Free Access
Issue
ESAIM: M2AN
Volume 37, Number 2, March/April 2003
Page(s) 389 - 416
DOI https://doi.org/10.1051/m2an:2003034
Published online 15 November 2003
  1. E. Audusse, M.O. Bristeau and B. Perthame, Kinetic schemes for Saint-Venant equations with source terms on unstructured grids. INRIA Report, RR-3989 (2000), http://www.inria.fr/RRRT/RR-3989.html. [Google Scholar]
  2. A. Bermudez and M.E. Vasquez, Upwind methods for hyperbolic conservation laws with source terms. Comput. & Fluids 23 (1994) 1049-1071. [Google Scholar]
  3. M.O. Bristeau and B. Coussin, Boundary conditions for the shallow water equations solved by kinetic schemes. INRIA Report, RR-4282 (2001), http://www.inria.fr/RRRT/RR-4282.html. [Google Scholar]
  4. M.O. Bristeau and B. Perthame, Transport of pollutant in shallow water using kinetic schemes. CEMRACS, ESAIM Proc. 10 (1999) 9-21, http://www.emath.fr/Maths/Proc/Vol.10. [Google Scholar]
  5. R. Eymard, T. Gallouet and R. Herbin, Finite volume methods, Handbook of numerical analysis, Vol. VIII, P.G. Ciarlet and J.L. Lions Eds., Amsterdam, North-Holland (2000). [Google Scholar]
  6. T. Gallouet, J.M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow water equations with topography. Comput. & Fluids 32 (2003) 479-513. [Google Scholar]
  7. J.F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete Contin. Dynam. Systems 1 (2001) 89-102. [Google Scholar]
  8. E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Springer-Verlag, New York, Appl. Math. Sci. 118 (1996). [Google Scholar]
  9. L. Gosse and A.Y. LeRoux, A well-balanced scheme designed for inhomogeneous scalar conservation laws. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996) 543-546. [Google Scholar]
  10. J.M. Hervouet, Hydrodynamique des écoulements à surface libre, apport de la méthode des éléments finis. EDF (2001). [Google Scholar]
  11. S. Jin, A steady state capturing method for hyperbolic system with geometrical source terms. ESAIM: M2AN 35 (2001) 631-646. [CrossRef] [EDP Sciences] [Google Scholar]
  12. R.J. LeVêque, Numerical Methods for Conservation Laws. Second edition, ETH Zurich, Birkhauser, Lectures in Mathematics (1992). [Google Scholar]
  13. R.J. LeVêque, Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346-365. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Martin, Fonctionnement écologique de la Seine à l'aval de la station d'épuration d'Achères: données expérimentales et modélisation bidimensionnelle. Ph.D. Thesis, École des Mines de Paris, France (2001). [Google Scholar]
  15. B. Perthame, Kinetic formulations of conservation laws. Oxford University Press (2002). [Google Scholar]
  16. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source term. Calcolo 38 (2001) 201-231. [CrossRef] [MathSciNet] [Google Scholar]
  17. P.L. Roe, Upwind differencing schemes for hyperbolic conservation laws with source terms, in Nonlinear Hyperbolic Problems, C. Carasso, P.A. Raviart and D. Serre Eds., Berlin, Springer-Verlag, Lecture Notes in Math. 1270 (1987) 41-51. [Google Scholar]
  18. A.J.C. de Saint-Venant, Théorie du mouvement non permanent des eaux, avec application aux crues de rivières et à l'introduction des marées dans leur lit. C. R. Acad. Sci. Paris Sér. I Math. 73 (1871) 147-154. [Google Scholar]
  19. J.J. Stoker, The formation of breakers and bores. Comput. Appl. Math. 1 (1948). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you