Adams-Bashforth-Moulton method with Savitzky-Golay filter to reduce reactivity fluctuations

Abstract

Abstract In this paper we present a new method of calculating reactivity with fluctuation reduction. First we propose the generalized predictor and corrector using the fourth order Adams-Basforth-Moulton (ABM) for the numerical solution of the point kinetic equations for the calculation of reactivity, without using the history of nuclear power. Due to the nature of point kinetic equations, we use modifiers of the different predictors to increase precision in the approximation obtained. Secondly, we use the filter known as Savitzky-Golay (SG), which permits the reduction of the fluctuation in reactivity. It is known that the SG filter smoothing without diminishing the value of the nuclear power, irrespective of its form; this guarantees the reduction of Gaussian random noise levels, which is distributed around the average value of the nuclear power of up to σ = 0.1, with a time step h = 0.01 s. This formulation uses the Gram polynomial approximation, with a degree d = 2 the results show better values in the maximum difference in reactivity in comparison with that reported in literature.