Free Access
Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 1071 - 1091
DOI https://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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  7. B. Engquist, P. Lötstedt and B. Sjögreen, Nonlinear filters for efficient shock computation. Math. Comp. 52 (1989) 509–537. [Google Scholar]
  8. A.F. Filippov, Differential equations with discontinuous right-hand side. (Russian). Mat. Sb. (N.S.) 51 (1960) 99–128. [MathSciNet] [Google Scholar]
  9. A.F. Filippov, Differential equations with discontinuous right-hand side. AMS Transl. 42 (1964) 199–231. [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  14. A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system. ESAIM: M2AN 36 (2002) 397–425. [CrossRef] [EDP Sciences] [Google Scholar]
  15. A. Kurganov and C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes (in preparation). [Google Scholar]
  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. [Google Scholar]
  17. A. Kurganov and G. Petrova, Central schemes and contact discontinuities. ESAIM: M2AN 34 (2000) 1259–1275. [CrossRef] [EDP Sciences] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  20. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  21. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source. Calcolo 38 (2001) 201–231. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]

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