Free access
Issue
ESAIM: M2AN
Volume 37, Number 2, March/April 2003
Page(s) 389 - 416
DOI http://dx.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.
  2. A. Bermudez and M.E. Vasquez, Upwind methods for hyperbolic conservation laws with source terms. Comput. & Fluids 23 (1994) 1049-1071.
  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.
  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.
  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).
  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.
  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.
  8. E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Springer-Verlag, New York, Appl. Math. Sci. 118 (1996).
  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.
  10. J.M. Hervouet, Hydrodynamique des écoulements à surface libre, apport de la méthode des éléments finis. EDF (2001).
  11. S. Jin, A steady state capturing method for hyperbolic system with geometrical source terms. ESAIM: M2AN 35 (2001) 631-646. [CrossRef] [EDP Sciences]
  12. R.J. LeVêque, Numerical Methods for Conservation Laws. Second edition, ETH Zurich, Birkhauser, Lectures in Mathematics (1992).
  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]
  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).
  15. B. Perthame, Kinetic formulations of conservation laws. Oxford University Press (2002).
  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]
  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.
  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.
  19. J.J. Stoker, The formation of breakers and bores. Comput. Appl. Math. 1 (1948).

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