Implementation and performance study of lpCMFD acceleration method for multi-energy group k-eigenvalue neutron transport problem in hexagonal geometry

Abstract

The recently developed lpCMFD acceleration scheme has been shown to be unconditionally stable and effective for SN neutron transport problems in Cartesian rectangular geometry. However, studies of lpCMFD performance for multi-energy group k-eigenvalue neutron transport problem in hexagonal geometries have not been previously investigated. In this paper, linear interpolation method on general convex polygon coarse mesh geometries is developed for lpCMFD in multi-energy group k-eigenvalue neutron transport problems. This method is tested on two hexagonal type reactor benchmark problems discretized with an equilateral triangular fine mesh for SN and different sizes of equilateral triangular and a mixed hexagonal-triangle coarse mesh grid for low order diffusion equation. It was found that lpCMFD was stable and effective for the benchmark problems investigated here with different coarse mesh grids, while CMFD became unstable when coarse mesh size increases. pCMFD was found to be stable in all configurations but was generally slower or as effective as lpCMFD and CMFD. The barycentric interpolation technique developed in this paper for lpCMFD in 2D hexagonal geometry is demonstrated to be effective and can be applied in realistic practical problems.