Robust and accurate filtered spherical harmonics expansions for radiative transfer

We present a novel application of filters to the spherical harmonics ( P N ) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (...

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Bibliographic Details
Published in:Journal of computational physics 2010-08, Vol.229 (16), p.5597-5614
Main Authors: McClarren, Ryan G., Hauck, Cory D.
Format: Article
Language:English
Subjects:
APPROXIMATIONS
CALCULATION METHODS
Computational techniques
Diffusion
DISCRETE ORDINATE METHOD
ENERGY DENSITY
ENERGY TRANSFER
EQUATIONS
Exact sciences and technology
FUNCTIONS
GEOMETRY
HEAT TRANSFER
Hohlraums
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical methods in physics
Mathematical models
MATHEMATICAL SOLUTIONS
MATHEMATICS
MONTE CARLO METHOD
Monte Carlo methods
Physics
Preserves
RADIANT HEAT TRANSFER
Radiative transfer
SPHERICAL HARMONICS
SPHERICAL HARMONICS METHOD
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Summary:We present a novel application of filters to the spherical harmonics ( P N ) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (ii) vanish as the expansion order tends to infinity. Our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first-order time integration scheme. The method is readily applied to existing codes that solve the P N equations. Numerical results demonstrate that the solution to the filtered P N equations are (i) more robust and less oscillatory than standard P N solutions and (ii) more accurate than discrete ordinates solutions of comparable order. In particular, the filtered P 7 solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem in 2D Cartesian geometry.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.03.043