Space-angle discontinuous Galerkin method for 2D RTE with diffusively and specularly reflective boundary conditions

Abstract

A space-angle discontinuous Galerkin (saDG) method for solving radiative transfer problems in arbitrary 2D domains is proposed. The space-angle domain is fully discretized by the DG formulation. The angular decomposition scheme is adopted to help accelerate the process by solving the radiative transfer equation iteratively. The performance of the method is analyzed in the square geometry with different types of boundary conditions. We found that the number of iteration or convergence rate of the iteration for the specular reflection problems is not only effected by the number of the reflective surfaces in the domain, but also by the scattering and extinction properties of the media. the uniformly and directionally diffuse reflective boundary conditions are compared in the same medium. In addition, the approach is applied to the simulation of radiative transfer in a parabolic reflector to obtain the localization at the focal point.