Quantifying spatial accuracy in the method of characteristics for neutron transport

Background: Accuracy Challenges in Neutron Transport Methods

Accurate modeling of neutron transport is essential for nuclear reactor analysis. The method of characteristics (MoC) is widely used because it can efficiently represent complex geometries and boundary conditions. However, its spatial discretization relies on approximations of the neutron source, and the associated error behavior has not been fully understood.

Source Approximation Determines Order of Accuracy

This study focuses on two commonly used approaches: the flat source (FS) approximation, which assumes a constant source within each spatial region, and the linear source (LS) approximation, which accounts for spatial variation.

Through rigorous theoretical analysis, the researchers demonstrate that the FS approximation achieves second-order accuracy, while the LS approximation reaches fourth-order accuracy. The difference arises from how well each method represents the spatial distribution of the neutron source.

Analytical Error Formulation and Interpretation

The work derives explicit analytical expressions for the error in the cell-averaged angular flux by comparing the exact source distribution with its approximation along characteristic rays. This formulation provides a clear framework for understanding how discretization errors originate and propagate in MoC.

Numerical Verification Using Manufactured Solutions

To verify the theoretical predictions, the researchers employed the method of manufactured solutions (MMS), which enables controlled verification by constructing exact analytical solutions. Numerical tests with different source forms confirm that the observed convergence behavior is consistent with the theoretical order of accuracy.

Implications for High-Fidelity Reactor Simulations

The findings offer practical guidance for selecting numerical schemes and spatial discretization strategies in neutron transport simulations. They are particularly relevant for modern reactor physics codes, where accuracy and efficiency must be carefully balanced.

Future Directions in Method Development

Future work will extend the analysis to more general conditions, including scattering media and multidimensional problems, to further improve the predictive capability of MoC-based simulation tools.

The complete study is via by DOI: https://doi.org/10.1007/s41365-026-01948-9