The analytic function expansion nodal method refined with transverse gradient basis functions and interface flux moments

A refinement of the analytic function expansion nodal (AFEN) method is desc ribed. By increasing the number of flux expansion terms in the way that the original basic functions are combined with the transverse-direction linear functions, the refined AFEN method can describe the flux shape in the node s more accurately, since the added flux expansion terms still satisfy the d iffusion equation. The additional nodal unknowns introduced are the interfa ce flux moments,, and the additional constraints required are provided by t he continuity conditions of the interface flux moments and the interface cu rrent moments. Also presented is an algebraically exact method for removing the numerical singularity that can occur in any analytic nodal method when the core contains nearly no-net-leakage nodes. The refined AFEN method was tested on the Organization for Economic Cooperation and Development (OECD) -L336 mixed-oxide benchmark problem in rectangular geometry, and the VVER-4 40 benchmark problem and a nearly no-net-leakage node embedded core problem , both in hexagonal geometry. The results show that the method improves not only the accuracy in predicting the flux distribution but also the computi ng time, and that it can replace the corner-point fluxes with the interface flux moments without accuracy degradation, unless the problem consists of strongly dissimilar nodes. The possibility of excluding the corner-point fl uxes increases the flexibility in implementing this method into the existin g codes that do have the corner-point fluxes scheme and may make it fit bet ter for the nonlinear scheme based on two-node problems.