(untitled) (Communications in Computational Physics, 2024)
In many applications, such as plasma edge simulation of a nuclear fusion reactor, a coupled PDE/kinetic description is required, which is usually solved with a coupled finite-volume/Monte-Carlo method. Different procedures have been proposed to estimate the source terms in the finite volume part that appear from the Monte Carlo part of the simulation. In this paper, we perform a systematic (analytical and numerical) comparison of the variance and computational cost of source term estimations using track-length based simulation techniques and track-length and next-event estimation procedures. We analyze in detail a scenario with forward-backward scattering in a one-dimensional slab. For this test case, we perform a parametric study of the expected statistical error and computational cost, revealing the large differences in performance of the estimation procedures depending on the problem parameters. The analytical part of the comparison is based on an invariant imbedding procedure, in which systems of ordinary differential equations (ODEs) are derived that quantify the statistical error and computational cost of each estimator in a simplified setting.