Eigenvalves of the discrete ordinates equations in slab geometry.
Loading...
Date
1975-09
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Australian Atomic Energy Commission
Abstract
The discrete ordinates approximation of the one—group, source—free, neutron transport equation has been solved analytically for slab geometry. The resulting eigenvalues are functions of both the angular quadrature and the spatial mesh used in the discrete ordinates equations. The dependence of the eigenvalues on the angular quadrature has been examined for the three limiting cases of c < < 1, | 1-c | < < 1 and c > > 1, where c = σε/σt. Both the diamond difference and step function approximations have been considered in the evaluation of the eigenvalue dependence on the spatial mesh size. When the neutron flux is well described by a function of the form exp(—κχ), the diamond difference approximation gives an eigenvalue κd≈κ(1 + (κ∆)2/12), where κ is the eigenvalue for small values of the mesh size ∆, while the step function approximation gives an eigenvalue κε≈κ(1—0.4 σε∆).
Description
Keywords
Analytical solution, Anisotropy, Geometry, Neutron flux, Scattering, Neutron transport theory
Citation
Donnelly, I. J. (1975). Eigenvalves of the discrete ordinates equations in slab geometry. (AAEC/E360). Lucas Heights, NSW: Australian Atomic Energy Commission.