Numerical simulation for a one-dimensional radiative transfer equation

This numerical simulation has been developed for the diffusion approximation of a one-dimensional stationary radiative transfer equation. Specifically, as the mean free path of the photons tends to zero this simulation depicts the formation of boundary layers and the fact that at the interior of the domain the radiation intensity becomes isotropic solving a Laplace equation. This numerical simulation supports the results obtained analyzing the radiative transfer equation via matched asymptotic expansions.

本数值模拟针对一维定态辐射传输方程（one-dimensional stationary radiative transfer equation）的扩散近似（diffusion approximation）方法开发。具体而言，当光子的平均自由程趋近于零时，本模拟可刻画边界层的形成过程，以及计算域内部辐射强度在求解拉普拉斯方程（Laplace equation）时趋于各向同性的特性。本数值模拟可验证通过匹配渐近展开法（matched asymptotic expansions）分析辐射传输方程所得的研究结果。