An Assessment of Acceleration Techniques in Scattering Source Iterations

Abstract

Discrete ordinates solutions of the neutron transport equation require the solution of the within-group transport equation by the method of iteration on the scattering source. Scattering source iterations are hampered by extremely slow convergence rates when the medium is highly scattering. Among the methods proposed for the acceleration of the scattering source iterations, the coarse mesh rebalance and the diffusion synthetic acceleration techniques appear to be the most prominent ones. Thus, one or the other has been adopted in most of the S_N codes. The numerical studies concerning the effectiveness of these acceleration methods have been made mostly for the planar geometry. There are some studies also for the multidimensional Cartesian geometries. In this study we have tried to assess the merits of these acceleration techniques in a curvilinear coordinate system that is spherical geometry. The performance of both of the acceleration methods have been determined by varying the scattering to total cross section ratio, the mesh size, the degree of anisotropy in scattering for a uniform spherical system. Then the study is extended to multiregion systems some of which are diffusive and in some of which transport effects are important.