Stiffness treatment of differential equations for the point reactor dynamic systems

Abstract

An original methodology based on the Padé and Chebyshev rational approximations for the solution of the non-linear point kinetics equations with temperature reactivity feedback is described and investigated. Piecewise constant approximations of the reactivity and source function are made. The technique is enhanced by explicitly accounting for the feedback and the reactivity variation within a time step through an iterative cycle. An important feature of the Chebyshev rational method is that good numerical approximations to the solutions of the stiff coupled kinetics differential equations can be obtained in a single time step, as opposed to several time steps required for the conventional methods. The CPU time required for the Chebyshev rational method is less than that time required for the conventional method (Padé approximations) by 72.64%, which is one advantage of the presented method. The cases of approximations which combined with its A(α)-stability, leads to a better reduction of the errors when intermediate and large times are reached after series of small time steps if the inserted reactivity is positive and sufficiently large. Numerical studies are presented for different benchmark problems of various reactivity insertions, time varying reactivity and temperature feedback reactivity. The results confirm the theoretical analysis and indicate the range of applicability of the methods presented. The computational results indicate that the method is efficient and accurate.