Improved Monte Carlo Variance Reduction for Space and Energy Self-Shielding

TL;DR

This paper introduces a Resonance Factor correction to FW-CADIS for Monte Carlo simulations, significantly improving variance reduction in problems with combined space and energy self-shielding, leading to faster and more accurate results.

Contribution

The paper proposes a novel Resonance Factor correction to FW-CADIS, enhancing variance reduction in complex self-shielding regions without affecting other areas.

Findings

Dramatic reduction in maximum 95% confidence interval relative error.

Significant decrease in computational time.

Improved accuracy in regions with combined space and energy self-shielding.

Abstract

Continued demand for accurate and computationally efficient transport methods to solve optically thick, fixed-source transport problems has inspired research on variance-reduction (VR) techniques for Monte Carlo (MC). Methods that use deterministic results to create VR maps for MC constitute a dominant branch of this research, with Forward Weighted-Consistent Adjoint Driven Importance Sampling (FW-CADIS) being a particularly successful example. However, locations in which energy and spatial self-shielding are combined, such as thin plates embedded in concrete, challenge FW-CADIS. In these cases the deterministic flux cannot appropriately capture transport behavior, and the associated VR parameters result in high variance in and following the plate. This work presents a new method that improves performance in transport calculations that contain regions of combined space and energy self-shielding without significant impact on the solution quality in other parts of the problem. This method is based on FW-CADIS and applies a Resonance Factor correction to the adjoint source. The impact of the Resonance Factor method is investigated in this work through an example problem. It is clear that this new method dramatically improves performance in terms of lowering the maximum 95% confidence interval relative error and reducing the compute time. Based on this work, we recommend that the Resonance Factor method be used when the accuracy of the solution in the presence of combined space and energy self-shielding is important.