Including the effects of temperature-dependent opacities in the implicit Monte Carlo algorithm

The Implicit Monte Carlo technique of Fleck and Cummings [1] is often employed to numerically simulate radiative transfer. This method achieves greater stability than one with a fully explicit time discretization by estimating the tn+1 value of T4 from the thermal emission term, which is proportional to T4. In the Fleck and Cummings algorithm, this results in decreasing the absorption by the so-called “Fleck factor”, and adding a corresponding amount of effective scattering. We show how to include the effects of the temperature-dependent opacity to the estimated tn+1 value of the thermal emission term. This results in the addition to the “Fleck factor” of a term that depends on dσdT. We demonstrate that this modification allows for more accurate solutions with much larger time steps for problems with opacities that have a strong temperature dependence.