Arbitrary-level coarse mesh finite difference acceleration with hierarchical coarsening in space and energy

Abstract

In this paper, we present an arbitrary-level coarse mesh finite difference (CMFD) scheme to accelerate discrete ordinates (SN) transport eigenvalue problems. It is a nested iterative scheme where a transport power iteration is accelerated with nested levels of CMFD eigenvalue problems whose space/energy grids can be hierarchically coarsened. The methodology provides a general framework independent of the space/angle discretization used to define the problem of interest. It is also readily extensible to solving diffusion eigenvalue problems. We present 2D and 3D numerical results on a representative quarter-core model from the VERA benchmark suite with different combinations of energy and spatial CMFD grids. We show that the methodology significantly reduces the diffusion and overall computational times required to solve large SN transport eigenvalue problems with CMFD on many parallel processes.