An optimized sweeping solution method for the three-dimensional Sn equations of neutron transport on hexahedral meshes

Abstract

We propose a new sweeping solution method for the three-dimensional (3D) discrete ordinates (Sn) equations of neutron transport on general hexahedral meshes, with particular focus on handling the surface integrals and sweeping deadlocks. The main contributions of this paper include three aspects. Firstly, the surface integrals on the non-planar cell faces are well discretized by virtue of the effective face method, which successfully addresses the reentrance problem without the decomposition of the cell faces. Secondly, based on the effective face method, we devise a new sorting algorithm which works for any hexahedral meshes. In this algorithm, the identification for dependent cycles is avoided and the physical characteristics of transport problems are taken into account in the choice of lagged cells used to decouple the sweeping deadlocks. Combining the above advancements, a splitting sweeping iterative method is proposed for the solution of the Sn equations on general hexahedral meshes. Finally, we prove theoretically that this sweeping iterative method always converges, and the decoupling method affects little on iterative convergence rate. Numerical experiments are presented to demonstrate the effectiveness of the proposed methods on both cubic and spherical domains. The ideas presented in this paper are also applicable to the polyhedral meshes or two-dimensional polygonal meshes.