Modified Spherical Harmonics Method For One-speed Transport Equation With Anisotropic Scattering
Free (open access)
M. S. Li & B. Yang
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
spherical harmonics method, anisotropic scattering, finite width delta functions.