An Unstructured Discontinuous Finite Element Method for Three-Dimensional Radiative Transfer in Participating Media

This paper presents a discontinuous finite element (or discontinuous Galerkin) computational methodology for the numerical solution of internal thermal radiation problems in three-dimensional geometries using unstructured meshes. Mathematical formulation and numerical details using the discontinuous Galerkin method for internal radiation heat transfer calculations are given. Computational procedures are presented. Numerical examples are given for radiative transfer in 3-D geometries filled with a non-scattering or scattering medium. The computed results are given and are compared well with analytical solutions whenever available or the data reported in references.