A Nonlinear Hyperbolic Model For Radiative Transfer Equation In Slab Geometry

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 Ply and MN 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, T. 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.