Three-dimensional transient radiative transfer modeling using discontinuous spectral element method

Discontinuous spectral element method (DSEM), the advanced version of discontinuous finite element method (DFEM), is formulated and applied to solve the three-dimensional transient radiative transfer problems. The method is applied in a cubic medium for the boundary-driven problems defined in the global coordinate system with x, y, z ε [0, L] and subdivided into many small rectangular hexahedral elements during the DSEM solution. The DSEM allows discontinuities at the element boundary ensuring accurate prediction of the wave front when it is located on the element boundary. In the second case, the DSEM is applied to model transient radiative transfer in an anisotropically scattering medium. The transient incident radiation and the radiative heat flux distribution along the centerline of the cube (x = 0, y = 0), obtained by the DSEM. The DSEM accurately predicts the wave front at different instants of time. The DSEM also shows very good performance in solving a transient collimated beam radiative transfer problem and can accurately capture the sharp wave fronts.