Volume 2, Issue 3
A Free Streaming Contact Preserving Scheme for the M1 Model

C. Berthon, J. Dubois, B. Dubroca, T.-H. Nguyen-Bui & R. Turpault

Adv. Appl. Math. Mech., 2 (2010), pp. 259-285.

Published online: 2010-03

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  • Abstract

The present work concerns the numerical approximation of the M1model 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.

  • Keywords

Radiative transfer equation $M_1$ model finite volume method Riemann solver HLLC scheme asymptotic preserving scheme

  • AMS Subject Headings

65M06 85A25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-2-259, author = {C. Berthon, J. Dubois, B. Dubroca, T.-H. Nguyen-Bui and R. Turpault}, title = {A Free Streaming Contact Preserving Scheme for the M1 Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {3}, pages = {259--285}, abstract = {

The present work concerns the numerical approximation of the M1model 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09105}, url = {http://global-sci.org/intro/article_detail/aamm/8331.html} }
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