Unified Nodal Method for Solution to the Space-Time Kinetics Problems

The two popular transverse integrated nodal methods (TINMs), the nodal expansion method (NEM) and analytical nodal method (ANM), and the analytic function expansion nodal (AFEN) method are integrated into a single unified nodal formulation for the space-time kinetics calculations in rectangular core geometry. In particular, the nodal coupling equations of the conventional ANM and AFEN method are reformulated by the matrix function theory based on the unified nodal method (UNM) principle for the solution to the transient two-group neutronics benchmark problems. The difference between the two transient AFEN formulations by the UNM and the conventional AFEN principles is pointed out. The performance of the UNM formulation is examined in terms of the solutions to the transient light water reactor benchmark problems such as the Nuclear Energy Agency Committee on Reactor Physics pressurized water reactor rod ejection kinetics benchmark problems. Through comparison of several nodal computational options by the UNM formulation, it is shown that one node-per-fuel assembly (N/A) calculations by the AFEN method are superior to those by the NEM and the ANM, but that 4 N/A calculations by the AFEN method are not better than those by ANM, in prediction accuracy at the sacrifice of the computational time. The advantages of the transient UNM formulation over the conventional TINM and AFEN method formulations are discussed.