Year: 2010
Author: C. Berthon, J. Dubois, B. Dubroca, T.-H. Nguyen-Bui, R. Turpault
Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 3 : pp. 259–285
Abstract
The present work concerns the numerical approximation of the $M_1$ model for radiative transfer. The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this model. We propose to derive an HLLC method which preserves the stationary contact waves. To supplement this essential property, the method is proved to be robust and to preserve the physical admissible states. Next, a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical regimes. The relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m09105
Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 3 : pp. 259–285
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Radiative transfer equation $M_1$ model finite volume method Riemann solver HLLC scheme asymptotic preserving scheme.
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