APPLICATION OF A DUAL VARIATIONAL FORMULATION TO FINITE-ELEMENT REACTOR CALCULATIONS

A number of improvements have been made to the nodal collocation method in order to obtain a high-order nodal technique capable of solving the neutron diffusion equation over full-core three-dimensional pressurized water reactors. First, the nodal collocation method is derived formally from a dual variational principle, using Gauss-Lobatto quadratures. Analytical integration and Gauss-Legendre quadratures are next applied to the same dual functional in order to obtain more accurate discretizations. An efficient ADI numerical technique with a supervectorization procedure was set up to solve the resulting matrix system. Validation results are given for the IAEA 2-D, Biblis and IAEA 3-D benchmarks and for a typical full-core 3-D representation of a pressurized water reactor at the beginning of the second cycle.