Time integration methods for reactor kinetics

Abstract

A technique based on the Padé approximations is applied to the solution of the point kinetics equations. The method consists of treating explicitly the roots of the inhour formula which would make the Padé approximations inaccurate. Also, an analytic method is developed which permits a fast inversion of polynomials of the point kinetics matrix and has direct applicability to the Pads approximations. Results are presented for several cases using various options of the method. It is concluded that the technique provides a fast and accurate computational method for the point kinetics equations. Also, an implicit solution method for the time-dependent multigroup diffusion equations known as the "theta method" is studied. Both the usual method and a variation of it, derived from the precursor integrated equations, are considered. Several properties of both versions of the theta method are demonstrated. An attempt is made to find better integration parameters (thetas) for the method, based on corresponding point kinetics calculations. Calculations are done for several test cases, leading to the conclusion that the improvements obtained are of limited value.