2D Shallow-Water Model Using Unstructured Finite-Volumes Methods
Publication: Journal of Hydraulic Engineering
Volume 132, Issue 3
Abstract
This paper presents a two-dimensional (2D) shallow-water numerical model, which is based on the resolution of the Saint–Venant equation using the unstructured finite-volumes method, combined with Green’s theorem technique. The model has been validated by several benchmarks. The numerical results obtained from the model are in good agreement with the analytical or experimental ones. The paper also presents an application of this model to flood diversion from the Red River into a water-retention zone for the purpose of reducing flood threat at Hanoi, capital of Vietnam.
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Acknowledgments
An important part of this work was realized during the one-year working stay of the first author at the NCCHE of the University of Mississippi. Mrs. Yu-E Shi and Mr. The Hung Nguyen have been financially supported by the European Commission (the FLOCODS Project, contract no. ICA4-CT2001-10035). The writers wish to thank ASCE journal editors and the anonymous review for their comments and suggestions.
References
Borthwick, A. G. L., and Karr, E. T. (1993). “Shallow flow modelling using curvilinear depth-averaged stream function and vorticity transport equations.” Int. J. Numer. Methods Fluids, 17(5), 417–445.
Bradford, S. F., and Sanders, B. F. (2002). “Finite-volume model for shallow-sater flooding of arbitrary topography.” J. Hydraul. Eng., 128(3), 289–298.
Brufau, P., and Garcia-Navarro, P. (2000). “Two-dimensional dam break flow simulation.” Int. J. Numer. Methods Fluids, 33(1), 35–58.
Chen, C. L. (1989). “Analytic solutions for tidal model testing.” J. Hydraul. Eng., 115(12), 1707–1714.
Chorin, A. J. (1968). “Numerical solution of the Navier-Stokes equations.” Math. Comput., 22, 745–762.
Fennema, R., and Chaudry, M. (1990). “Explicit methods for 2-D transient free-surface flows.” J. Hydraul. Eng., 116(8), 1013–1034.
Fraccarollo, L., and Toro, E. F. (1995). “Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems.” J. Hydraul. Res., 33(6), 843–864.
Guillou, S., and Nguyen, K. D. (1999). “An improved technique for solving two-dimensional shallow water problems.” Int. J. Numer. Methods Fluids, 29(4), 465–483.
Hanich, L. (1996). “Résolution des equations de la mécanique des fluids par des methods TVD en coordonnées généralisées.” PhD thesis, Université de Caen, Caen, France.
Hervouet, J. M. (2003). “Hydrodynamique des écoulements à surface libre: Modélisation numérique avec la méthode des élements finis.” Edition Presses de l'Ecole Nationale des Ponts et Chaussées, Paris, 312.
Kobayashi, M. H., Pereira, J. M. C., and Pereira, J. C. F. (1999). “A conservative finite-volume second-order accurate projection method on hybrid unstructured grids.” J. Comp. Phys, 150(1), 40–75.
Lien, F. S. (2000). “A pressure-based unstructured grid method for all-speed flows.” Int. J. Numer. Methods Fluids, 33(3), 355–374.
Nguyen, K. D., and Ouahsine, A. (1997). “2D numerical study on tidal circulation in strait of Dover.” J. Waterw., Port, Coastal, Ocean Eng., 123(1), 8–15.
Nguyen, V. H., Nguyen, V. D., and Ngo, H. C. (2003). “On some numerical methods for solving the 1-D Saint-Venant Equations of general flow regime, Part 2: Verification and application.” Vietnam J. of Mechanics, National Centre for Natural Sciences and Technology of Vietnam, 25(1), 2–38.
Rhie, C. M., and Chow, W. L. (1983). “Numerical study of the turbulent flow past an airfoil with trailing edge separation.” AIAA J., 21(11), 1525–1532.
Roe, P. L. (1981). “Approximate Riemann Solvers, parameter vectors and difference schemes.” J. Comp. Phys., 43(2), 357–372.
Sleigh, P. A., Gaskell, P. H., Berzins, M., and Wright, N. G. (1998). “An unstructured finite-volume algorithm for predicting flow in rivers and estuaries.” Comput. Fluids, 27(4), 479–508.
Tannehill, J. C., Anderson, D. A., and Pletcher, R. H. (1997). Computational fluid mechanics and heat transfer, 2nd Ed., Taylor and Francis, Washington, D.C., 156–158.
Waterways Experiment Stations (WES). (1960). “Floods resulting from suddently breached dam.” Miscellaneous Paper No. 2-374, Rep. 1: Conditions of Minimum Resistance, U.S. Army Corp of Engineers, Vicksburg, Miss.
Zhao, D. H., Shen, H. W., Tabious, G. Q., Lai, J. S., and Tan, W. Y. (1994). “Finite-volume two-dimensional unsteady-flow model for river basins.” J. Hydraul. Eng., 120(7), 864–883.
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Published In
Journal of Hydraulic Engineering
Volume 132 • Issue 3 • March 2006
Pages: 258 - 269
Copyright
© 2006 ASCE.
History
Received: Dec 30, 2003
Accepted: Jan 18, 2005
Published online: Mar 1, 2006
Published in print: Mar 2006
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