A limitation of the hydrostatic reconstruction technique for Shallow Water equations

Comptes Rendus Mathematique

Volumn 350, Issue 13-14, 2012, Pages 677-681

  Delestre, Olivier ^a,c   Cordier, Stéphane ^a   Darboux, Frédéric ^b   James, François ^a  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b Centre d'Orléans   (France)

^c UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84866761774     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2012.08.004     Document Type: Article

References (11)

1. Audusse E., Bouchut F., Bristeau M.-O., Klein R., Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 2004, 25(6):2050-2065.
2. Bermudez A., Vazquez M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. & Fluids 1994, 23:1049-1071.
3. Berthon C., Fouchet F. Efficient well-balanced hydrostatic upwind schemes for shallow-water equations. J. Comput. Phys. 2012, 231(15):4993-5015.
4. Bouchut F. Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws, and Well-Balanced Schemes for Sources. Frontiers in Mathematics 2004, Birkhäuser.
5. Bouchut F., Morales T. A subsonic-well-balanced reconstruction scheme for shallow water flows. SIAM J. Numer. Anal. 2010, 48(5):1733-1758.
6. Castro M., Pardo A., Parés C. Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique. Math. Models Methods Appl. Sci. 2007, 17(12):2055-2113.
7. O. Delestre, Simulation du ruissellement d'eau de pluie sur des surfaces agricoles (Rain water overland flow on agricultural fields simulation), PhD thesis, Université d'Orléans, 2010 (in French), http://tel.archives-ouvertes.fr/INSMI/tel-00531377/fr.
8. O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T.N.T. Vo, F. James, S. Cordier, SWASHES: a library of shallow water analytic solutions for hydraulic and environmental studies, Int. J. Numer. Methods Fluids (July 2012), in press.
9. Greenberg J.M., Leroux A.-Y. A well-balanced scheme for the numerical processing of source terms in hyperbolic equation. SIAM J. Numer. Anal. 1996, 33:1-16.
10. Liang Q., Marche F. Numerical resolution of well-balanced shallow water equations with complex source terms. Adv. Water Resour. 2009, 32:873-884.
11. Popinet S. Quadtree-adaptive tsunami modelling. Ocean Dynam. 2011, 61(9):1261-1285.