Numerical stability analysis of lp-CMFD acceleration for the discrete ordinates neutron transport calculation discretized with discontinuous Galerkin Finite Element Method

Abstract

A projection operator was recently developed to extend the linear prolongation Coarse Mesh Finite Difference acceleration (lp-CMFD) method to accelerate the discrete ordinate (SN) neutron transport calculation discretized with the Discontinuous Galerkin Finite Element Method (DGFEM) based spatial discretization scheme, which is more stable and effective than the conventional scaling based Coarse Mesh Finite Difference (CMFD) method. A thorough investigation of the stability of lp-CMFD was carried out using a series of numerical tests for homogeneous and heterogeneous test problems with vacuum and reflective boundary conditions. It was observed that the lp-CMFD method for the SN calculation discretized with the DGFEM based spatial discretization scheme becomes unstable when the coarse mesh optical thickness becomes large with vacuum boundary conditions and in strongly heterogeneous problems, which was not previously observed. The linear prolongation of the partial current based Coarse Mesh Finite Difference method (lp-pCMFD) is proposed to enhance the stability. Numerical testing showed that lp-pCMFD is stable and effective for the homogeneous and heterogeneous test problems. The linear prolongation update step of lp-pCMFD stabilizes both lp-CMFD and pCMFD for neutron transport problems with the DGFEM spatial discretization scheme.