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Title: Eigenvalves of the discrete ordinates equations in slab geometry.
Keywords: Analytical solution
Neutron flux
Neutron transport theory
Issue Date: Sep-1975
Publisher: Australian Atomic Energy Commission
Citation: Donnelly, I. J. (1975). Eigenvalves of the discrete ordinates equations in slab geometry. (AAEC/E360). Lucas Heights, NSW: 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∆).
Gov't Doc #: 577
ISBN: 0642996911
Appears in Collections:Scientific and Technical Reports

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