Free Access
Issue
ESAIM: M2AN
Volume 45, Number 3, May-June 2011
Page(s) 423 - 446
DOI https://doi.org/10.1051/m2an/2010060
Published online 11 October 2010
  1. R. Abgrall, On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J. Comput. Phys. 114 (1994) 45–58. [CrossRef] [MathSciNet] [Google Scholar]
  2. N. Andrianov, Testing numerical schemes for the shallow water equations. Preprint available at http://www-ian.math.uni-magdeburg.de/home/andriano/CONSTRUCT/testing.ps.gz (2004). [Google Scholar]
  3. P. Arminjon, M.-C. Viallon and A. Madrane, A finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for conservation laws on unstructured grids. Int. J. Comput. Fluid Dyn. 9 (1997) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  4. 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]
  5. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in Math Series, Birkhäuser Verlag, Basel (2004). [Google Scholar]
  6. S. Bryson and D. Levy, Balanced central schemes for the shallow water equations on unstructured grids. SIAM J. Sci. Comput. 27 (2005) 532–552. [CrossRef] [MathSciNet] [Google Scholar]
  7. I. Christov and B. Popov, New nonoscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws. J. Comput. Phys. 227 (2008) 5736–5757. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.J.C. de Saint-Venant, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivière et à l'introduction des marées dans leur lit. C. R. Acad. Sci. Paris 73 (1871) 147–154. [Google Scholar]
  9. L.J. Durlofsky, B. Engquist and S. Osher, Triangle based adaptive stencils for the solution of hyperbolic conservation laws. J. Comput. Phys. 98 (1992) 64–73. [CrossRef] [Google Scholar]
  10. 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]
  11. 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. [Google Scholar]
  12. 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]
  13. M.E. Hubbard, Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids. J. Comput. Phys. 155 (1999) 54–74. [CrossRef] [MathSciNet] [Google Scholar]
  14. M.E. Hubbard, On the accuracy of one-dimensional models of steady converging/diverging open channel flows. Int. J. Numer. Methods Fluids 35 (2001) 785–808. [CrossRef] [Google Scholar]
  15. S. Jin, A steady-state capturing method for hyperbolic system with geometrical source terms. ESAIM: M2AN 35 (2001) 631–645. [CrossRef] [EDP Sciences] [Google Scholar]
  16. S. Jin and X. Wen, Two interface-type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations. SIAM J. Sci. Comput. 26 (2005) 2079–2101. [CrossRef] [MathSciNet] [Google Scholar]
  17. D. Kröner, Numerical Schemes for Conservation Laws. Wiley, Chichester (1997). [Google Scholar]
  18. A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system. ESAIM: M2AN 36 (2002) 397–425. [CrossRef] [EDP Sciences] [Google Scholar]
  19. A. Kurganov and C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes. Commun. Comput. Phys. 2 (2007) 141–163. [MathSciNet] [Google Scholar]
  20. A. Kurganov and G. Petrova, Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws. Numer. Methods Partial Diff. Equ. 21 (2005) 536–552. [CrossRef] [Google Scholar]
  21. A. Kurganov and G. Petrova, A second-order well-balanced positivity preserving scheme for the Saint-Venant system. Commun. Math. Sci. 5 (2007) 133–160. [MathSciNet] [Google Scholar]
  22. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 214–282. [Google Scholar]
  23. A. Kurganov and E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Numer. Methods Partial Diff. Equ. 18 (2002) 584–608. [CrossRef] [Google Scholar]
  24. A. Kurganov, S. Noelle and G. Petrova, Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23 (2001) 707–740. [CrossRef] [MathSciNet] [Google Scholar]
  25. R.J. LeVeque, 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]
  26. R. LeVeque, Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics, Cambridge University Press (2002). [Google Scholar]
  27. K.-A. Lie and S. Noelle, On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comput. 24 (2003) 1157–1174. [CrossRef] [MathSciNet] [Google Scholar]
  28. 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]
  29. S. Noelle, N. Pankratz, G. Puppo and J. Natvig, Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. J. Comput. Phys. 213 (2006) 474–499. [CrossRef] [MathSciNet] [Google Scholar]
  30. 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]
  31. G. Russo, Central schemes for balance laws, in Hyperbolic problems: theory, numerics, applications II, Internat. Ser. Numer. Math. 141, Birkhäuser, Basel (2001) 821–829. [Google Scholar]
  32. G. Russo, Central schemes for conservation laws with application to shallow water equations, in Trends and applications of mathematics to mechanics: STAMM 2002, S. Rionero and G. Romano Eds., Springer-Verlag Italia SRL (2005) 225–246. [Google Scholar]
  33. 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]
  34. 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] [Google Scholar]
  35. M. Wierse, A new theoretically motivated higher order upwind scheme on unstructured grids of simplices. Adv. Comput. Math. 7 (1997) 303–335. [CrossRef] [MathSciNet] [Google Scholar]
  36. Y. Xing and C.-W. Shu, High order finite difference WENO schemes with the exact conservation property for the shallow water equations. J. Comput. Phys. 208 (2005) 206–227. [CrossRef] [MathSciNet] [Google Scholar]
  37. Y. Xing and C.-W. Shu, A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Commun. Comput. Phys. 1 (2006) 100–134. [Google Scholar]

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