Superconvergent Finite Difference Discretization for Reactor Calculations

Abstract

Mesh centered and mesh corner finite difference discretizations can be derived formally from a primal and dual variational principle, using Gauss-Lobatto quadratures. We show that Gauss-Legendre quadratures can also be applied to the same primal and dual functional in order to obtain a more accurate discretization: the superconvergent finite difference method. An efficient A DI numerical technique with a supervectorization procedure was set up to solve the resulting matrix system. Validation results are given for the IAEA 2-0, Biblis and IAEA 3-0 benchmarks and for a typical full-core 3-0 representation of a pressurized water reactor at beginning of second cycle.