References
- Anastasiou, K., Chan, C.T., 1997. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. Int. J. Numer. Meth. Fluids, 24, 1225-1245.
- Audusse, E, Bristeau, M.O., 2005. A well-balanced positivity preserving ‘second-order’ scheme for shallow water flows on unstructured meshes. J. Comp. Phys., 206, 1, 311-333.
- Bellos, C.V., Soulis, J.V., Sakkas, J.G., 1991. Computation of two-dimensional dam break induced flows. Adv. Water Resour., 14, 1, 31-41.
- Barth, T.J., Jespersen, D.C., 1989. The design and application of upwind schemes on unstructured meshes. The 27th Aerospace Science Meeting, Reno, Nevada, AIAA-89-0366.
- Bellos, C.V., Soulis, J.V., Sakkas, J.G., 1992. Experimental investigation of two-dimensional dam-break induced flows. J. Hydr. Res., 30, 1, 47-63.
- Bermudez, A., Vazquez, M.E., 1994. Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids, 23, 1049-1071.
- Bradford, S.F., Sanders, B.F., 2002. Finite-volume model for shallow-water flooding of arbitrary topography. J. Hydr. Eng., 128, 3, 289-298.
- Brufau, P., Vazquez-Cendon, M.E., Garcia-Navarro, P., 2002. A numerical model for the flooding and drying of irregular domains. Int. J. Numer. Meth. Fluids, 39, 247-275.
- Brufau, P., Garcia-Navarro, P., Vazquez-Cendon, M.E., 2004. Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography. Int. J. Numer. Meth. Fluids, 45, 1047-1082.
- Cea, L., French, J.R., Vazquez-Cendon, M.E., 2006. Numerical modeling of tidal flows tidal flows in complex estuaries including turbulence: an unstructured finite volume solver and experimental validation. Int. J. Numer. Meth. Fluids, 67, 1909-1932.
- Godunov, S., 1959. A divergence scheme for numerical computation of discontinuous solution of hydrodynamic equations. Math. Sbornik, 43, 271-306.
- Hubbard, M.F., Garcia-Navarro, P., 2000. Flux difference splitting and the balancing of source terms and flux gradients. J. Comp. Phys., 165, 89-125.
- Ivanov, V.Y., Vivoni, E.R., Bras, R.L., Entekhabi, D., 2004. Catchment hydrologic response with a fully distributed triangulated irregular network model. Water Resour. Res., 40, W11102, 1-23.
- Kettani, E.E.-C.B., Ouazar, D., 1994. Object-oriented finite volume dam-break model. In: Proceedings of Modeling of Flood Propagation over Initially Dry Areas, Milan, Italy, pp. 186-196.
- Kim, J., Ivanov, V.Y., Katopodes, N.D., 2013. Modeling erosion and sedimentation coupled with hydrological and overland flow processes at the watershed scale. Water Resour. Res., 49, 5134-5154.
- LeVeque, R.J., 2002. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge.
- Mackie, R., 1992. Object-oriented programming of the finite element method. Int. J. Numer. Meth. Fluids, 35, 2, 425-436.
- Malan, A.G., Lewis, R.W., 2004. On the development of highperformance C++ object-oriented code with application to an explicit edge-based fluid dynamics scheme. Computers and Fluids, 33, 1291-1304.
- Pan, D., Cheng, J.C., 1993. Upwind finite-volume Navier- Stokes computations on unstructured triangular meshes. AIAA J., 31, 9, 1618-1625.
- Roe, P.L., 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys., 43, 357-372.
- Rogers, B.D., Borthwick, A.G.L., Taylor, P.H., 2003. Mathematical balancing of flux gradient and source terms prior to use Roe’s approximate Riemann solver. J. Comp. Phys., 192, 422-451.
- Simpson, B.R., 2003. C++ Classes for 2-D Unstructured Mesh Programming. INRIA Scientific Report, No. 3592, ISSN 0249-6399. ftp://ftp.inria.fr/INRIA/publication/publicpdf/RR/RR-3592.pdf
- Usul, N., Turan, B., 2006. Flood Analysis within the Ulus Basin, Turkey, using geographic information systems. Natural Hazards, 39, 2, 213-229.
- Valiani, A., Begnudelli, L., 2006. Divergence form for bed slope source term (DFB) in shallow water equations. J. Hydr. Eng., 132, 7, 652-665.
- Ying, X., Wang, S.S.Y., 2008. Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows. J. Hydr. Res., 46, 1, 21-34.
- Zhao, D.H., Shen, H.W., Lai, J.S., Tabios, G.Q., 1996. Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling. J. Hydr. Eng., 122, 12, 692-702.
- Zoppou, C., Roberts, S., 2003. Explicit schemes for dam-break simulations. J. Hydr. Eng., 129, 1, 11-34.