A cascadic multigrid asymptotic-preserving discrete ordinate discontinuous streamline diffusion method for radiative transfer equations with diffusive scalings

Abstract

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.