Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method

Transient (time-dependent) polarized radiative transfer in a scattering medium exposed to an external collimated beam illumination is conducted based on the time-dependent polarized radiative transfer theory. The transient term, which persists the nanosecond order time and cannot be ignored for the time-dependent radiative transfer problems induced by a short-pulsed beam, is considered as well as the polarization effect of the radiation. A discontinuous finite element method (DFEM) is developed for the transient vector radiative transfer problem and the derivation of the discrete form of the governing equation is presented. The correctness of the developed DFEM is first verified by comparing the DFEM solutions with the results from the literature. The DFEM is then applied to study the transient polarized radiative transfer induced by a pulsed beam. The time-dependent Stokes vector components are calculated, plotted and analyzed as functions of the axis coordinate and discrete direction. Effects of the diffuse/specular boundary and the incident beam polarization state with respect to the Stokes vector components are further analyzed for cases of different boundary reflection modes and incident beam illuminations.