Multi-level coarse mesh finite difference acceleration with local two-node nodal expansion method

Abstract

A computationally efficient and effective multi-level coarse mesh finite difference (CMFD) acceleration is proposed using the local two-node nodal expansion method for solving the three-dimensional multi-group neutron diffusion equation. The multi-level CMFD acceleration method consists of two essential features: (1) a new one-group (1G) CMFD linear system is established by using cross sections, flux and current information from the multi-group (MG) CMFD to accelerate the MG CMFD calculation, (2) an adaptive Wielandt shift method is proposed to accelerate the inverse power iteration of 1G CMFD in order to provide an accurate estimate of the eigenvalue at the beginning of the iteration for both 1G and MG CMFD linear system. Additionally, a nodal discontinuity factor and a diffusion coefficient correction factor are defined to achieve equivalence of the 1G and MG CMFD system. The accuracy and acceleration performance of multi-level CMFD are examined for a variety of well-known multi-group benchmarks problems. The numerical results demonstrate that superior accuracy is achievable and the multi-level CMFD acceleration method is efficient, particularly for the larger, multi-group systems.