Free access
Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 1071 - 1091
DOI http://dx.doi.org/10.1051/m2an:2004051
Published online 15 December 2004
  1. E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050–2065. [CrossRef] [MathSciNet]
  2. E. Audusse and M.-O. Bristeau, Transport of pollutant in shallow water. A two time steps kinetic method. ESAIM: M2AN 37 (2003) 389–416. [CrossRef] [EDP Sciences]
  3. D.S. Bale, R.J. LeVeque, S. Mitran and J.A. Rossmanith, A wave propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM J. Sci. Comput. 24 (2002) 955–978. [CrossRef] [MathSciNet]
  4. M.-O. Bristeau and B. Perthame, Transport of pollutant in shallow water using kinetic schemes. CEMRACS, Orsay (electronic), ESAIM Proc., Paris. Soc. Math. Appl. Indust. 10 (1999) 9–21.
  5. A. Chertock, A. Kurganov and G. Petrova, Finite-volume-particle methods for models of transport of pollutant in shallow water. J. Sci. Comput. (to appear).
  6. A. Cohen and B. Perthame, Optimal approximations of transport equations by particle and pseudoparticle methods. SIAM J. Math. Anal. 32 (2000) 616–636. [CrossRef] [MathSciNet]
  7. B. Engquist, P. Lötstedt and B. Sjögreen, Nonlinear filters for efficient shock computation. Math. Comp. 52 (1989) 509–537. [CrossRef] [MathSciNet]
  8. A.F. Filippov, Differential equations with discontinuous right-hand side. (Russian). Mat. Sb. (N.S.) 51 (1960) 99–128. [MathSciNet]
  9. A.F. Filippov, Differential equations with discontinuous right-hand side. AMS Transl. 42 (1964) 199–231.
  10. A.F. Filippov, Differential equations with discontinuous right-hand side, Translated from the Russian. Kluwer Academic Publishers Group, Dordrecht. Math. Appl. (Soviet Series) 18 (1988).
  11. T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. Fluids 32 (2003) 479–513. [CrossRef] [MathSciNet]
  12. J.F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. Discrete Contin. Dyn. Syst. Ser. B 1 (2001) 89–102. [CrossRef] [MathSciNet]
  13. S. Gottlieb, C.-W. Shu and E. Tadmor, High order time discretization methods with the strong stability property. SIAM Rev. 43 (2001) 89–112. [NASA ADS] [CrossRef] [MathSciNet]
  14. A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system. ESAIM: M2AN 36 (2002) 397–425. [CrossRef] [EDP Sciences]
  15. A. Kurganov and C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes (in preparation).
  16. A. Kurganov, S. Noelle and G. Petrova, Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21 (2001) 707–740. [CrossRef] [MathSciNet]
  17. A. Kurganov and G. Petrova, Central schemes and contact discontinuities. ESAIM: M2AN 34 (2000) 1259–1275. [CrossRef] [EDP Sciences]
  18. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 241–282. [NASA ADS] [CrossRef] [MathSciNet]
  19. B. van Leer, Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 101–136. [NASA ADS] [CrossRef]
  20. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [CrossRef] [MathSciNet]
  21. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source. Calcolo 38 (2001) 201–231. [CrossRef] [MathSciNet]
  22. P.A. Raviart, An analysis of particle methods, in Numerical methods in fluid dynamics (Como, 1983). Lect. Notes Math. 1127 (1985) 243–324. [CrossRef]
  23. A.J.C. de Saint-Venant, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit. C. R. Acad. Sci. Paris 73 (1871) 147–154.
  24. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 (1984) 995–1011. [NASA ADS] [CrossRef] [MathSciNet]

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