Derivation of a Non-Local Model for Diffusion Asymptotics — Application to Radiative Transfer Problems (Communications in Computational Physics, 2010)
In this paper, we introduce a moment closure which is intended to providea macroscopic approximation of the evolution of a particle distribution function, solutionof a kinetic equation. This closure is of non-local type in the sense that it involvesconvolution or pseudo-differential operators. We show it is consistent with the diffusionlimit and we propose numerical approximations to treat the non-local terms. Weillustrate how this approach can be incorporated in complex models involving a couplingwith hydrodynamic equations, by treating examples arising in radiative transfer.We pay a specific attention to the conservation of the total energy by the numericalscheme.