Free Access
Issue
ESAIM: M2AN
Volume 35, Number 1, January/February 2001
Page(s) 107 - 127
DOI https://doi.org/10.1051/m2an:2001108
Published online 15 April 2002
  1. L. Armi, The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163 (1986) 27-58. [CrossRef] [MathSciNet] [Google Scholar]
  2. L. Armi and D. Farmer, Maximal two-layer exchange through a contraction with barotropic net flow. J. Fluid Mech. 164 (1986) 27-51. [CrossRef] [Google Scholar]
  3. A. Bermúdez and M.E. Vázquez, Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids 23 (1994) 1049-1071. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Berthon and F. Coquel, Travelling wave solutions of a convective diffusive system with first and second order terms in nonconservation form, in Hyperbolic Problems: Theory, Numerics, Applications, Vol. I of Internat. Ser. Numer. Math. 129, Birkhäuser (1999) 47-54. [Google Scholar]
  5. M.J. Castro, J. Macías and C. Parés, Simulation of two-layer exchange flows through a contraction with a finite volume shallow water model, in Actas de las II Jornadas de Análisis de Variables y Simulación Numérica del Intercambio de Masas de Agua a través del Estrecho de Gibraltar, Cádiz (2000) 205-221. [Google Scholar]
  6. M.J. Castro, J. Macías and C. Parés, Simulation of two-layer exchange flows through the combination of a sill and contraction with a finite volume shallow-water model. Internal Journal 1610, group on ``Differential Equations, Numerical Analysis and Applications'', University of Málaga (2000). [Google Scholar]
  7. F. Coquel, K. El Amine, E. Godlewski, B. Perthame and P. Rascle, Une méthode numérique decentrée pour la résolution d'ecoulements diphasiques. C. R. Acad. Sci. Paris, Sér. I 324 (1997) 717-723. [Google Scholar]
  8. S.B. Dalziel, Two-layer Hydraulics Maximal Exchange Flows. Ph.D. thesis, University of Cambridge (1988). [Google Scholar]
  9. D. Farmer and L. Armi, Maximal two-layer exchange over a sill and through a combination of a sill and contraction with barotropic flow. J. Fluid Mech. 164 (1986) 53-76. [CrossRef] [Google Scholar]
  10. P. García-Navarro and F. Alcrudo, Implicit and explicit TVD methods for discontinuous open channel flows, in Proc. of the 2nd Int. Conf. on Hydraulic and Environmental Modelling of Coastal, Estuarine and River Waters, R.A. Falconer, K. Shiono, and R.G.S. Matthew, Eds. 2 Ashgate (1992). [Google Scholar]
  11. P. García-Navarro, F. Alcrudo and J.M. Savirón, 1D open channel flow simulation using TVD McCormack scheme. J. Hydraul. Eng. 118 (1992) 1359-1373. [CrossRef] [Google Scholar]
  12. A.E. Gill, Atmosphere-Ocean Dynamics, Int. Geophys. Series 30, Springer-Verlag, San Diego (1982) 662 p. [Google Scholar]
  13. E. Godlewski and P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Appl. Math. Sc. 118, Springer-Verlag, New York (1996). [Google Scholar]
  14. A. Harten, On a class of high resolution total-variation-stable finite-difference schemes. SIAM J. Numer. Anal. 21 (1984) 1-23. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Harten, P. Lax and A. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35-61. [Google Scholar]
  16. K.R. Helfrich, Time-dependent two-layer hydraulic exchange flows. J. Phys. Oceanogr. 25 (1995) 359-373. [CrossRef] [Google Scholar]
  17. P.K. Kundu, Fluid Mechanics. Academic Press Inc., San Diego (1990) 638 p. [Google Scholar]
  18. P.G. Lefloch and A.E. Tzavaras, Existence theory for the Riemann problem for non-conservative hyperbolic systems. C. R. Acad. Sci. Paris, Sér. I 323 (1996) 347-352. [Google Scholar]
  19. P.G. Lefloch and A.E. Tzavaras, Representation of weak limits and definition of nonconservative products. SIAM J. Math. Anal. 30 (1999) 1309-1342. [CrossRef] [MathSciNet] [Google Scholar]
  20. P.L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43 (1981) 357-371. [Google Scholar]
  21. P.L. Roe, Upwinding differenced schemes for hyperbolic conservation laws with source terms, in Proc. of the Conference on Hyperbolic Problems, C. Carasso, P.-A. Raviart, and D. Serre, Eds., Springer-Verlag, Berlin (1986) 41-51. [Google Scholar]
  22. J.A. Rubal and M.E. Vázquez, Aplicación del método de volúmenes finitos y esquemas tipo Godunov a un modelo bicapa, in Actas de las II Jornadas de Análisis de Variables y Simulación Numérica del Intercambio de Masas de Agua a través del Estrecho de Gibraltar, Cádiz (2000) 223-239. [Google Scholar]
  23. J.B. Schijf and J.C. Schonfeld, Theoretical considerations on the motion of salt and fresh water, in Proc. of the Minn. Int. Hydraulics Conv. Joint meeting IAHR and Hyd. Div. ASCE., Sept. 1953 (1953) 321-333. [Google Scholar]
  24. J.J. Stoker, Water Waves. Interscience, New York (1957). [Google Scholar]
  25. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction. Springer-Verlag, Berlin (1997). [Google Scholar]
  26. M.E. Vázquez-Cendón, Estudio de Esquemas Descentrados para su Aplicación a las leyes de Conservación Hiperbólicas con Términos Fuente. PhD thesis, Universidad de Santiago de Compostela (1994). [Google Scholar]
  27. M.E. Vázquez-Cendón, Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comp. Physics 148 (1999) 497-526. [Google Scholar]

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