A 2D shallow flow model for practical dam-break simulations

Journal of Hydraulic Research

Volumn 49, Issue 3, 2011, Pages 307-316

  Wang, Yueling ^a   Liang, Qiuhua ^a   Kesserwani, Georges ^a   Hall, Jim W ^a  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

Dam break; friction term; Godunov type method; shallow water equation; well balanced scheme; wetting and drying

Indexed keywords

DAM-BREAKS; FRICTION TERM; GODUNOV-TYPE METHOD; SHALLOW WATER EQUATIONS; WELL- BALANCED SCHEMES; WETTING AND DRYING;

BENCHMARKING; EQUATIONS OF MOTION; FRICTION; TWO DIMENSIONAL;

DAMS;

BENCHMARKING; DAM; FINITE VOLUME METHOD; FLOODPLAIN; GEOMETRY; SHALLOW WATER; SURFACE ROUGHNESS; TOPOGRAPHIC MAPPING; TWO-DIMENSIONAL FLOW; WETTING-DRYING CYCLE;

EID: 79959423655     PISSN: 00221686     EISSN: None     Source Type: Journal    
DOI: 10.1080/00221686.2011.566248     Document Type: Article

References (23)

1. 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. Scientific Computing 25(6), 2050-2065.
2. Bermúdez, A., Vázquez, M.E. (1994). Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23(8), 1049-1071.
3. Brufau, P., García-Navarro, P., Vázquez-Cendón, M.E. (2004). Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography. Int. J. Numer. Methods Fluids 45(10), 1047-1082. (Pubitemid 39039881)
4. Brufau, P., Vázquez-Cendón, M.E., García-Navarro, P. (2002). A numerical model for the flooding and drying of irregular domains. Int. J. Numer. Methods Fluids 39(3), 247-275. (Pubitemid 34573114)
5. Burguete, J., García-Navarro, P.,Murillo, J. (2008). Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: Application to unsteady irrigation and river flow. Int. J. Numer. Methods Fluids 58(4), 403-425.
6. Caleffi, A., Valiani, A., Zanni, A. (2003). Finite volume method for simulating extreme flood events in natural channels. J. Hydraulic Res. 41(2), 167-177. (Pubitemid 36845042)
7. Glaister, P. (1988). Approximate Riemann solutions of the shallow water equations. J. Hydraulic Res. 26(3), 293-306. (Pubitemid 207379)
8. Glaister, P. (1992). Prediction of supercritical flow in open channels. Comput. & Math. Appl. 24(7), 69-75.
9. Greenberg, J.M., LeRoux, A.-Y. (1996). Awell-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numerical Analysis 33(1), 1-16. (Pubitemid 126431700)
10. Hervouet, J.-M., Petitjean, A. (1999). Malpasset dam-break revisited with two-dimensional computations. J. Hydraulic Res. 37(6), 777-788.
11. Liang, D., Lin, B., Falconer, R.A. (2007). A boundary-fitted numerical model for flood routing with shock-capturing capability. J. Hydrology 332(3-4), 477-486. (Pubitemid 44969661)
12. Liang, Q., Borthwick, A.G.L. (2009). Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Comput. Fluids 38(2), 221-234.
13. Liang, Q., Marche, F. (2009). Numerical resolution of wellbalanced shallow water equations with complex source terms. Adv. Water Resour. 32(6), 873-884.
14. 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. Methods Fluids 53(5), 867-894. (Pubitemid 46152274)
15. Nujic, M. (1995). Efficient implementation of non-oscillatory schemes for the computation of free-surface flows. J. Hydraulic Res. 33(1), 101-111.
16. Rogers, B.D., Borthwick, A.G.L., Taylor, P.H. (2003). Mathematical balancing of flux gradient and source terms prior to using Roe's Approximate Riemann Solver. J. Comput. Phys. 192(2), 422-451. (Pubitemid 37445639)
17. Sampson, J., Easton, A., Singh, M. (2006). Moving boundary shallow water flow above parabolic bottom topography. ANZIAM J. 47, 373-387.
18. Schwanenberg, D., Harms, M. (2004). Discontinuous Galerkin Finite-Element Method for transcritical two-dimensional shallow water flows. J. Hydraulic Eng. 130(5), 412-421. (Pubitemid 38554544)
19. Thacker, W.C. (1981). Some exact solutions to the nonlinear shallow-water wave equations. J. Fluid Mech. 107, 499-508.
20. Toro, E.F., García-Navarro, P. (2007). Godunov-type methods for free-surface shallow flows: A review. J. Hydraulic Res. 45(6), 736-751.
21. Toro, E.F. (2001). Shock-capturing methods for free-surface shallow flows. Wiley, Chichester.
22. Valiani, A., Caleffi, V., Zanni, A. (2002). Case study: Malpasset dam-break simulation using a two-dimensional finite volume method. J. Hydraulic Eng. 128(5), 460-472. (Pubitemid 34527612)
23. Zhou, J.G., Causon, D.M., Mingham, C.G., Ingram, D.M. (2001). The surface gradient method for the treatment of source terms in the shallow-water equations. J. Comput. Phys. 168(1), 1-25. (Pubitemid 33668235)