Recent advances in acceleration of source iterations for fixed-source slab-geometry S_N calculations based on P_N synthetic initial guess

The scattering source iterative (SI) scheme is applied traditionally to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S_N) neutron transport problems with linearly anisotropic scattering. 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 media (low absorption) with several mean free paths in extent. In this work we describe two acceleration techniques based on improved initial guesses for the SI scheme, wherein we initialize the scattering source distribution within the slab using the P₁ and P₃ approximations. In order to estimate these initial guesses, we use the coarse-mesh solution of the PN equations with special boundary conditions to account for the classical S_N prescribed boundary conditions, including vacuum boundary conditions. To apply this coarse-mesh P_N solution for the accelerated scheme, we first perform within-node spatial reconstruction, and then we determine the fine-mesh average scalar flux and total current for initializing the linearly anisotropic scattering source terms for the SI scheme. We consider a number of numerical experiments to illustrate the efficiency of the offered P_N synthetic acceleration (P_NSA) technique based on initial guess. (author)