In this paper, we develop a cascadic multigrid asymptotic-preserving discrete ordinate discontinuous streamline diffusion scheme for radiative transfer equations (RTE) with multiple scalings. Our new method employs a simple and efficient cascadic multigrid method to the discretized RTE system as well as a diffusion synthetic acceleration technique as an efficient smoother to accelerate the convergence of the iteration in diffusive region. Furthermore, by applying the discontinuous streamline diffusion schemes, improved convergence condition in heterogeneous media and the asymptotic-preserving (AP) property can be achieved. The AP property of these methods will be explained formally and demonstrated numerically. Numerical results are presented to show the effectiveness and efficiency of the proposed numerical scheme for solving radiative transfer equations, especially in diffusive and heterogeneous media.

在本文中，我们针对具有多个比例的辐射传递方程（RTE），开发了级联多网格保渐近离散坐标不连续流线扩散方案。我们的新方法对离散RTE系统采用了一种简单而有效的级联多网格方法，并采用了一种扩散合成加速技术作为一种有效的平滑器来加速扩散区域中迭代的收敛。此外，通过应用非连续流线扩散方案，可以改善非均质介质中的收敛条件和渐近保持（AP）性质。这些方法的AP特性将被正式解释并通过数值进行演示。