A Functional Expansion Tally Method for Gray Radiative Transfer Equations in Implicit Monte Carlo

Abstract

The Implicit Monte Carlo (IMC) method is widely used for solving the nonlinear thermal radiative transport problems. This method often exhibits teleportation error in problems with strong coupling between radiation and matter. In this article, we propose a new Legendre functional expansion tally method to reduce the teleportation error for gray radiative transfer equations in the IMC method. The piecewise functional expansion tallies of absorbed energy in the previous time step is employed for the distribution of emission energy at the current time step within a cell. Numerical simulations show that our method significantly reduces the teleportation error relative to the source tilting method, and enables the use of lower spatial resolutions that would be required to mitigate the teleportation error using the source tilting method.