A modified implicit Monte Carlo method for time-dependent radiative transfer with adaptive material coupling

In this paper we develop a robust implicit Monte Carlo (IMC) algorithm based on more accurately updating the linearized equilibrium radiation energy density. The method does not introduce oscillations in the solution and has the same limit as Δ t → ∞ as the standard Fleck and Cummings IMC method. Moreover, the approach we introduce can be trivially added to current implementations of IMC by changing the definition of the Fleck factor. Using this new method we develop an adaptive scheme that uses either standard IMC or the modified method basing the adaptation on a zero-dimensional problem solved in each cell. Numerical results demonstrate that the new method can avoid the nonphysical overheating that occurs in standard IMC when the time step is large. The method also leads to decreased noise in the material temperature at the cost of a potential increase in the radiation temperature noise.