Implementation of track length estimator for flux distribution tallies using proper orthogonal decomposition in one-dimensional geometry

In a recent study, we have developed an efficient flux distribution tallying method in the Monte Carlo calculation toward the high-fidelity, large scale multi-physics simulation. In this method, the proper orthogonal decomposition is applied to the flux distribution tallies. While the tallying method was implemented with the collision estimator in the previous study, the track length estimator is implemented in the present study to obtain the tally with lower statistical error. The implementation of the flux distribution tally with the track length estimator is compared with that of the collision estimator and the normal track length estimator in a one-dimensional problem. The numerical results reveal that the distribution tally using the proper orthogonal decomposition with the track length estimator can obtain a more precise solution compared with that with the collision estimator. Therefore, in terms of the statistical error, the relationship between the distribution tally with track length and collision estimators is similar to that between the conventional track length and collision estimators.