Asymptotic derivation and numerical investigation of time-dependent simplified <inf>P N</inf> equations
Genre
Journal ArticleDate
2013-04-01Author
Olbrant, ELarsen, EW
Frank, M
Seibold, B
Subject
Simplified PN equationsSpherical harmonics
Time-dependent radiative transfer
Transport equation
Asymptotic analysis
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http://hdl.handle.net/20.500.12613/5965
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10.1016/j.jcp.2012.10.055Abstract
The steady-state simplified P N (SP N) approximations to the linear Boltzmann equation have been proven to be asymptotically higher-order corrections to the diffusion equation in certain physical systems. In this paper, we present an asymptotic analysis for the time-dependent simplified P N equations up to N = 3. Additionally, SP N equations of arbitrary order are derived in an ad hoc way. The resulting SP N equations are hyperbolic and differ from those investigated in a previous work by some of the authors. In two space dimensions, numerical calculations for the P N and SP N equations are performed. We simulate neutron distributions of a moving rod and present results for a benchmark problem, known as the checkerboard problem. The SP N equations are demonstrated to yield significantly more accurate results than diffusion approximations. In addition, for sufficiently low values of N, they are shown to be more efficient than P N models of comparable cost. © 2012 Elsevier Inc.Citation to related work
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http://dx.doi.org/10.34944/dspace/5947