Development of time-dependent reaction rates to optimize predictor-corrector algorithm in ALEPH burn-up tool

The dynamic of a burn-up problem is described by a system of coupled ordinary differential equations (ODE's) with a generally stiff matrix of the coefficients. Matrix coefficients represent decay constants and microscopic reaction rates of the numerous nuclides involved in the calculations. Current codes solve the system depleting the fuel by using constant matrix coefficients. This thesis work presents the unique and innovative feature for depletion codes by using time-dependent matrix coefficients when solving the system of ODE’s. Linear regression are computed to describe the evolution of the matrix coefficients along a few consecutive time steps. They allow to extrapolate the effective reaction rates of the following steps reducing the required computational time spent in the neutronic calculation and granting a slight improvement in the accuracy of the results, as well. In this thesis work, this technique has been tested, in combination with the second version of the ALEPH Monte-Carlo burn-up code, on the REBUS experimental up benchmark and simulating irradiation of the MYRRHA critical core configuration.