Free Access
Issue
ESAIM: M2AN
Volume 37, Number 5, September-October 2003
Page(s) 755 - 772
DOI https://doi.org/10.1051/m2an:2003043
Published online 15 November 2003
  1. A. Bermudez, A. Dervieux, J.A. Desideri and M.E.V. Cendón, Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes. Comput. Methods Appl. Mech. Engrg. 155 (1998) 49-72. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Bermúdez and M.E.V. Cendón, Upwind Methods for Hyperbolic Conservation Laws with Source Terms. Comput. & Fluids 23 (1994) 1049-1071. [Google Scholar]
  3. F. Bouchut, An introduction to finite volume methods for hyperbolic systems of conservation laws with source. Actas Ecole CEA-EDF-INRIA, Free surface geophysical flows, 7-10 Octobre, INRIA Rocquencourt, France (2002). [Google Scholar]
  4. F. Dubois and G. Mehlman, A non-parameterized entropy correction for Roe's approximate Riemann solver. Numer. Math. 73 (1996) 169-208. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Brufau, Simulación bidimensional de flujos hidrodinámicos transitorios en gemotrías irregulares. Ph.D. thesis, Universidad de Zaragoza (2000). [Google Scholar]
  6. T.C. Rebollo, E.D.F. Nieto and M.G. Mármol, A flux-splitting solver for shallow watter equations with source terms. Int. J. Num. Methods Fluids 42 (2003) 23-55. [Google Scholar]
  7. T.C. Rebollo, A.D. Delgado and E.D.F. Nieto, A family of stable numerical solvers for Shallow Water equations with source terms. Comput. Methods Appl. Mech. Engrg. 192 (2003) 203-225. [Google Scholar]
  8. 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. [Google Scholar]
  9. E. Godlewski and P.A. Raviart, Hyperbolic systems of conservation laws. Math. Appl. (1991). [Google Scholar]
  10. E. Godlewski and P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer-Verlag (1996). [Google Scholar]
  11. A. Harten, P. Lax and A. Van Leer, On upstream differencing and Godunov-type scheme for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35. [Google Scholar]
  12. S. Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms. ESAIM: M2AN 35 (2001) 631-645. [CrossRef] [EDP Sciences] [Google Scholar]
  13. A. Kurganov and D. Levy, Central-upwind schemes for the saint-venant system. ESAIM: M2AN 36 (2002) 397-425. [CrossRef] [EDP Sciences] [Google Scholar]
  14. A. Kurganov and E. Tadmor, New High-Resolution Central Schemes for Nonlinear Conservations Laws and Convection-Diffusion Equations. J. Comput. Phys. 160 (2000) 214-282. [Google Scholar]
  15. R.J. Le Veque and H.C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms. J. Comput. Phys. 86 (1990) 187-210. [CrossRef] [MathSciNet] [Google Scholar]
  16. R.J. Le Veque, Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm. J. Comp. Phys. 146 (1998) 346-365. [Google Scholar]
  17. 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]
  18. P.L. Roe, Upwind differencing schemes for hyperbolic conservation laws with source terms, in Nonlinear Hyperbolic Problems, C. Carraso, P.A. Raviart and D. Serre, Eds., Springer-Verlag, Lecture Notes in Math. 1270 (1986) 41-51. [Google Scholar]
  19. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer (1997). [Google Scholar]
  20. M.E.V. Cendon, Estudio de esquemas descentrados para su aplicacion a las leyes de conservación hiperbólicas con términos fuente. Ph.D. thesis, Universidad de Santiago de Compostela (1994). [Google Scholar]
  21. M.E.V. Cendón, Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry. J. Comp. Phys. 148 (1999) 497-526. [Google Scholar]
  22. J.P. Vila, High-order schemes and entropy condition for nonlinear hyperbolic systems of conservations laws. Math. Comp. 50 (1988) 53-73. [CrossRef] [MathSciNet] [Google Scholar]
  23. J.G. Zhou, D.M. Causon, C.G. Mingham and D.M. Ingram, The Surface Gradient Method for the Treatment of Source Terms in the Sallow-Water Equations. J. Comput. Phys. 168 (2001) 1-25. [CrossRef] [MathSciNet] [Google Scholar]

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