Free Access
Volume 47, Number 2, March-April 2013
Page(s) 507 - 538
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]
  2. E. Audusse, A multilayer Saint-Venant model : derivation and numerical validation. Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 189–214. [CrossRef] [MathSciNet]
  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.
  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)
  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]
  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]
  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.
  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.
  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.
  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]
  11. C. Bourdarias, M. Ersoy and S. Gerbi, Unsteady mixed flows in non uniform closed water pipes : a full kinetic approach (2011). Submitted.
  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]
  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]
  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]
  15. C.M. Dafermos, Generalized characteristics in hyperbolic systems of conservation laws. Arch. Ration. Mech. Anal. 107 (1989) 127–155. [CrossRef] [MathSciNet]
  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.
  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).
  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]
  19. A.T. Fuller, Root location criteria for quartic equations. IEEE Trans. Autom. Control 26 (1981) 777–782. [CrossRef]
  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]
  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]
  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]
  23. T. Hibiki and M. Ishii, Thermo-fluid dynamics of two-phase flow. With a foreword by Lefteri H. Tsoukalas. Springer, New York (2006).
  24. L.V. Ovsjannikov, Models of two-layered “shallow water”. Zh. Prikl. Mekh. i Tekhn. Fiz. 180 (1979) 3–14.
  25. C. Parés, Numerical methods for nonconservative hyperbolic systems : a theoretical framework. SIAM J. Numer. Anal. 44 (2006) 300–321. [CrossRef] [MathSciNet]
  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]
  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).
  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]
  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]
  30. C. Savary, Transcritical transient flow over mobile beds, boundary conditions treatment in a two-layer shallow water model. Ph.D. thesis, Louvain (2007).
  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.
  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.
  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.
  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]
  35. H.B. Stewart and B. Wendroff, Two-phase flow : models and methods. J. Comput. Phys. 56 (1984) 363–409. [CrossRef] [MathSciNet]
  36. I. Tiselj and S. Petelin, Modelling of two-phase flow with second-order accurate scheme. J. Comput. Phys. 136 (1997) 503–521. [CrossRef]
  37. D.C. Wiggert and M.J. Sundquist, The effects of gaseous cavitation on fluid transients. J. Fluids Eng. 101 (1979) 79–86. [CrossRef]
  38. E.B. Wylie and V.L. Streeter, Fluid transients in systems. Prentice Hall, Englewood Cliffs, NJ (1993).

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you