Analysis of transient radiative transfer in two-dimensional scattering graded index medium with diffuse energy pulse irradiation

The natural element method (NEM) is extended to solve transient radiative transfer in two-dimensional semitransparent graded index media with energy pulse irradiation diffusely incident on the left boundary. The surfaces of the medium are diffusely reflecting and semitransparent. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation and employing the least-squares (LS) weighted residuals approach to discretize the radiative transfer equation, a LSNEM approach is devised. Firstly, LSNEM solutions to transient radiative transfer are validated by comparison with results reported in the literature. Afterward, LSNEM is employed to investigate two-dimensional transient radiative transfer in graded index medium with a refractive index discontinuity at the surfaces. Effects of the optical thickness, scattering phase function and scattering albedo on transmittance and reflectance signals are investigated. Finally, the transient radiative transfer process of the medium subject to square diffuse pulse irradiation train are investigated, and the transient behavior of the radiative energy transport inside the medium with two complex graded index distributions is analyzed.