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.