Double PN Benchmark Solution for the 1D Monoenergetic 
Neutron Transport Equation in Plane Geometry

Barry D. Ganapol

doi:10.20944/preprints202406.1186.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 17 June 2024 / Approved: 18 June 2024 / Online: 18 June 2024 (08:13:38 CEST)

Abstract: As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation. There are numerous ways of solving the transport equation, such as the Wiener-Hopf method based on analyticity, method of singular eigenfunctions, Laplace and Fourier transforms and analytical discrete ordinates, which is arguably one of the most straightforward, to name a few. Another potential method is the PN method, where the solution is expanded in terms of full range orthogonal Legendre polynomials and with orthogonality and truncation, the moments form a set of second order ODEs. Because of the half-range boundary conditions for incoming particles however, full range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion is more appropriate, where the incoming and exit-ing flux distributions are expanded separately to preserve the discontinuity at material interfaces. Here, a new method of solution for the DPN equations is proposed and demonstrated for an iso-tropically scattering medium.

Neutron transport; Isotropic scattering; Analytic discrete ordinates; Response matrix; Matix diagonalization; Wynn-epsilon acceleration

Physical Sciences, Mathematical Physics

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Double PN Benchmark Solution for the 1D Monoenergetic Neutron Transport Equation in Plane Geometry

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