Uncertainty benchmarks for time-dependent transport problems

TL;DR

This paper introduces verification benchmarks for uncertainty quantification in time-dependent transport problems, utilizing polynomial chaos expansions and analytical uncollided solutions to assess accuracy and confidence interval growth.

Contribution

It provides a systematic approach to verify UQ methods for transport problems with uncertain scattering ratios, highlighting the number of moments needed and the behavior of confidence intervals.

Findings

Approximately six moments are needed for accurate polynomial chaos representation.

Confidence intervals grow when the uncertainty spans the critical value c=1.

Percentile values can verify the accuracy of polynomial chaos expansions.

Abstract

Verification solutions for uncertainty quantification are presented for time dependent transport problems where $c$, the scattering ratio, is uncertain. The method of polynomial chaos expansions is employed for quick and accurate calculation of the quantities of interest and uncollided solutions are used to treat part of the uncertainty calculation analytically. We find that approximately six moments in the polynomial expansion are required to represent the solutions to these problems accurately. Additionally, the results show that if the uncertainty interval spans c=1, which means it is uncertain whether the system is multiplying or not, the confidence interval will grow in time. Finally, since the QoI is a strictly increasing function, the percentile values are known and can be used to verify the accuracy of the expansion. These results can be used to test UQ methods for time-dependent transport problems.