In this Note, we present a scheme for nonlinear radiative systems which are compatible with diffusive asymptotics. The scheme is based on a splitting: firstly we use a relaxation step to change the problem into 2 identical systems of linear transport systems and, secondly, we use a so-called ‘well balanced’ scheme for each of the 2 systems. The main advantages of our scheme is that it is fully implicit and compatible with physical properties (positivity); it can be used with a nonconstant cross section and for nonuniform mesh.
Dans cette Note, nous présentons un schéma pour un modèle non linéaire de transfert radiatif, qui soit compatible avec la limite diffusion. Ce schéma est composé de deux étapes : une étape de relaxation qui transforme le système non linéaire en deux systèmes d'équation de transport linéaire identiques et un schéma « équilibre » pour chacun de ces systèmes. L'intérêt principal de notre schéma est d'être totalement implicite, de préserver les propriétés physiques (positivité) et d'être utilisable avec une section efficace variable et un maillage non uniforme.
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@article{CRMATH_2004__338_12_951_0,
author = {Buet, Christophe and Cordier, St\'ephane},
title = {Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models},
journal = {Comptes Rendus. Math\'ematique},
pages = {951--956},
publisher = {Elsevier},
volume = {338},
number = {12},
year = {2004},
doi = {10.1016/j.crma.2004.04.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.04.006/}
}
TY - JOUR AU - Buet, Christophe AU - Cordier, Stéphane TI - Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models JO - Comptes Rendus. Mathématique PY - 2004 SP - 951 EP - 956 VL - 338 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.04.006/ DO - 10.1016/j.crma.2004.04.006 LA - en ID - CRMATH_2004__338_12_951_0 ER -
%0 Journal Article %A Buet, Christophe %A Cordier, Stéphane %T Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models %J Comptes Rendus. Mathématique %D 2004 %P 951-956 %V 338 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.04.006/ %R 10.1016/j.crma.2004.04.006 %G en %F CRMATH_2004__338_12_951_0
Buet, Christophe; Cordier, Stéphane. Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 951-956. doi : 10.1016/j.crma.2004.04.006. http://www.numdam.org/articles/10.1016/j.crma.2004.04.006/
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