An asymptotic-preserving (AP) implicit-explicit PN numerical scheme is proposed for the gray model of the radiative transfer equation, where the first- and second-order numerical schemes are discussed for both the linear and nonlinear models. The AP property of this numerical scheme is proved theoretically and numerically, while the numerical stability of the linear model is verified by Fourier analysis. Several classical benchmark examples are studied to validate the efficiency of this numerical scheme.

翻译：本文针对辐射传输方程的灰度模型，提出了一种渐近保持（AP）隐式-显式PN数值格式，并对线性和非线性模型分别讨论了一阶和二阶数值格式。该数值格式的渐近保持性质在理论和数值上均得到了证明，同时通过傅里叶分析验证了线性模型的数值稳定性。通过多个经典基准算例的研究，验证了该数值格式的有效性。