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Continuity Conditions for a Homogeneous or Heterogeneous PN Approximation

James A. Davis

Nuclear Science and Engineering

Volume 27 / Number 3 / March 1986 / Pages 542-548


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The problem of obtaining continuity conditions for a PN approximation is approached from a variational point of view. A functional is defined that admits piecewise discontinuous trial functions and has the transport equation and flux continuity conditions as its Euler equations. A reduced functional, formed by adopting a truncated spherical-harmonics expansion as a trial function, has as its Euler equations the PN equations and approximate flux-continuity conditions. These variational continuity conditions, which involve full-range angular integrals, are seen to be the same as those of Rumyantsev. Marshak continuity conditions, which involve half-range angular integrals obtained by Marshak matching, are shown to be equivalent to Rumyantsev's continuity conditions. Continuity conditions for a heterogeneous PN approximation are obtained by extending the notion of Marshak matching are shown to the case where a PN,approximation is employed in an adjacent region.

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