Radiative transfer with Monte Carlo predictor-corrector methods

In this paper we explore the time discretization error introduced into the Implicit Monte Carlo (IMC) method and contrast IMC with the Carter-Forest (CF) method which should be more accurate. The IMC method is the current standard even though it makes two approximations to solve the linear Radiative Transfer (RT) equations while the CF method solves them exactly. When the opacity and β are functions of temperature, both IMC and CF must approximate the values of the opacity and β as constant during a time step, adding a source of error to both methods. To determine the effect of the approximations in the IMC and CF methods, a detailed analysis was conducted to quantify the accumulated effect of each assumption. The residual analysis demonstrates the existence of a bias in the IMC method based on the value of alpha, and the truncation analysis shows that a significant source of truncation error in both the IMC and CF method originates with the constant opacity approximation over a time step in a non-linear problem. A predictor-corrector method is demonstrated that changes the CF method to be second order accurate in 0D while the IMC method will remain first order accurate. (authors)