Polynomial interpolation of few-group neutron cross sections on sparse grids

Abstract

Few group, homogenized neutron cross sections are represented as a function of various state parameters through multidimensional Lagrange interpolation. The interpolation is built on a Clenshaw-Curtis sparse grid by applying the method of mean weighted residuals. Unlike traditional approaches, which use either the Smolyak construction or the combinatorial formula for interpolation on a sparse grid, our approach is based on the properties of multidimensional cardinal functions, built as a tensor product of one-dimensional basis functions. The interpolation technique combines the efficiency of Chebyshev interpolation with low calculation and storage requirements of sparse grid methods, which makes it scalable in dimensionality. In addition, the method provides a way to optimize the size of the library, while still keeping control of the accuracy of the representation. The representation method was applied to the few group homogenized cross sections of diverse light water reactors: PWR and MTR fuel assemblies and a VVER fuel pin. These examples differ in terms of intervals of state parameters, number of energy groups, the number of microscopic cross sections treated explicitly, and transport codes used for calculations. The analysis of the results obtained allows one to conclude that the method is capable of providing cross section representation with an accuracy that is sufficient for use in practical applications with reasonable calculational resources.