A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren and Hauck (2010)  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 threedimensional (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.
Additional Information© 2013 Elsevier Inc. Received 7 September 2012; Received in revised form 21 January 2013; Accepted 23 January 2013; Available online 24 February 2013. We are happy to acknowledge helpful exchanges with Adam Burrows, Filippo Galeazzi, Cory D. Hauck, Ryan G. McClarren, Christian Reisswig and Erik Schnetter. This work was supported in part by NSF under Grant N. AST-0855535, OCI-0905046, by the Sherman Fairchild Foundation and the Alfred P. Sloan Foundation, by the DFG Grant SFB/Transregio 7, and by ''Comp- Star'' a Research Networking Programme of the European Science Foundation. Results presented in this article were obtained through computations on the AEI computer cluster ''Datura'', on machines of the Louisiana Optical Network Initiative under Grant loni_numrel07, on the Caltech compute cluster ''Zwicky'' (NSF MRI award No. PHY-0960291), on the NSF XSEDE network under computer time Grant TG-PHY100033, and at the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy under contract DE-AC03-76SF00098. This work was initiated at the MICRA workshop at the Perimeter Institute in 2011.
Submitted - 1209.1634.pdf