A Finite Volume Solver for Radiation Hydrodynamics in the Non Equilibrium Diffusion Limit

  • D. ChauveheidEmail author
  • J.-M. Ghidaglia
  • M. Peybernes
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)


We derive an Implicit Explicit finite volume scheme for the computation of radiation hydrodynamics. The convective part is handled through a classical upwind method while the reactive and diffusive parts are discretized thanks to a centered scheme. These results are compared to semi-analytic solutions obtained by Lowrie and Edwards [10].


Cell centered finite volume scheme Radiation hydrodynamics Implicit/Explicit schemes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Braeunig J.-P., Desjardins B., Ghidaglia J.-M., A totally Eulerian Finite Volume solver for multi-material fluid flows, Eur. J. Mech. B/Fluids, Vol. 28, pp. 475-485, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Buet, C., Despres B.: Asymptotic preserving and positive schemes for radiation hydrodynamic. J. Comput. Phys. 215, 717–740, 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chauveheid D., Thesis, École normale supérieure, in preparation.Google Scholar
  4. 4.
    Ghidaglia J.-M., Kumbaro A., Le Coq G.: On the numerical solution to two fluid models via a cell centered finite volume method, Eur. J. Mech. B/Fluids, 20, 841-867, 2001.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ghidaglia J.-M., Flux schemes for solving monlinear systems of conservation laws, in Innovative Methods for Numerical Solution of Partial Differential Equations, Chattot J.J. and Hafez M. Eds, pp 232-242, WORLD SCIENTIFIC, Singapore, 2001.Google Scholar
  6. 6.
    Ghidaglia J.-M., Pascal F.: The normal flux method at the boundary for multidimensional finite volume approximations in CFD. Eur. J. Mech. B/Fluids, Vol. 24(1), pp. 1-17, 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kadioglu, S.Y., Knoll, D.A., Lowrie, R.B., Rauenzahn, R.M.: A second order self-consistent IMEX method for radiation hydrodynamics. J. Comput. Phys. 229, 8313–8332, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kadioglu, S.Y., Knoll: A fully second order implicit/explicit time integration technique for hydrodynamics plus nonlinear heat conduction problems. J. Comput. Phys. 229, 3237–3249 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lowrie, R.B., Morel, J.E.: The coupling of radiation and hydrodynamics. Astrophys. J. 521, 423–450, 1999.CrossRefGoogle Scholar
  10. 10.
    Lowrie, R.B., Edwards J.D.: Radiative shock solutions with grey nonequilibrium diffusion. Shock Waves 18, 129–143, 2008.CrossRefGoogle Scholar
  11. 11.
    Saad, Y.: Iterative methods for sparse linear systems 2nd edition, SIAM, 2003.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.CEA, DAM, DIFArpajonFrance
  2. 2.CMLAENS Cachan and CNRS UMR 8635Cachan CedexFrance

Personalised recommendations