A Study of Source Term Estimators in Coupled Finite-Volume/Monte-Carlo Methods with Applications to Plasma Edge Simulations in Nuclear Fusion: Track-Length and Next-Event Methods (Communications in Computational Physics, 2024)
In many applications, such as plasma edge simulation of a nuclear fusionreactor, a coupled PDE/kinetic description is required, which is usually solved witha coupled finite-volume/Monte-Carlo method. Different procedures have been proposed to estimate the source terms in the finite volume part that appear from theMonte Carlo part of the simulation. In this paper, we perform a systematic (analytical and numerical) comparison of the variance and computational cost of source termestimations using track-length based simulation techniques and track-length and next-event estimation procedures. We analyze in detail a scenario with forward-backwardscattering in a one-dimensional slab. For this test case, we perform a parametric studyof the expected statistical error and computational cost, revealing the large differencesin 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 quantifythe statistical error and computational cost of each estimator in a simplified setting.