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 4.4 Theory Manual

“…(6.15b), use a quartic Legendre expansion. However, the flux also has two additional hyperbolic terms [162]:…”

Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

“…For discretising the neutron diffusion equation, the most commonly used methods are the finite difference method, the finite element method, and nodal methods [40][41][42]. The latter give fast and accurate solutions, but require a reconstruction step to obtain the pin-power distribution [37].…”