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

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 $M_1$ 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.

• Keywords

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

• AMS Subject Headings

65M06, 85A25

• BibTex
• RIS
• TXT
@Article{AAMM-2-259, author = {Berthon , C.Dubois , J.Dubroca , B.Nguyen-Bui , T.-H. and Turpault , R.}, 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 $M_1$ 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09105}, url = {http://global-sci.org/intro/article_detail/aamm/8331.html} }
TY - JOUR T1 - A Free Streaming Contact Preserving Scheme for the M1 Model AU - Berthon , C. AU - Dubois , J. AU - Dubroca , B. AU - Nguyen-Bui , T.-H. AU - Turpault , R. JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 259 EP - 285 PY - 2010 DA - 2010/03 SN - 2 DO - http://doi.org/10.4208/aamm.09-m09105 UR - https://global-sci.org/intro/article_detail/aamm/8331.html KW - Radiative transfer equation, $M_1$ model, finite volume method, Riemann solver, HLLC scheme, asymptotic preserving scheme. AB -

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.

C. Berthon, J. Dubois, B. Dubroca, T.-H. Nguyen-Bui & R. Turpault. (1970). A Free Streaming Contact Preserving Scheme for the M1 Model. Advances in Applied Mathematics and Mechanics. 2 (3). 259-285. doi:10.4208/aamm.09-m09105
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