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Volume 37, Issue 1
A Study of Source Term Estimators in Coupled Finite-Volume/Monte-Carlo Methods with Applications to Plasma Edge Simulations in Nuclear Fusion: Analog and Collision Estimators

Bert Mortier, Martine Baelmans & Giovanni Samaey

DOI: 10.4208/cicp.OA-2022-0303

Commun. Comput. Phys., 37 (2025), pp. 104-136.

Published online: 2025-01

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  • Abstract

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.

  • Keywords

Monte Carlo, reaction rate estimation, invariant imbedding, survival biasing, collision estimator.

  • AMS Subject Headings

65C05, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-37-104, author = {Mortier , BertBaelmans , Martine and Samaey , Giovanni}, title = {A Study of Source Term Estimators in Coupled Finite-Volume/Monte-Carlo Methods with Applications to Plasma Edge Simulations in Nuclear Fusion: Analog and Collision Estimators}, journal = {Communications in Computational Physics}, year = {2025}, volume = {37}, number = {1}, pages = {104--136}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0303}, url = {http://global-sci.org/intro/article_detail/cicp/23782.html} }
TY - JOUR T1 - A Study of Source Term Estimators in Coupled Finite-Volume/Monte-Carlo Methods with Applications to Plasma Edge Simulations in Nuclear Fusion: Analog and Collision Estimators AU - Mortier , Bert AU - Baelmans , Martine AU - Samaey , Giovanni JO - Communications in Computational Physics VL - 1 SP - 104 EP - 136 PY - 2025 DA - 2025/01 SN - 37 DO - http://doi.org/10.4208/cicp.OA-2022-0303 UR - https://global-sci.org/intro/article_detail/cicp/23782.html KW - Monte Carlo, reaction rate estimation, invariant imbedding, survival biasing, collision estimator. AB -

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.

Mortier , BertBaelmans , Martine and Samaey , Giovanni. (2025). A Study of Source Term Estimators in Coupled Finite-Volume/Monte-Carlo Methods with Applications to Plasma Edge Simulations in Nuclear Fusion: Analog and Collision Estimators. Communications in Computational Physics. 37 (1). 104-136. doi:10.4208/cicp.OA-2022-0303
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