A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries

Advances in Water Resources

Volumn 23, Issue 4, 2000, Pages 359-372

  Heniche, Mourad ^a   Secretan, Yves ^a   Boudreau, Paul ^a   Leclerc, Michel ^a  

^a CENTRE EAU TERRE ENVIRONNEMENT   (Canada)

Author keywords

Conservative form; Free surface flow; Mixed finite element; Moving boundary; Shallow water

Indexed keywords

ALGORITHMS; DISCHARGE (FLUID MECHANICS); DRYING; ESTUARIES; FINITE ELEMENT METHOD; FLOW OF WATER; MATHEMATICAL MODELS; RIVERS; WATER LEVELS; WETTING;

SHALLOW WATER MODEL;

SURFACE WATER RESOURCES;

ESTUARY; FLOW MODELING; FREE SURFACE FLOW; RIVER CHANNEL; SHALLOW WATER;

ESTUARY; FLOW MODELING; FREE SURFACE FLOW; RIVER CHANNEL; SHALLOW WATER;

EID: 0034635198     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(99)00031-7     Document Type: Article

References (25)

1. Babuska I. Error bounds for finite element method. Num Math 1971;16.
2. Bercovier M, Pironneau O. Error estimates for finite element method solution of the Stokes problems in the primitive variables. Num Math 1979;33.
3. Brezzi F On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers. RAIRO, Série Rouge. R2:1974;129-151.
4. Connor JJ, Wang JD. Finite element modelling of hydrodynamic circulation. In: Brebbia CA, Connor JJ, editors. Num Meth in Fluid Dynamics. Plymouth: Pentech Press, 1974.
5. Dhatt G, Gao DM, Bencheick M A finite simulation of metal flow in moulds. IJNME. 30:1990;821-831.
6. Dhatt G, Soulaimani A, Ouellet Y, Fortin M Development of new triangular elements for free surface flows. IJNMF. 6:1986;895-911.
7. Galland JC, Goutal N, Hervouet J-M TELEMAC: a new numerical model for solving shallow water equations. Advances in Water Resources. 14:1991;138-148.
8. Ghanem AHM. Two-dimensional finite element modeling of flow in aquatics habitats. Ph.D. Thesis, The University of Edmonton, Alberta (Canada), 1995.
9. Heniche M. Modélisation tridimensionnelle par éléments finis d'écoulements à surface libre. Ph.D. Thesis, Université de Technologie de Compiègne, France, 1995.
10. Holz K-P, Nitsche G Tidal wave analysis for estuaries with intertidal flats. Advances in Water Resources. 5:1982;142-148.
11. Hughes TJR, Brooks A. A multi-dimensionnal upwind scheme with no crosswind diffusion. In: Hughes TJR, editor. Finite Element Methods for Convection Dominated Flows, ASME, New York, 1979.
12. Jansen Ph, Van Bendegom L, Van den Berg J, de Vries M, Zanen A. Principles of rivers engineering. The non tidal alluvial river. London: Pitman, 1979.
13. Kawahara M, Umetsu T Finite element method for moving boundary problems in river flow. IJNMF. 6:1986;365-386.
14. Lapidus A A detached shock calculation by second order finite difference. J Comput Phys. 2:1967;154-177.
15. Leclerc M, Secretan Y, Heniche M, Roy Y. Projet MÉTRIQUE: Bilan scientifique. Rapport d'étape #3 au Fonds de recherche et de développement technologique en environnement (MEF). Report INRS-Eau R482, 1996.
16. Leclerc M, Boudreau P, Bechara J, Corfa G. Modélisation de la dynamique de l'habitat des ouananiches (Salmo salar) juvéniles de la rivière Ashuapmushuan (Québec Canada). Report INRS-Eau R482, 1994.
17. Leclerc M, Bellemare J-F, Dumas G, Dhatt G A finite element model of estuarian and river flows. Advances in Water Resources. 4:1990;158-168.
18. Lynch DR, Gray WG. Finite element simulation of shallow water problems moving boundaries. Finite Elements in Water Resources. In: Proceedings of the Second International Conference on F.E. in Water Resources. London: Pentech Press, July 1978.
19. Rodi W. Turbulence models and their application in hydraulics. State-of-the-art paper, IAHR-AIRH, 1984.
20. Saad Y, Schultz M.H GMRES: a generalized minimal residual algorithm for solving non symmetric linear systems. SIAM J. Sci. Stat. Comp. 7(3):1986;856-869.
21. Secretan Y. Un schéma élément fini simple et adaptatif pour les écoulements de Navier-Stokes compressibles. A simple and adaptative finite element scheme for the compressible Navier-Stokes flows. Revue Européenne des Éléments Finis 1992;1(1):31-50.
22. Shanahan P, Harleman DRF. Linked hydrodynamic and biochemical models of water quality in shallow lakes. Report 268, Ralph Parson Lab. Cambridge, MA: MIT Press, 1982.
23. Taylor C, Hood P. Numerical solution of the Navier-Stokes equations using the finite element technique. Comp and Fluids 1973;1:1-28.
24. Zienkiewicz OC, Taylor RL. The finite element method, vol. 2, 4th ed. New York: Mc Graw Hill, 1992.
25. Zhang BN, Bouttes F, Dhatt G. A shallow water finite element model for moving fronts. VIII International Conference on Computational Method in Water Resources, Venice, Italy, 1990.