New basis functions for reactor core calculations using the nodal expansion method

Abstract

In 1977 Finnemann, Bennewitz and Wagner introduced the Nodal Expansion Method (NEM), by combining neutron diffusion theory, polynomial expansions, interface currents continuity, and weighted residual techniques. Extensive testing clearly indicated that it was consistent, computationally efficient, and accurate for meshes up to the typical size of assemblies. Two classical two-dimensional benchmarks were simulated: IAEA and LRABWR. Moments weighting was suggested to be preferable to Galerkin weighting. However, considering nodes of the size of assemblies, the fifth-order expansion using Galerkin weighting provided more accurate results than the fourth-order expansion using moments weighting (G3 and M2 on Finnemann's notation, respectively). The quadratic approximation has been considered appropriate to represent the transverse leakage terms (B2 on Finnemann's notation). Several studies seeking more accurate representations for the transverse leakage have been published since then. However, fourth-order expansion using moments weighting remains widely used as the most appropriate choice to approximate the average transverse fluxes, which may restrict the potentiality of the method.A detailed analysis of the NEM's basis functions has been performed, which allowed the development of formalism capable of generating polynomial expansions of any order. The new basis functions should introduce the additional terms required to describe the average transverse flux more properly, considering its distortions at fuel-reflector interfaces. In the same way that increasing the number of terms in convergent series leads to more accurate results, increasing the expansion order should bring the result closer to the expected solution. Comparisons of two- and three-dimensional LWR static benchmarks simulations are presented using up to tenth-order polynomial expansions, using both weight functions: moments and Galerkin. The introduced basis functions have led to more accurate results for keff and normalized assembly power distribution, including nodes at fuel-reflector interfaces. The increases in computing time using up to tenth-order expansions, for both weight functions, have not exceeded 40% for the simulated two-dimensional benchmarks and 90% for three-dimensional ones.