Extension of Roe’s approximate Riemann solver to equilibrium and nonequilibrium flows

  • Rémi Abgrall
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


In this paper, we first develop a generalization of Roe’s Riemann solver to the case of a frozen mixture of perfect gases which equation of state contains vibrational terms. We assume that each species are at thermal equilibrium with the others. We then show how to obtain a class of Roe average in the thermal and chemistry equilibrium limits.

These Riemann solvers are tested on a two dimensional test case. The scheme is semi implicit for the source terms because of stiffness. The results show the capacity of these methods.


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  1. [1]
    C. Park. On the Convergence of Chemically Reacting Flows. AIAA Paper no 85-0247, 23rd Aerospace Sciences Meeting, Reno, Nevada, January, 14-17 1985.Google Scholar
  2. [2]
    M. Vinokur Flux Jacobian Matrices and Generalized Roe Averaging for Real Gas NASA Contractor Report 177512, December 1988.Google Scholar
  3. [3]
    M.S. Liou J.S. Shuen, B. Van Leer. A Detailed Analysis of Inviscid Flux Splitting Algorithms for Real Gases with Equilibrium of Finite-Rate Chemistry. International Conference in Numerical Methods, Williamsburg, June 1988.Google Scholar
  4. [4]
    J.S. Shuen M.S. Liou, B. Van Leer. Splitting of Inviscid Fluxes for Real Gases. Technical Report NASA TM 100856, NASA, April 1988.Google Scholar
  5. [5]
    P. Glaister. An Approximate Linearised Riemann Solver for the Euler Equation for Real Gases Journal of Computational Physics, vol. 74, 1988. pages 382–408ADSzbMATHCrossRefGoogle Scholar
  6. [6]
    P.L. Roe. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics, Vol 43, 1981, pages 357,372.MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. [7]
    R. Abgrall. Généralisation du solveur de Roe pour le calcul d’écoulements de mélanges de gaz parfaits à concentrations variables. La Recherche Aérospatiale, no 1988-6, 1988, pages 31–43.Google Scholar
  8. [8]
    R. Abgrall. Extension of Roe’s Riemann solver to equilibrium and non equilibrium flows submitted to Computer and Fluids Google Scholar
  9. [9]
    L. Fezoui. Résolution des équations d’Euler par un schéma de Van Leer en éleémants finis. INRIA report n o 358 January 1985.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • Rémi Abgrall
    • 1
  1. 1.INRIAValbonneFrance

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