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The $\phi$-divergence-based moment method was recently introduced Abdelmaliket al. (2023) for the discretization of the radiative transfer equation. At thecontinuous level, this method is very close to the entropy-based MN methods andpossesses its main properties, i.e. entropy dissipation, rotational invarianceand energy conservation. However, the $\phi$-divergence based moment systemsare easier to resolve numerically due to the improved conditioning of thediscrete equations. Moreover, exact quadrature rules can be used to computemoments of the distribution function, which enables the preservation of energyconservation, entropy dissipation and rotational invariants, discretely. Inthis paper we consider different variants of the $\phi$-divergence closuresthat are based on different approximations of the exponential function and thePlanck function. We compare the approximation properties of the proposedclosures in the numerical benchmarks.

Some extensions of the $\phi$-divergence moment closures for the radiative transfer equation