Modified Spherical Harmonics Method For
One-speed Transport Equation With
Anisotropic Scattering
Author(s)
M. S. Li & B. Yang
Abstract
The criticality type eigenvalues of the one-speed transport equation in a
homogeneous slab with anisotropic scattering and Marshak boundary conditions
have been studied. The scattering function is assumed to be a combination of
linearly anisotropic and strongly forward-backward scattering. When the forward
and backward scattering completely dominate over the ‘ordinary’ scattering, or
the thickness of the slab approaches zero, the highly peaked angular flux at the
central point of the slab was expressed by finite width delta functions. Using the
finite width delta functions to analyse the high-order truncation error of the
angular flux we could accurately obtain results with a low-order approximation.
Numerical results for critical eigenvalues are obtained and tabulated for different
scattering parameters including the extreme cases, while the standard spherical
harmonics method gets a singularity.
Keywords: spherical harmonics method, anisotropic scattering, finite width
delta functions.
1 Introduction
Criticality type eigenvalues are needed for a variety of applications in reactor
physics. The problem of anisotropy and its effects on the size of the system is
one of the most important problems of transport theory. Many methods for
computing transport equations have been proposed, such as the spherical
harmonics ( N P ) method [1,2] and the discrete ordinates ( N S ) method [3, 4, 5].
When the forward and backward scattering completely dominate over the
‘ordinary’ scattering (the extreme case) or the thickness of the slab approaches to
Keywords
spherical harmonics method, anisotropic scattering, finite width
delta functions.
Related Book
Other papers in this volume
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