Reducing Spatial Discretization Error with Linear Discontinuous Source Tilting in Iterative Quasi-Monte Carlo for Neutron Transport

TL;DR

This paper introduces a linear discontinuous source tilting scheme in iterative Quasi-Monte Carlo methods to reduce spatial discretization errors in neutron transport simulations, improving convergence accuracy.

Contribution

The paper presents a novel history-based source tilting approach that mitigates spatial errors in iQMC, enhancing solution accuracy for neutron transport problems.

Findings

Reduced spatial discretization error in iQMC

Improved convergence in neutron transport simulations

Effective in 2D reactor-like benchmark problem

Abstract

Recently, iterative Quasi-Monte Carlo (iQMC) was introduced as a new method of neutron transport which combines deterministic iterative methods and quasi-Monte Carlo simulation for more efficient solutions to the neutron transport equation. Previous iQMC results utilized a uniform Cartesian grid with a piecewise-constant source. Similar to "teleportation error" in Implicit Monte Carlo (IMC) methods, the spatial discretization and piecewise-constant source can lead to a significant spatial error that limits convergence of the overall method. Taking concepts from IMC, we have developed a history-based discontinuous piecewise-linear source tilting scheme to reduce spatial error in iQMC. The source tilting method is described below and afterward we present results from a fixed-source 2D reactor-like problem adapted from the Takeda-1 Benchmark problem.