Hybrid Weight Window Method for Global Time-Dependent Monte Carlo Particle Transport Calculations

TL;DR

This work addresses slow convergence in time-dependent Monte Carlo simulations by introducing a global variance-reduction technique that uses automatic weight windows whose centers are defined by a hybrid MC/deterministic LOSM auxiliary solution. The LOSM equations are discretized with second-order accuracy in time and space and closures are supplied by MC, with optional noise filtering to suppress stochastic fluctuations. A time-step update mechanism redefines weight windows using the previous step’s LOSM solution, and the approach is validated against a 1D slab benchmark, including a parameter study of window settings and filtering strategies. Results show that the hybrid weight window method yields a more uniform particle distribution and improved figures of merit compared to lagged windows or analog MC, especially when combined with moving-average or Fourier filtering, highlighting its potential for efficient time-dependent transport calculations and easy integration with multiphysics workflows.

Abstract

This paper presents a new Monte Carlo (MC) algorithm for time-dependent particle transport problems with global variance reduction based on automatic weight windows (WWs). The centers of WWs at a time step are defined by the solution of an auxiliary hybrid MC / deterministic problem formed by the low-order second-moment (LOSM) equations. The closures for the hybrid LOSM equations are calculated by the MC method. The LOSM equations are discretized by a scheme of the second-order accuracy in time and space. Filtering techniques are applied to reduce noise effects in the LOSM closures. The WWs defined with the auxiliary solution give rise to sufficiently uniform MC particle distribution in space on each time step. The algorithm is analyzed by means of an analytic transport benchmark. We study performance of the MC algorithm depending on a set parameters of WWs. Figure of merit and relative error results are presented, demonstrating the performance of the hybrid MC method and quantifying its computational efficiency.

Figures (20)

• Figure 1: Tally options in Monte Carlo space-time cell
• Figure 2: Relative solution change
• Figure 3: Hybrid solutions ${\phi}_{hlosm}$ computed with the BE and CN time integration schemes and the benchmark solution at time steps $n=3,5,10$
• Figure 4: Relative $L_2$-norm of the error in the Monte Carlo scalar flux ($\langle\phi\rangle^n$) versus number of histories simulated before each weight-window updates over time steps $n=4$ and $n=19$ for different numbers of updates $u_{ww}^n$.
• Figure 5: Relative $L_2$-norm of the error in the hybrid scalar flux ($\phi_{hlosm}$) versus number of histories simulated before each weight-window updates over time steps $n=4$ and $n=19$ for different numbers of updates $u_{ww}^n$.