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

Authors:
Laurent Gosse;Giuseppe Toscani
Affiliations:
Applicazioni del Calcolo (sezione di Bari), Istituto per le, via G. Amendola 122, 70126, Bari, Italy;Universita di Pavia, Dipartimento di matematica, via Ferrata 1, 27100, Pavia, Italy
Venue:
Numerische Mathematik
Year:
2004

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Abstract

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.