Volume 8, Issue 5
Derivation of a Non-Local Model for Diffusion Asymptotics — Application to Radiative Transfer Problems

C. Besse & T. Goudon

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

Published online: 2010-08

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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.

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@Article{CiCP-8-1139, author = {C. Besse and T. Goudon}, title = {Derivation of a Non-Local Model for Diffusion Asymptotics — Application to Radiative Transfer Problems}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {5}, pages = {1139--1182}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.211009.100310a}, url = {http://global-sci.org/intro/article_detail/cicp/7611.html} }
TY - JOUR T1 - Derivation of a Non-Local Model for Diffusion Asymptotics — Application to Radiative Transfer Problems AU - C. Besse & T. Goudon JO - Communications in Computational Physics VL - 5 SP - 1139 EP - 1182 PY - 2010 DA - 2010/08 SN - 8 DO - http://dor.org/10.4208/cicp.211009.100310a UR - https://global-sci.org/intro/cicp/7611.html KW - AB -

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.

C. Besse & T. Goudon. (1970). Derivation of a Non-Local Model for Diffusion Asymptotics — Application to Radiative Transfer Problems. Communications in Computational Physics. 8 (5). 1139-1182. doi:10.4208/cicp.211009.100310a
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