The $\phi$-divergence-based moment method was recently introduced Abdelmalik et al. (2023) for the discretization of the radiative transfer equation. At the continuous level, this method is very close to the entropy-based MN methods and possesses its main properties, i.e. entropy dissipation, rotational invariance and energy conservation. However, the $\phi$-divergence based moment systems are easier to resolve numerically due to the improved conditioning of the discrete equations. Moreover, exact quadrature rules can be used to compute moments of the distribution function, which enables the preservation of energy conservation, entropy dissipation and rotational invariants, discretely. In this paper we consider different variants of the $\phi$-divergence closures that are based on different approximations of the exponential function and the Planck function. We compare the approximation properties of the proposed closures in the numerical benchmarks.

翻译：基于$\phi$-散度的矩方法由Abdelmalik等人(2023)近期提出，用于辐射传输方程的离散化。在连续层面上，该方法与基于熵的MN方法高度相似，并继承其主要性质，即熵耗散、旋转不变性和能量守恒。然而，由于离散方程条件数的改善，基于$\phi$-散度的矩系统更容易在数值上求解。此外，可利用精确求积规则计算分布函数的矩，从而在离散层面保持能量守恒、熵耗散和旋转不变性。本文考虑基于指数函数和普朗克函数不同近似形式的多种$\phi$-散度封闭变体，并通过数值基准测试比较所提出封闭的近似特性。