Nuclear Science and Engineering / Volume 139 / Number 1 / September 2001 / Pages 78-95
The rate equation for neutronic population is derived from the transient neutron diffusion equation. Neutronic imbalance is defined as the difference between the solution of the rate equation and the neutronic population obtained by spatial kinetics. If the transient neutron diffusion equation in the fully implicit formulation is discretized in such a manner as to satisfy the Gauss theorem and to retain a conservation form, neutronic imbalance decreases as the convergence criteria become strict. The iterative implicit method for neutronics and thermal hydraulics requires continuity of all the variables involved, which, in turn, facilitates the automatic time-step width control. From the viewpoints not only of well-posedness of a transient problem but also of code verification, a transient code should be capable of a null transient analysis for stable systems. Sample calculations are performed for a pressurized water reactor main-steam-line-break accident. An overall thermal-hydraulic trend model is conjectured to help compare and explain the calculated results. Spatial kinetics is found to clearly influence even the temporal behaviors of the secondary system.