On a family of differential approximations of the radiative transfer equation

The radiative transfer equation (RTE) arises in a variety of applications and is challenging to solve numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the direction variable. For this reason, various approximations of RTE have been proposed in the literature. In this paper, we study a family of differential approximations of the RTE in three spatial variables. We explain the idea of constructing the differential approximations, and comment on the usefulness of the approximations.

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