Multi-group unified nodal method with two-group coarse-mesh finite difference formulation

Abstract

The one-node kernels of the unified nodal method (UNM) which were originally developed for two-group (2 G) problems are extended to solve multi-group (MG) problems within the framework of the 2 G coarse-mesh finite difference (CMFD) formulation. The analytic nodal method (ANM) kernel of UNM is reformulated for the MG application by adopting the Padé approximation to avoid the similarity transform required to diagonalize the G × G buckling matrix. In addition, a one-node semi-analytic nodal method (SANM) kernel which is considered adequate for multi-group calculations is also integrated into the UNM formulation by expressing it in the form consistent with the other UNM kernels. As an efficient global solution framework, the 2 G CMFD formulation with dynamic group condensation and prolongation is established and the performance of the various MG kernels is examined using various static and transient benchmark problems. It turns out that the SANM kernel is the best one for MG problems not only because it retains accuracy comparable to MGANM with a shorter computing time but also because its accuracy or its convergence does not depend on the eigenvalue range of the buckling matrix of the system. The 2 G CMFD formulation with MG one-node UNM kernels turns out to be very effective in that it conveniently accelerates the MG source iteration.