SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2388-2419, January 2020.
Linear models for the radiative transfer equation have been well developed, while nonlinear models are seldom investigated even for slab geometry due to some essential difficulties. We have proposed a moment model in [Y. Fan, R. Li, and L. Zheng, J. Comput. Phys., 404 (2020), 109128] for slab geometry, which combines the ideas of the classical $P_N$ and $M_N$ model. Though the model is far from perfect, it was demonstrated to be quite efficient in numerically approximating the solution of the radiative transfer equation, and we are motivated to improve this model further. Consequently, we propose in this paper a new model following the chartmap in [Y. Fan, R. Li, and L. Zheng, J. Comput. Phys., 404 (2020), 109128] with some significant theoretic progress. The new model is derived with global hyperbolicity, and meanwhile some necessary physical properties are preserved. We give a complete analysis of the characteristic structure and propose a numerical scheme for the new model. Numerical examples are presented to demonstrate the numerical performance of the new model.

中文翻译：

---

平板几何中辐射传递方程的非线性双曲模型

SIAM应用数学杂志，第80卷，第6期，第2388-2419页，2020年1月。
辐射传递方程的线性模型已经得到很好的开发，而由于某些基本困难，即使对于平板几何形状，也很少研究非线性模型。我们在[Y. 范R. Li，和L. Zheng，J。Comput。Phys。，404（2020），109128]，结合了经典的$ P_N $和$ M_N $模型的思想。尽管该模型远非完美，但已证明在数值上近似辐射传递方程的解时非常有效，因此我们有动力进一步改进该模型。因此，我们根据[Y. 范R. Li，和L. Zheng，J。Comput。Phys。，404（2020），109128]，并在理论上取得了重大进展。新模型是根据全局双曲导出的，同时保留了一些必要的物理性质。我们对特征结构进行了完整的分析，并提出了新模型的数值方案。数值算例说明了新模型的数值性能。