Discontinuous finite element method with unstructured meshes for polarized radiative transfer in irregular media

A discontinuous finite element method (DFEM) with unstructured meshes is extended for solving the polarized radiative transfer problem in participating media. Two-dimensional media with irregular geometries and exposure to external irradiation are considered. The computational domain is divided into unstructured triangular meshes to handle the inclined and curved boundaries. The radiative intensities are assumed to be discontinuous across the inner-element boundaries of the adjacent elements. By utilizing a numerical flux with an up-winding scheme, all the discrete elements are connected and this guarantees the continuity of the computational domain. The correctness of the DFEM model for solving the polarized radiative transfer is first verified by comparing the DFEM solutions with published data of polarized radiative flux scenarios. Then the DFEM is applied to solve the polarized radiative transfer problems in irregular media, and the Stokes vector variables are analyzed.