A simplified SP3 NEM solver within a unified formulation for pin-by-pin core multi-group calculations

Abstract

This study addresses the development and verification of a pin-by-pin core multigroup SP3 solver CTRP-Clouds that employs NEM (Nodal Expansion Method) and three simplified NEM methods within a unified formulation for simultaneously solving the coupling 0th and 2nd SP3 equations. In this work, the solver using this unified formulation does not only include the original NEM and its simplifications but also the EFEN (Exponential Function Expansion Nodal) method and FDM (Finite Difference Method) for the comprehensive evaluation. Also, the solver was accelerated using CMFD (Coarse Mesh Finite Difference) method and parallelized using OpenMP. The computational efficiency of different solution methods was investigated for the 2D KAIST benchmark problems and their modified one for considering 3D extension. The results showed the simplified NEM with flat leakage approximation gives acceptable accuracies of less than 1.2 % in RMS of pin-power discrepancies of all the cases with 1x1 mesh per pin-cell, with a reduction of 20 % computing time compared to the original NEM. Particularly, the calculation time of flat leakage NEM is comparable to EFEN while the pin-wise accuracy is better. Besides, the simplified NEM with 2nd-order flux expansion gives substantially improved accuracy in comparison with FDM within comparable computing time.

Keywords

• SP3 theory
• Pin-by-pin core calculation
• Nodal method
• NEM
• Simplified NEM