Coarse-Mesh Diffusion Synthetic Acceleration of the Scattering Source Iterative Scheme for One-Speed Discrete Ordinates Neutron Transport Calculations in Slab Geometry

Abstract

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source one-speed discrete ordinates (SN) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive slabs (low absorption) with several mean free paths in extent.
In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as
initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the
classical SN prescribed boundary conditions, including vacuum boundary conditions.
Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we
reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source to begin the
SN transport sweep (forward and backward) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered
acceleration technique.