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Technical note

An improved hydrostatic reconstruction method for shallow water model

(Research Associate) , (Research Associate) , (IAHR Member), Senior Lecturer & (IAHR Member), Professor
Pages 432-439 | Received 12 Jul 2012, Accepted 20 Oct 2013, Published online: 29 May 2014

References

  • An, H., Yu, S. (2012). Well-balanced shallow water flow simulation on quadtree cut cell grids. Adv. Water Resour. 39, 60–70. doi: 10.1016/j.advwatres.2012.01.003
  • Audusse, E., Bristeau, M.O. (2005). A well-balanced positivity preserving second-order scheme for shallow water flows on unstructured meshes. J. Comput. Phys. 206(1), 311–333. doi: 10.1016/j.jcp.2004.12.016
  • Audusse, E., Bouchut, F., Bristeau, M.O., Klein, R., Perthame, B. (2004). A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25(6), 2050–2065. doi: 10.1137/S1064827503431090
  • Begnudelli, L., Sanders, B. (2006). Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying. J. Hydraulic Eng. 132(4), 371–384. doi: 10.1061/(ASCE)0733-9429(2006)132:4(371)
  • Bermudez, A., Vazquez, M.E. (1994). Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23(8), 1049–1071. doi: 10.1016/0045-7930(94)90004-3
  • Berthon, C., Foucher, F. (2012). Efficient well-balanced hydrostatic upwind schemes for shallow-water equations. J. Comput. Phys. 231(15), 4993–5015. doi: 10.1016/j.jcp.2012.02.031
  • Delestre, O. (2010). Simulation du ruissellement d'eau de pluie sur des surfaces agricoles. PhD Thesis, Université d'Orléans, France.
  • Goutal, N. (1999). The Malpasset dam failure: An overview and test case definition. Proc. 4th CADAM Meeting Zaragoza, Spain, 1–8.
  • Greenberg, J.M., Leroux, A.Y. (1996). A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33(1), 1–16. doi: 10.1137/0733001
  • Hou, J., Liang, Q., Simons, F., Hinkelmann, R. (2013). A 2D well-balanced shallow flow model for unstructured grids with novel slope source treatment. Adv. Water Resour. 52, 107–131. doi: 10.1016/j.advwatres.2012.08.003
  • Hubbard, M.E. (1999). Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids. J. Comput. Phys. 155(1), 54–74. doi: 10.1006/jcph.1999.6329
  • Liang, Q., Marche, F. (2009). Numerical resolution of well-balanced shallow water equations with complex source terms. Adv. Water Resour. 32(6), 873–884. doi: 10.1016/j.advwatres.2009.02.010
  • Marche, F., Bonneton, P., Fabrie, P., Seguin, N. (2007). Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes. Int. J. Numer. Meth. Fluids 53(5), 867–894. doi: 10.1002/fld.1311
  • Song, L., Zhou, J., Guo, J., Zou, Q., Liu, Y. (2011). A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain. Adv. Water Resour. 34(7), 915–932. doi: 10.1016/j.advwatres.2011.04.017
  • Thacker, W.C. (1981). Some exact solutions to the nonlinear shallow-water wave equations. J. Fluid Mech. 107, 499–508. doi: 10.1017/S0022112081001882
  • Toro, E.F. (2009). Riemann solvers and numerical methods for fluid dynamics: A practical introduction. Springer-Verlag, Berlin.
  • Wang, Y., Liang, Q., Kesserwani, G., Hall, J.W. (2011). A 2D shallow flow model for practical dam-break simulations. J. Hydraulic Res. 49(3), 307–316. doi: 10.1080/00221686.2011.566248

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