EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 48 / No 3 (May-June 2014) ESAIM: M2AN, 48 3 (2014) 895-918 References
Free Access
Issue
ESAIM: M2AN
Volume 48, Number 3, May-June 2014
Page(s) 895 - 918
DOI https://doi.org/10.1051/m2an/2013125
Published online 24 April 2014
  1. M.S. Adimurthi and G.D.V. Gowda, Optimal entropy solutions for conservation laws with discontinuous flux-functions. J. Hyperbolic Differ. Equ. 2 (2005) 783–837. [CrossRef] [MathSciNet] [Google Scholar]
  2. D. Amadori, L. Gosse, G. Graziano, Godunov-type approximation for a general resonant balance law with large data. J. Differ. Equ. 198 (2004) 233–274. [CrossRef] [Google Scholar]
  3. A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutiere, P.-A. Raviart and N. Seguin, The coupling of homogeneous models for two-phase flows. Int. J. Finite Volumes 4 (2007) 1–39. [Google Scholar]
  4. A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutiere, P.-A. Raviart and N. Seguin, Coupling of general Lagrangian systems. Math. Comput. 77 (2008) 909–941. [CrossRef] [Google Scholar]
  5. A. Ambroso, J.-M. Hérard and O. Hurisse, A method to couple HEM and HRM two-phase flow models. Comput. Fluids 38 (2009) 738–756. [CrossRef] [Google Scholar]
  6. E. Audusse and B. Perthame, Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies. Proc. Roy. Soc. Edinburgh Sect. A 135 (2005) 253–265. [Google Scholar]
  7. F. Bachmann and J. Vovelle, Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients. Commun. Partial Differential Equations 31 (2006) 371–395. [Google Scholar]
  8. D. Bestion, M. Boucker, P. Boudier, P. Fillion, M. Grandotto, A. Guelfi, J.M. Hérard, E. Hervieu, P. Péturaud, Neptune: a new software platform for advanced nuclear thermal hydraulics. Nuclear Science and Engineering 156 (2007) 281–324. [Google Scholar]
  9. F. Bouchut, Nonlinear stability of Finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources. Frontiers in Mathematics, Birkhauser (2004). [Google Scholar]
  10. B. Boutin, C. Chalons and P.A. Raviart, Existence result for the coupling problem of two scalar conservation laws with Riemann initial data. Math. Models Methods Appl. Sci. 20 (2010) 1859–1898. [CrossRef] [Google Scholar]
  11. B. Boutin, F. Coquel and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011) 921–956. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Bucci and P. Fillion, Analysis of the NUPEC PSBT Tests with FLICA-OVAP. Science and Technology of Nuclear Installations. Article ID 2012 (2012) 436142. [Google Scholar]
  13. R. Bürger and K.H. Karlsen, Conservation laws with discontinuous flux: a short introduction. J. Engrg. Math. 60 (2008) 241–247. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Bürger, K.H. Karlsen and J.D. Towers, An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. SIAM J. Numer. Anal. 47 (2009) 1684–1712. [CrossRef] [Google Scholar]
  15. C. Chalons, P.-A. Raviart and N. Seguin, The interface coupling of the gas dynamics equations. Quaterly of Applied Mathematics 66 (2008) 659–705. [Google Scholar]
  16. C.M. Dafermos, Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method. Arch. Rational Mech. Anal. 52 (1973) 1–9. [CrossRef] [MathSciNet] [Google Scholar]
  17. S. Diehl, On scalar conservation laws with point source and discontinuous flux function. SIAM J. Math. Anal. 26 (1995) 1425–1451. [CrossRef] [MathSciNet] [Google Scholar]
  18. S. Diehl, Scalar conservation laws with discontinuous flux function. I. The viscous profile condition, Commun. Math. Phys. 176 (1996) 23–44. [CrossRef] [Google Scholar]
  19. W.H. Hager, Wastewater Hydraulics, Theory and Practice. Springer (2010). [Google Scholar]
  20. T. Galié, Couplage interfacial de modèles pour la thermoohydraulique des réacteurs, Ph.D. thesis, Université Pierre et Marie Curie Paris 6 (2008). [Google Scholar]
  21. T. Gimse and N.H. Risebro, Solution of the Cauchy problem for a conservation law with a discontinuous flux function. SIAM J. Math. Anal. 23 (1992) 635–648. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Glimm, D. Marchesin and O. McBryan, Numerical method for two phase flow with unstable interface. J. Comput. Phys. 39 (1981) 179–200. [CrossRef] [Google Scholar]
  23. P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant hyperbolic systems of balance laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 881–902. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Godlewski, K.-C. Le Thanh and P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. II. The case of systems. M2AN Math. Model. Numer. Anal. 39 (2005) 649–692. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  25. E. Godlewski and P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I. The scalar case. Numer. Math. 97 (2004) 81–130. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Gosse, A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11 (2001) 339–365. [CrossRef] [MathSciNet] [Google Scholar]
  27. L. Gosse, Localization effects and measure source terms in numerical schemes for balance laws. Math. Comp. 71 (2001) 553–582. [CrossRef] [Google Scholar]
  28. J.M. Greenberg and A.Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  29. E. Isaacson and B.J. Temple, Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52 (1992) 1260–1278. [CrossRef] [MathSciNet] [Google Scholar]
  30. J.M. Greenberg, A.Y.L. Roux, R. Baraille and A. Noussair, Analysis and approximation of conservation laws with source terms. SIAM J. Numer. Anal. 34 (1997) 1980–2007. [CrossRef] [MathSciNet] [Google Scholar]
  31. J.-M. Hérard, Schemes to couple flows between free and porous medium. Proceedings of AIAA (2005) 2005–4861. [Google Scholar]
  32. J.-M. Hérard and O. Hurisse, Coupling two and one-dimensional models through a thin interface. Proceedings of AIAA (2005) 2005–4718. [Google Scholar]
  33. J.-M. Hérard and O. Hurisse, Boundary conditions for the coupling of two-phase flow models. 18th AIAA CFD conference. [Google Scholar]
  34. I.E. Idel’cik, Memento des pertes de charges. Coefficients de pertes de charges singulières et de pertes de charges par frottement. Collection Direction des Etudes et Recherches d’EDF. Eyrolles [in French] (1986). [Google Scholar]
  35. S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48 (1995) 235–276. [Google Scholar]
  36. V.G. Kourakos, P. Rambaud, S. Chabane and J.M. Buchlin, Modeling of pressure drop in two-phase flow in singular geometries. 6th International Symposium on Multiphase Flow, Heat Mass Transfert and Energy Conservation. Xi’an, China, 11-15 July 2009, Paper No MN-30, 2009. [Google Scholar]
  37. D.S. Miller (Ed.), Discharge Characteristics: IAHR Hydraulic Structures Design Manuals 8. Balkema: Rotterdam (1994). [Google Scholar]
  38. S.N. Kruzkov, First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (1970) 228–255. [MathSciNet] [Google Scholar]

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