A Continuous Source Tilting Scheme for Radiative Transfer Equations in Implicit Monte Carlo

Abstract The implicit Monte Carlo (IMC) method can exhibit teleportation error in problems with strong coupling between radiation and material. Source tilting method is a technique to reduce the teleportation error by representing the emission source as a linear or higher order function in each zone. In this paper, we propose a new spatial reconstruction scheme for the emission source term in the implicit Monte Carlo method. The new reconstruction scheme takes into account of the propagation direction of each photon. A spatially continuous representation for the emission source can be obtained by the reconstruction. We demonstrate that the new scheme can capture the asymptotic diffusion limit in optically thick regions under certain conditions. Numerical simulations show that the continuous reconstruction scheme can significantly reduce the teleportation error and performs better than the one-sided or central difference reconstruction schemes.