(untitled) (Communications in Computational Physics, 2025)
In many applications, such as plasma edge simulation of a nuclear fusion reactor, a coupled PDE/kinetic description is required. Such systems can be 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 series of papers, we present a systematic (analytical and numerical) comparison of the variance and computational cost of a coherent set of such estimation procedures. 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 this paper, we discuss analog and collision simulation and estimation procedures. We analyze in detail a scenario with forward-backward scattering in a one-dimensional slab, uncovering and quantifying the effects determining the performance of the estimation procedures.