Convergence diagnostics for Monte Carlo fission source distributions using the Wasserstein distance measure

Abstract

The power iteration technique is commonly used in Monte Carlo (MC) criticality simulations to obtain converged neutron source distributions. Entropy is a typical indicator used to examine source distribution convergence. However, spatial meshing is required to calculate entropy, and the performance of a convergence diagnostic is sensitive to the chosen meshing scheme. A new indicator based on the Wasserstein distance (WD) measure is proposed; it is intuitive and easy to implement in MC codes. In addition, the usage of the WD-based indicator is almost input-free, which not only lowers the thresholds that users must meet but also reduces modeling errors. Numerical tests are conducted with typical source convergence problems and a full-core problem. The results show that the WD-based indicator is more conservative and reliable than the existing entropy-based indicators. For the BEAVRS problem, the average relative errors of the axial fission rate obtained using the entropy-based indicator are larger than 4%, while it is less than 1% when using the WD-based indicator. An extra computational cost is required to calculate the WD values, but the performance penalty is acceptable, with the slowdown less than 2% for large-scale problems.