A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations

TL;DR

This paper extends the filtered spherical harmonics method for radiation transport from 2D to 3D, demonstrating its efficiency, robustness, and improved accuracy with second-order filters, making it promising for complex 3D calculations.

Contribution

The authors generalize the filtered spherical harmonics method to three dimensions and reformulate the filter operation to be timestep- and discretization-independent.

Findings

Filtered spherical harmonics performs well in 3D as in 2D.

Second-order filters outperform fourth-order ones.

The method is efficient, robust, and accurate for 3D radiation transport.

Abstract

Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations.