Finite element method for radiative heat transfer in absorbing and anisotropic scattering media

This article proposes a finite element method (FEM) for simulation of radiative heat transfer in absorbing, emitting and anisotropic scattering media. This simulation is developed on the base of discrete ordinates method and theories of finite element. The finite element formulations of triangle isoparametric element and detailed steps of numerical calculation are given. Unstructured triangular element grids are employed in spatial discretization, azimuthal discretization strategy is used in the angular discretization. Two efficient iterative solvers are employed to solve the sparse equations of FEM. Some typical two-dimensional problems are used to verify the method. Pure absorbing cases and anisotropic scattering cases with four different scattering phase functions are investigated and analyzed. A simple irregular geometry case is also used to verify the method. The results of present research have a good agreement with the Monte-Carlo method or published reference.