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

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.