A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

Authors:
David Radice;Ernazar Abdikamalov;Luciano Rezzolla;Christian D. Ott
Affiliations:
Max Planck Institute für Gravitationsphysik, Albert Einstein Institute, Potsdam, Germany;TAPIR, California Institute of Technology, Pasadena, CA, USA;Max Planck Institute für Gravitationsphysik, Albert Einstein Institute, Potsdam, Germany and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA;TAPIR, California Institute of Technology, Pasadena, CA, USA
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

Recent work by McClarren and Hauck (2010) [31] 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.