Transverse net leakage into the second-order Nodal expansion method

Abstract

A new formulation of the second-order version of the Nodal Expansion Method (NEM) is presented, based on the inclusion of a high-order transverse leakage source term into the Galerkin-weighted one-dimensional equations. This is done in a way that enhances the coupling between average group fluxes and incoming partial currents in the nodal balance equation. The equations for outgoing partial currents then take into account the transverse leakage contributions from the node of interest and the neighboring ones, in a manner similar to the standard fourth-order nodal expansion method. This formulation establishes a more physically coherent neutron balance inside an arbitrary node and preserves the iterative structure of the various versions of the NEM family, i.e., equations for outgoing currents and average fluxes in the inner iterations and fission source in the outer iterations. To illustrate the efficiency and accuracy of this second-order approach, numerical results for a typical 2-D, two-group benchmark model problem are presented.