A comparison of source term estimators in coupled finite-volume/Monte-Carlo methods with applications to plasma edge simulations in nuclear fusion

TL;DR

This paper systematically compares various source term estimators in coupled finite-volume/Monte-Carlo methods, focusing on variance, cost, and optimality in plasma edge simulations relevant to nuclear fusion.

Contribution

It provides a comprehensive analysis of estimator performance, revealing how their effectiveness depends on model parameters and the specific quantities of interest.

Findings

Estimator choice affects variance and cost significantly.

Different estimators are optimal for different physical quantities.

Analytical and numerical comparisons guide estimator selection.

Abstract

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 present a systematic comparison of the variance and computational cost of a coherent set of such estimation procedures. We compare the different estimation procedures for mass in a simplified forward-backward scattering model problem, where an analytical comparison is possible, and for mass and momentum in a model problem with realistic scattering. Our results reveal a non-trivial dependence of the optimal choice of estimator on the model parameters and show that different estimation procedures prevail for different quantities of interest.