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

TL;DR

This paper introduces a new double PN benchmark solution for the 1D monoenergetic neutron transport equation, improving accuracy near material discontinuities by separately expanding incoming and outgoing fluxes.

Contribution

The paper develops a novel solution method for the double PN equations, enhancing the accuracy of neutron transport modeling in plane geometry with material interfaces.

Findings

Demonstrated improved accuracy of the DPN method near discontinuities

Provided a benchmark solution for validation of numerical neutron transport codes

Validated the method with isotropic scattering medium simulations

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 ana-lytical 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 exiting 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 isotropically scattering medium.