimensional depth-averaged numerical model using PIV and 3D Scanning technologies. Journal of Hydraulic Research, 46(4), 489–503. https://doi.org/10.3826/jhr.2008.2737
- Rhie, C. M., & Chow, W. L. (1983). Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 21(11), 1525–1532. https://doi.org/10.2514/3.8284
- Rulot, F., Dewals, B. J., Erpicum, S., Archambeau, P., & Pirotton, M. (2012). Modelling sediment transport over partially non-erodible bottoms. International Journal for Numerical Methods in Fluids, 70(2), 186–199. https://doi.org/10.1002/fld.v70.2
- Serrano-Pacheco, A., Murillo, J., & Garcia-Navarro, P. (2009). Exact solutions for unsteady 1D shallow water flow over mobile bed. Proceedings of the 6th IAHR Symposium on River, Coastal and Estuarine Morphodynamics, Argentina (pp. 963–967).
- Serrano-Pacheco, A., Murillo, J., & Garcia-Navarro, P. (2012). Finite volumes for 2D shallow-water flow with bed-load transport on unstructured grids. Journal of Hydraulic Research, 50(2), 154–163. https://doi.org/10.1080/00221686.2012.669142
- Shi, Y., Ray, R. K., & Nguyen, K. D. (2013). A projection method-based model with the exact C-property for shallow-water flows over dry and irregular bottom using unstructured finite-volume technique. Computers & Fluids, 76, 178–195. https://doi.org/10.1016/j.compfluid.2013.02.002
- Siviglia, A., Stecca, G., Vanzo, D., Zolezzi, G., Toro, E. F., & Tubino, M. (2013). Numerical modelling of two-dimensional morphodynamics with applications to river bars and bifurcations. Advances in Water Resources, 52, 243–260. https://doi.org/10.1016/j.advwatres.2012.11.010
- Soares-Frazão, S., & Zech, Y. (2011). HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed. International Journal for Numerical Methods in Fluids, 66(8), 1019–1036. https://doi.org/10.1002/fld.v66.8
- Vidović, D., Segal, A., & Wesseling, P. (2006). A superlinearly convergent Mach-uniform finite volume method for the Euler equations on staggered unstructured grids. Journal of Computational Physics, 217(2), 277–294. https://doi.org/10.1016/j.jcp.2006.01.031
- Wu, W. (2004). Depth-averaged two-dimensional numerical modeling of unsteady flow and nonuniform sediment transport in open channels. Journal of Hydraulic Engineering, 130(10), 1013–1024. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:10(1013)
- Xia, J., Lin, B., Falconer, R. A., & Wang, G. (2010). Modelling dam-break flows over mobile beds using a 2D coupled approach. Advances in Water Resources, 33(2), 171–183. https://doi.org/10.1016/j.advwatres.2009.11.004
- Yoon, T. H., & Kang, S. K. (2004). Finite volume model for two-dimensional shallow water flows on unstructured grids. Journal of Hydraulic Engineering, 130(7), 678–688. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:7(678)
- Zhao, J. H., Özgen, I., Liang, D. F., & Hinkelmann, R. (2017). Comparison of depth-averaged concentration and bed load flux sediment transport models of dam-break flow. Water Science and Engineering, 10(4), 287–294. https://doi.org/10.1016/j.wse.2017.12.006