Two-dimensional time dependent Riemann solvers for neutron transport

Authors:
Thomas A. Brunner;James Paul Holloway
Affiliations:
Sandia National Laboratories,1Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy and National Nuclear Securit ...;Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2014, United States
Venue:
Journal of Computational Physics
Year:
2005

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Abstract

A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P"1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem.