High-Order Schemes for Neutron Kinetics Calculations, Based on a Local Polynomial Approximation

A systematic study of the accuracy and efficiency of a class of asymmetric weighted residual methods, as applied to neutron diffusion equations, is presented. Polynomials up to the sixth order are considered, with and without mixed spatial derivative terms. It turns out that the sixth-order polynomial with mixed derivative terms is most efficient: yet, for normal reactor conditions, sufficiently accurate results can already be obtained with a third-order polynomial without mixed-derivative terms.