Simulating radiative transfer with filtered spherical harmonics |
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Authors: | Ryan G. McClarren Cory D. Hauck |
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Affiliation: | a Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, TX 77843-3133, USA b Computational Mathematics Group, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA11Oak Ridge National Laboratory is operated for the US Government under Contract No. DE-AC05-00OR22725. |
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Abstract: | This Letter presents a novel application of filters to the spherical harmonics (PN) expansion for radiative transfer problems in the high-energy-density regime. The filter, which is based on non-oscillatory spherical splines, preserves both the equilibrium diffusion limit and formal convergence properties of the unfiltered expansion. While the method requires further mathematical justification and computational studies, preliminary results demonstrate that solutions to the filtered PN equations are (1) more robust and less oscillatory than standard PN solutions and (2) more accurate than discrete ordinates solutions of comparable order. The filtered P7 solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem. Given the benefits of this method we believe it will enable more routine use of high-fidelity radiation-hydrodynamics calculations in the simulation of physical systems. |
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Keywords: | Radiation transport High energy density physics Kinetic equations Spherical harmonics method |
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