Stability preservation in the numerical treatment of a nuclear reactor

Abstract

The tendency of certain numerical discretization methods towards super-stability or instability is investigated in this work. To this end, the coupled ordinary differential equations which govern the kinetic behavior of a class of Advanced Heavy Water nuclear Reactors (AHWR) are taken into account. Single step explicit and implicit methods and the multi-step central difference scheme, also known as the leapfrog or the midpoint method, have been applied to these coupled ODEs. Pertaining stability regions have been delineated in the parametric plane characterized by the pair of inherent thermal feedback coefficients (αv,αf) present in the model. To this effect, the bifurcation framework has been employed and the discretized schemes were compared to the original (continuous) system. Results pointed out that the implicit schemes enjoy a super-stable behavior for large enough time-steps while characterizing a broader stability region. The explicit scheme on the other hand is quite susceptible to an unstable dynamic regime. Besides, the super-stable behavior is quite more pronounced in the midpoint rule owing basically to the higher order accuracy thereof.