Adaptive Finite Element Simulation of the Time-dependent Simplified P (N) Equations

The steady-state simplified PN approximation to the radiative transfer equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified PN equations have been derived by an asymptotic analysis similar to the asymptotic derivation of the steady-state SPN equations (Frank et al. in J. Comput. Phys. 226:2289-2305, 2007). In this paper, we present computational results for the time-dependent SPN equations in two dimensions, obtained by using an adaptive finite element approach. Several numerical comparisons with other existing models are shown