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A hierarchy of nonlocal models for the radiative transfer equation

Published online by Cambridge University Press:  01 June 2004

J.-L. FEUGEAS
Affiliation:
Centre Lasers Intenses et Applications, UMR Commissariat à l'Energie Atomique–Centre National de la Recherche Scientifique–Université de Bordeaux 1, Talence Cedex, France

Abstract

For the classic diffusion description of radiative transfer, the specific intensity can be represented by a small angular deviation of the local Planckian equilibrium. In a transparent media, the angular anisotropy becomes strong and one has to solve the general transfer equation. We propose a hierarchy of models that can describe the regime that lies between those two limits. Every member of this family is hyperbolic, flux-limited, and possesses a locally dissipated entropy. This hierarchy also formally recovers the diffusion limit. This study demonstrates that the two-polynomial model is already capable of capturing strong anisotropies.

Type
Research Article
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Audit, E., Charrier, P., Chièze, J.-P. & Dubroca, B. (2002). A radiation-hydrodynamics scheme valid from the transport to the diffusion limit. J. Comp. Phys. 20, 263.Google Scholar
Castor, J.I., Lutz, J.H. & Seaton, M.J. (1981). Ultraviolet spectra of planetary nebulae. Royal Astronomical Society, Monthly Notices 194, 547567.CrossRefGoogle Scholar
Charrier, P., Dubroca, B., Feugeas, J.L. & Mieussens, L. (1998). Modèles à vitesse discrètes pour le calcul d'ćoulements hors équilibre cinétique. C.R. Acad. Sci., Série 1 326, 13471352.Google Scholar
Charrier, P., Dubroca, B. & Feugeas, J.L. (1998). Levermore's Moment Method of Boltzmann Equation for Non-Equilibrium Kinetic Flows. R. Brun, R. Campargue, R. Gatignol, J.-C. Lengrand (Eds.). 21th International Symposium On Rarefied Gas Dynamic, >103, 1110. Marseille: Cépaduès Editions, Toulouse.
Dubroca, B. & Feugeas, J.-L. (1999). Etude théorique et numérique d'une hiérarchie de modèles aux moments pour le transfert radiatif. C.R. Acad. Sci., Série 1 329, 915920.Google Scholar
Dubroca, B. & Klar, A. (2002). Half moment closure for radiative transfer equations. J. Comp. Phys. 180, 113.CrossRefGoogle Scholar
Feugeas, J.-L. (1997). Etude numérique des systèmes aux moments de Levermore pour la modélisation d'écoulements hors equilibre cinétique. Thèse de l'Université de Bordeaux I.
Fort, J. (1997). Information-theoretical approach to radiative transfer. Physica A 243, 275303.CrossRefGoogle Scholar
Grad, H. (1949). On the kinetic theory of rarefied gases. Comm. Pure and Appl. Math. Ii, 331407.CrossRefGoogle Scholar
Klar, A., Dubroca, B. Frank, M., &Thoemmes, G. (2003). A half space moment approximation to the radiative heat transfer equations. Z. Angew. Math. Mech. 83, 16.Google Scholar
Klar, A. & Dubroca, B. (2002). A half moment model to take into account strong kinetic non-equilibrium. C.R. Acad. Sci., Série 1 335, 16.Google Scholar
Levermore, D. (1996). Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83, 10211065.CrossRefGoogle Scholar
Mihalas, D. & Mihalas, B.W. (1984). Foundations of radiation hydrodynamics. New York: Oxford University Press.
Muller, I. & Ruggeri, T. (1993). SprinTracts on Natural Philosophy, Vol. 37. New York: Springer-Verlag.
Pomraning, G.C. (1992). The Equations Of Radiation Thermodynamics. New York: Pergamon Press.
Struchtrup, H. (1997). Extended moment method in radiative transfer. Annals of Physics 257, 111135.CrossRefGoogle Scholar
Turpault, R. (2002). Multigroup half space moment approximations. C.R. Acad. Sci., Série 1 334, 331.Google Scholar