Free access
Issue
ESAIM: M2AN
Volume 37, Number 3, May-June 2003
Page(s) 451 - 478
DOI http://dx.doi.org/10.1051/m2an:2003037
Published online 15 April 2004
  1. R. Abgrall, An extension of Roe's upwind scheme to algebraic equilibrium real gas models. Comput. and Fluids 19 (1991) 171–182. [CrossRef]
  2. R.A. Baurle and S.S. Girimaji, An assumed PDF Turbulence-Chemistery closure with temperature-composition correlations. 37th Aerospace Sciences Meeting (1999).
  3. C. Berthon and F. Coquel, Travelling wave solutions of a convective diffusive system with first and second order terms in nonconservation form, Hyperbolic problems: theory, numerics, applications, vol. I, Zürich (1998) 47–54, Intern. Ser. Numer. Math. 129 Birkhäuser (1999).
  4. C. Berthon and F. Coquel, About shock layers for compressible turbulent flow models, work in preparation, preprint MAB 01-29 2001 (http://www.math.sciences.univ-nantes.fr/).
  5. C. Berthon and F. Coquel, Nonlinear projection methods for multi-entropies Navier–Stokes systems, Innovative methods for numerical solutions of partial differential equations, Arcachon (1998), World Sci. Publishing, River Edge (2002) 278–304.
  6. C. Berthon, F. Coquel and P. LeFloch, Entropy dissipation measure and kinetic relation associated with nonconservative hyperbolic systems (in preparation).
  7. J.F. Colombeau, A.Y. Leroux, A. Noussair and B. Perrot, Microscopic profiles of shock waves and ambiguities in multiplications of distributions. SIAM J. Numer. Anal. 26 (1989) 871–883. [CrossRef] [MathSciNet]
  8. F. Coquel and P. LeFloch, Convergence of finite difference schemes for conservation laws in several space dimensions: a general theory. SIAM J. Numer. Anal. 30 (1993) 675–700. [CrossRef] [MathSciNet]
  9. F. Coquel and C. Marmignon, A Roe-type linearization for the Euler equations for weakly ionized multi-component and multi-temperature gas. Proceedings of the AIAA 12th CFD Conference, San Diego, USA (1995).
  10. F. Coquel and B. Perthame, Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. SIAM J. Numer. Anal. 35 (1998) 2223–2249. [CrossRef] [MathSciNet]
  11. G. Dal Maso, P. LeFloch and F. Murat, Definition and weak stability of a non conservative product. J. Math. Pures Appl. 74 (1995) 483–548. [MathSciNet]
  12. A. Forestier, J.M. Herard and X. Louis, A Godunov type solver to compute turbulent compressible flows. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 919–926.
  13. E. Godlewski and P.A. Raviart, Hyperbolic systems of conservations laws. Springer, Appl. Math. Sci. 118 (1996).
  14. A. Harten, P.D. Lax and B. Van Leer, On upstream differencing and Godunov type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35–61. [CrossRef] [MathSciNet]
  15. T.Y. Hou and P.G. LeFloch, Why nonconservative schemes converge to wrong solutions: error analysis. Math. Comp. 62 (1994) 497–530. [CrossRef] [MathSciNet]
  16. L. Laborde, Modélisation et étude numérique de flamme de diffusion supersonique et subsonique en régime turbulent. Ph.D. thesis, Université Bordeaux I, France (1999).
  17. B. Larrouturou, How to preserve the mass fractions positivity when computing compressible multi-component flows. J. Comput. Phys. 95 (1991) 59–84. [CrossRef] [MathSciNet]
  18. B. Larrouturou and C. Olivier, On the numerical appproximation of the K-eps turbulence model for two dimensional compressible flows. INRIA report, No. 1526 (1991).
  19. P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under non conservation form. Comm. Partial Differential Equations 13 (1988) 669–727. [CrossRef] [MathSciNet]
  20. B. Mohammadi and O. Pironneau, Analysis of the K-Epsilon Turbulence Model. Masson Eds., Rech. Math. Appl. (1994).
  21. P.A. Raviart and L. Sainsaulieu, A nonconservative hyperbolic system modelling spray dynamics. Part 1. Solution of the Riemann problem. Math. Models Methods Appl. Sci. 5 (1995) 297–333. [CrossRef] [MathSciNet]
  22. P.L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43 (1981) 357–372. [NASA ADS] [CrossRef] [MathSciNet]
  23. L. Sainsaulieu, Travelling waves solutions of convection-diffusion systems whose convection terms are weakly nonconservative. SIAM J. Appl. Math. 55 (1995) 1552–1576. [CrossRef] [MathSciNet]
  24. E. Tadmor, A minimum entropy principle in the gas dynamics equations. Appl. Numer. Math. 2 (1986) 211–219. [CrossRef] [MathSciNet]

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