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A PN Solution to the Multigroup Slowing-Down Problem - I: Basic Formulation
Volume 130 · Number 1 · September 1998 · Pages 60-69
Technical Paper
A. D. Caldeira, A. F. Dias, R. D. M. Garcia
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The PN method is used to solve the multigroup slowing-down problem in plane geometry. A scalar (group-by-group) PN solution that is less limited by computational resources than previously reported vector solutions is developed. The solution is expressed, for a given group, as a combination of homogeneous and particular solutions that satisfies the first N + 1 moments of the corresponding transport equation. An interesting feature of the proposed approach is that the particular PN solution can be written in a form analogous to that of the homogeneous solution, except that a newly introduced class of generalized Chandrasekhar polynomials takes the place of the usual Chandrasekhar polynomials. Numerical results are given for two test problems and compared, for various orders of the approximation, with reference results available in the literature.
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