Commun. Comput. Phys., 8 (2010), pp. 1139-1182.


Derivation of a Non-Local Model for Diffusion Asymptotics - Application to Radiative Transfer Problems

C. Besse 1*, T. Goudon 1

1 Project Team SIMPAF, INRIA Lille Nord Europe Research Centre Park Plazza, 40 avenue Halley, F-59650 Villeneuve d'Ascq, France; and Laboratoire Paul Painleve, UMR 8524, CNRS-Universite des Sciences et Technologies de Lille, Cite Scientifique, F-59655 Villeneuve d'Ascq Cedex, France.

Received 21 October 2009; Accepted (in revised version) 10 March 2010
Available online 23 June 2010
doi:10.4208/cicp.211009.100310a

Abstract

In this paper, we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function, solution of a kinetic equation. This closure is of non local type in the sense that it involves convolution or pseudo-differential operators. We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non local terms. We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations, by treating examples arising in radiative transfer. We pay a specific attention to the conservation of the total energy by the numerical scheme.

AMS subject classifications: 35Q99, 35B25

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Key words: Diffusion approximation, nonlocal transport, asymptotic preserving methods, radiative hydrodynamics.

*Corresponding author.
Email: christophe.besse@math.univ-lille1.fr (C. Besse), thierry.goudon@inria.fr (T. Goudon)
 

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