Multiscale Modeling &Simulation, Volume 19, Issue 1, Page 1-24, January 2021.
We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite-volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.

中文翻译：

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辐射输运方程的混合有限体积、不连续伽辽金离散化

多尺度建模与仿真，第 19 卷，第 1 期，第 1-24 页，2021 年 1 月。
我们为辐射输运方程提出了一种混合空间离散化，它结合了二阶不连续伽辽金 (DG) 方法和二阶有限体积 (FV) 方法。该策略依赖于先前用于组合不同角度离散化的简单算子拆分。与具有逆风通量的标准 FV 方法不同，混合方法能够准确模拟散射主导区域中的问题。然而，它需要更少的内存，并且比均匀的 DG 离散化产生更快的计算时间。此外，底层分裂允许自然地在空间和角度上进行混合。给出了数值结果以证明混合方法在离散纵坐标角度离散化和笛卡尔空间网格的背景下的效率。