A hierarchy of nonlocal models for the radiative transfer equation

For the classic diffusion description of radiative transfer, the specific intensity can be represented by a small angular deviation of the local Planckian equilibrium. In a transparent media, the angular anisotropy becomes strong and one has to solve the general transfer equation. We propose a hierarchy of models that can describe the regime that lies between those two limits. Every member of this family is hyperbolic, flux-limited, and possesses a locally dissipated entropy. This hierarchy also formally recovers the diffusion limit. This study demonstrates that the two-polynomial model is already capable of capturing strong anisotropies.