Super-Nodal Methods for Space-Time Kinetics

A Super-Nodal method is developed to improve computational efficiency of core simulations for three-dimensional (3-D) core neutronics models. Computational performance of the neutronics model is increased by reducing the number of spatial nodes used in the core modeling. The Super-Nodal method reduces the errors associated with the use of coarse nodes in the analyses by providing a new set of cross sections and discontinuity factors for the new nodalization. These so-called homogenization parameters are obtained by employing a consistent collapsing technique.

During this research a new type of singularity, namely, "fundamental mode singularity," is addressed in the analytical nodal method solution. The "coordinate shifting" approach is developed as a method to address this singularity. Also, the "buckling shifting" approach is developed as an alternative to address the "zero buckling singularity." In the course of addressing the treatment of these singularities, an effort was made to provide better and more robust results from the Super-Nodal method by developing several new methods for determining the collapsed diffusion coefficient. A simple error analysis based on the relative residual in the 3-D few-group diffusion equation at the fine mesh level is also introduced in this work.