A New Spherical Harmonics Scheme for Multi-Dimensional Radiation   Transport I: Static Matter Configurations
  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. 
David Radice (1), Ernazar Abdikamalov (2), Luciano Rezzolla (1),   Christian D. Ott (2) ((1) AEI, (2) Caltech)
astro-ph.HE gr-qc physics.comp-ph