# American Institute of Mathematical Sciences

April  2012, 5(2): 245-255. doi: 10.3934/dcdss.2012.5.245

## A numerical correction of the $M1$-model in the diffusive limit

 1 Université de Nantes - Laboratoire de Mathématiques Jean Leray, 2, rue de la Houssinière, 44322 Nantes Cedex 03, France, France

Received  July 2009 Revised  March 2010 Published  September 2011

The present work concerns the numerical simulations of radiative transfer. To address such an issue, the $M1$-model is here adopted. Indeed, this moment model is known to preserve several essential physical properties about radiative energy and radiative flux. In addition, it reduces drastically the numerical cost of the simulations. Unfortunately, the model is not able to restore the expected diffusive regime as prescribed by physics. To correct such a failure, a suitable numerical procedure is derived. The proposed approximation technique enforces, in a sense to be specified, a numerical diffusive regime governed by the Rosseland's mean value of the opacity as imposed by the radiative transfer equation. Numerical experiments issuing from relevant physical benchmarks, illustrate the interest of the derived method.
Citation: Christophe Berthon, Rodolphe Turpault. A numerical correction of the $M1$-model in the diffusive limit. Discrete & Continuous Dynamical Systems - S, 2012, 5 (2) : 245-255. doi: 10.3934/dcdss.2012.5.245
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