A Space-angle Discontinuous Galerkin Method for Two-Dimensional Radiative Transfer Equation with Reflective Boundary Conditions

Abstract

The propagation of radiation in the form of electromagnetic waves through a medium is affected by absorption, emission, and scattering processes. The radiative transfer equation (RTE) mathematically describes this interaction, which has a wide range of applications in such areas as heat transfer, neutron transport, atmospheric science, optical molecular imaging and some other applications. The discontinuous Galerkin (DG) finite element method (FEM) is one of the most popular grid-based numerical methods for solving the RTE due to its high order accuracy and flexibility in mesh grids. The basis functions used in the DG method are discontinuous across element interfaces; accordingly, the jump condition between interior traces of solution and the so-called numerical flux is weakly enforced on the interface boundaries. The space-angle DG methods that fully discretize the spatial and angular domain are specially suitable for the RTE, since the evolution of solution along characteristics can be strongly discontinuous when there are local radiation sources or radiation incidence coming from the boundary surface, especially the reflective ones. Previous work has proved that the space-angle DG method can be applied to solving the RTEs with high order precision in parallel with the domain decomposition (DD) and angular decomposition (AD) schemes [1]–[4]. In this paper, a parallel space-angle DG method is used to solve the steady state radiative transfer problems with the diffuse and specular reflection boundary conditions in the 2D complex geometries. Fig. 1. A schematic of the radiative intensity reflected from a surface.