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Asymptotic-preserving & well-balanced schemes for radiative transfer and the Rosseland approximation

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We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow the Well-Balanced approach’s canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type Δt≤O(Δx2) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.

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Authors and Affiliations

  1. Istituto per le, Applicazioni del Calcolo (sezione di Bari), via G. Amendola 122, 70126, Bari, Italy

    Laurent Gosse

  2. Dipartimento di matematica, Universita di Pavia, via Ferrata 1, 27100, Pavia, Italy

    Giuseppe Toscani

Authors
  1. Laurent Gosse
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  2. Giuseppe Toscani
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Correspondence to Laurent Gosse.

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Mathematics Subject Classification (1991): 82C70, 65M06, 35B25

Work partially supported by EEC network #HPRN-CT-2002-00282.

Revised version received July 21, 2003

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Gosse, L., Toscani, G. Asymptotic-preserving & well-balanced schemes for radiative transfer and the Rosseland approximation. Numer. Math. 98, 223–250 (2004). https://doi.org/10.1007/s00211-004-0533-x

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  • DOI: https://doi.org/10.1007/s00211-004-0533-x

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