Including the effects of temperature-dependent opacities in the implicit Monte Carlo algorithm
The Implicit Monte Carlo technique of Fleck and Cummings is often employed to numerically simulate radiative transfer. This method achieves greater stability than one with a fully explicit time discretization by estimating the t{sup n+1} value of T{sup 4} from the thermal emission term, which is proportional to T{sup 4}. 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 t{sup n+1} value of the thermal emission term. This results in the addition to the 'Fleck factor' of a term that depends on (d{sigma})/(dT) . 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.