The application of isogeometric analysis to the neutron diffusion equation for a pincell problem with an analytic benchmark

Abstract

In this paper the neutron diffusion equation is solved using Isogeometric Analysis (IGA), which is an attempt to generalise Finite Element Analysis (FEA) to include exact geometries. In contrast to FEA, the basis functions are rational functions instead of polynomials. These rational functions, called non-uniform rational B-splines, are used to capture both the geometry and approximate the solution.The method of manufactured solutions is used to verify a MatLab implementation of IGA, which is then applied to a pincell problem. This is a circular uranium fuel pin within a square block of graphite moderator. A new method is used to compute an analytic solution to a simplified version of this problem, and is then used to observe the order of convergence of the numerical scheme.Comparisons are made against quadratic finite elements for the pincell problem, and it is found that the disadvantage factor computed using IGA is less accurate. This is due to a cancellation of errors in the FEA solution. A modified pincell problem with vacuum boundary conditions is then considered. IGA is shown to outperform FEA in this situation.