Free Access
Issue
ESAIM: M2AN
Volume 47, Number 2, March-April 2013
Page(s) 507 - 538
DOI https://doi.org/10.1051/m2an/2012036
Published online 11 January 2013
  1. R. Abgrall and S. Karni, Two-layer shallow water system : a relaxation approach. SIAM J. Sci. Comput. 31 (2009) 1603–1627. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. Audusse, A multilayer Saint-Venant model : derivation and numerical validation. Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 189–214. [CrossRef] [MathSciNet] [Google Scholar]
  3. R. Barros and W. Choi, On the hyperbolicity of two-layer flows, in Frontiers of applied and computational mathematics. World Sci. Publ., Hackensack, NJ (2008) 95–103. [Google Scholar]
  4. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, in Frontiers in Mathematics. Birkhäuser Verlag, Basel (2004) [Google Scholar]
  5. F. Bouchut and T. Morales, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment. ESAIM : M2AN 42 (2008) 683–689. [CrossRef] [EDP Sciences] [Google Scholar]
  6. C. Bourdarias and S. Gerbi, A finite volume scheme for a model coupling free surface and pressurised flows in pipes. J. Comput. Appl. Math. 209 (2007) 109–131. [CrossRef] [Google Scholar]
  7. C. Bourdarias, M. Ersoy and S. Gerbi, A kinetic scheme for pressurised flows in non uniform closed water pipes. Monografias de la Real Academia de Ciencias de Zaragoza 31 (2009) 1–20. [Google Scholar]
  8. C. Bourdarias, M. Ersoy and S. Gerbi, A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme. International Journal on Finite Volumes 6 (2009) 1–47. [Google Scholar]
  9. C. Bourdarias, M. Ersoy and S. Gerbi, A kinetic scheme for transient mixed flows in non uniform closed pipes : a global manner to upwind all the source terms. J. Sci. Comput. (2011) 1–16. [Google Scholar]
  10. C. Bourdarias, M. Ersoy and S. Gerbi, A mathematical model for unsteady mixed flows in closed water pipes. Science China Math. 55 (2012) 221–244. [CrossRef] [Google Scholar]
  11. C. Bourdarias, M. Ersoy and S. Gerbi, Unsteady mixed flows in non uniform closed water pipes : a full kinetic approach (2011). Submitted. [Google Scholar]
  12. M. Castro, J. Macías and C. Parés, A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. ESAIM : M2AN 35 (2001) 107–127. [CrossRef] [EDP Sciences] [Google Scholar]
  13. S. Cerne, S. Petelin and I. Tiselj, Coupling of the interface tracking and the two-fluid models for the simulation of incompressible two-phase flow. J. Comput. Phys. 171 (2001) 776–804. [CrossRef] [Google Scholar]
  14. M.H. Chaudhry, S.M. Bhallamudi, C.S. Martin and M. Naghash, Analysis of transient pressures in bubbly, homogeneous, gas-liquid mixtures. J. Fluids Eng. 112 (1990) 225–231. [CrossRef] [Google Scholar]
  15. C.M. Dafermos, Generalized characteristics in hyperbolic systems of conservation laws. Arch. Ration. Mech. Anal. 107 (1989) 127–155. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Dal Maso, P.G. Lefloch and F. Murat, Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74 (1995) 483–548. [Google Scholar]
  17. M. Ersoy, Modélisation, analyse mathématique et numérique de divers écoulements compressibles ou incompressibles en couche mince. Ph.D. thesis, Université de Savoie, Chambéry (2010). [Google Scholar]
  18. I. Faille and E. Heintze, A rough finite volume scheme for modeling two-phase flow in a pipeline. Comput. Fluids 28 (1999) 213–241. [CrossRef] [MathSciNet] [Google Scholar]
  19. A.T. Fuller, Root location criteria for quartic equations. IEEE Trans. Autom. Control 26 (1981) 777–782. [CrossRef] [Google Scholar]
  20. 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]
  21. M.A. Hamam and A. McCorquodale, Transient conditions in the transition from gravity to surcharged sewer flow. Can. J. Civ. Eng. 9 (1982) 189–196. [CrossRef] [Google Scholar]
  22. T. Hibiki and M. Ishii, One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimesaa. Int. J. Heat Mass Transfer 46 (2003) 4935–4948. [CrossRef] [Google Scholar]
  23. T. Hibiki and M. Ishii, Thermo-fluid dynamics of two-phase flow. With a foreword by Lefteri H. Tsoukalas. Springer, New York (2006). [Google Scholar]
  24. L.V. Ovsjannikov, Models of two-layered “shallow water”. Zh. Prikl. Mekh. i Tekhn. Fiz. 180 (1979) 3–14. [Google Scholar]
  25. C. Parés, Numerical methods for nonconservative hyperbolic systems : a theoretical framework. SIAM J. Numer. Anal. 44 (2006) 300–321. [CrossRef] [MathSciNet] [Google Scholar]
  26. 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]
  27. L. Sainsaulieu, An Euler system modeling vaporizing sprays, in Dynamics of Hetergeneous Combustion and Reacting Systems, Progress in Astronautics and Aeronautics, AIAA, Washington, DC 152 (1993). [Google Scholar]
  28. L. Sainsaulieu, Finite volume approximate of two-phase fluid flows based on an approximate Roe-type Riemann solver. J. Comput. Phys. 121 (1995) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
  29. S.B. Savage and K. Hutter, The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199 (1989) 177–215. [CrossRef] [MathSciNet] [Google Scholar]
  30. C. Savary, Transcritical transient flow over mobile beds, boundary conditions treatment in a two-layer shallow water model. Ph.D. thesis, Louvain (2007). [Google Scholar]
  31. J.B. Schijf and J.C. Schönfled, Theoretical considerations on the motion of salt and fresh water, in Proc. of Minnesota International Hydraulic Convention. IAHR (1953) 322–333. [Google Scholar]
  32. C.S.S. Song, Two-phase flow hydraulic transient model for storm sewer systems, in Second international conference on pressure surges, BHRA Fluid engineering. Bedford, England (1976) 17–34. [Google Scholar]
  33. C.S.S. Song, Interfacial boundary condition in transient flows, in Proc. of Eng. Mech. Div. ASCE, on advances in civil engineering through engineering mechanics (1977) 532–534. [Google Scholar]
  34. C.S.S. Song, J.A. Cardle and K.S. Leung, Transient mixed-flow models for storm sewers. J. Hydraul. Eng. 109 (1983) 1487–1503. [CrossRef] [Google Scholar]
  35. H.B. Stewart and B. Wendroff, Two-phase flow : models and methods. J. Comput. Phys. 56 (1984) 363–409. [CrossRef] [MathSciNet] [Google Scholar]
  36. I. Tiselj and S. Petelin, Modelling of two-phase flow with second-order accurate scheme. J. Comput. Phys. 136 (1997) 503–521. [CrossRef] [Google Scholar]
  37. D.C. Wiggert and M.J. Sundquist, The effects of gaseous cavitation on fluid transients. J. Fluids Eng. 101 (1979) 79–86. [CrossRef] [Google Scholar]
  38. E.B. Wylie and V.L. Streeter, Fluid transients in systems. Prentice Hall, Englewood Cliffs, NJ (1993). [Google Scholar]

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