A diffusion synthetic acceleration approach to k-eigenvalue neutron transport using PJFNK

Abstract

This paper investigates a diffusion synthetic acceleration (DSA) approach to the k-eigenvalue problem of the neutron transport equation. The novelties of this study reside in 1) casting the low-order diffusion equation directly as a nonlinear problem, which is solved with the PJFNK (preconditioned Jacobian-free Newton Krylov) method, circumventing the need for power iteration; 2) showing the appealing features on solving the diffusion equation with DSA compared with nonlinear diffusion acceleration (NDA) with a simplified model of ATR (Advanced Test Reactor); 3) proposing the DSA weak form for the discretization scheme with SAAF (self-adjoint angular flux) formulation that is stable with anisotropic scatterings; 4) showing the impact of the vacuum boundary coefficient of the low-order equation on the convergence of DSA. Both DSA and NDA are implemented in and tested with Rattlesnake code, the INL MOOSE-based radiation transport application for multi-physics modeling and simulations.