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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  • 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.

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@Article{CiCP-8-1139, author = {}, 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 JO - Communications in Computational Physics VL - 5 SP - 1139 EP - 1182 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.211009.100310a UR - https://global-sci.org/intro/article_detail/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. (2020). 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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