Two-Level Coarse Mesh Finite Difference Formulation with Multigroup Source Expansion Nodal Kernels

Abstract

As an effort to establish a fast, yet accurate multigroup nodal solution method that is crucial in repeated static and transient calculations for advanced reactors, the source expansion form of the semi-analytic nodal method (SANM) is introduced within the framework of the coarse mesh finite difference (CMFD) formulation. The source expansion is to expand the analytic form of the source appearing in the groupwise neutron diffusion equation with a set of orthogonal polynomials in order to obtain a group decoupled analytic solution. Both one-and two-node formulations are examined to determine the best nodal kernel. For the acceleration, a two-level CMFD scheme is established employing a multigroup and two-group CMFD. In addition, an alternative two-node direct SANM formulation with a quartic polynomial is examined to assess the direct vs. iterative resolution of the group coupling. The performance of the CMFD formulation with three different multigroup SANM nodal kernels is examined for a wide variety of multigroup benchmark problems including several MOX-loaded LWR cores and large FBR cores. It is demonstrated that superior accuracy is achievable with all the SANM kernels while the iterative two-node SANM kernel outperforms the others in the multigroup calculations employing more than two groups, and the two-level CMFD formulation is quite efficient in the acceleration of the outer iteration.

MPACT Theory Manual (V.4.3)

“…(6.15b), use a quartic Legendre expansion. However, the flux also has two additional hyperbolic terms [151]:…”

Application of Backward Differentiation Formula to Spatial Reactor Kinetics Calculation With Adaptive Time Step Control

“…In the following section, a backward differentiation formula is derived for the variable time step case and a generic adaptive time step control method based on the BDF method is presented. The BDF method is applied in Section 3 to three-dimensional kinetics calculation employing the coarse mesh finite difference (CMFD) formulation with the source expansion nodal method (SENM) kernels 10 and a practical adaptive time control scheme for the BDF-based spatial kinetics calculation is introduced. The performances of the BDF spatial kinetics calculation and the adaptive time step control scheme are assessed in Section 4 through the analyses of the NEACRP control rod ejection 11 and withdrawal 12 benchmark problems.…”

Convergence analysis of coarse mesh finite difference method applied to two-group three-dimensional neutron diffusion problem

“…Depending on the local kernel, there are two CMFD methods: one-node (1-N) CMFD and two-node (2-N) CMFD. The advantage of 1-N CMFD is a simpler implementation and the possibility of the direct 2-G CMFD formulation for multi-group (MG) problems, and the disadvantage is the fact that additional spatial sweeps are needed to make the convergence behavior more stable [1][2][3][4]. The advantage of 2-N CMFD is a stable convergence, and the disadvantage is the difficulty in applying the method to hexagonal lattice and the lack of applicability to direct 2-G CMFD for MG problems [1,4].…”