The modified source iteration method for few-group space-time dependent neutron kinetic equations

Time-dependent formulations of the few-group space-dependent neutron kinetic equations are obtained using fully-implicit (backward-difference) approximations to the time derivatives. The fully-implicit equations can be solved at each time step using iterative procedures similar to those applied in static calculations. Usually, it is traditional source iteration method based on the standard combination of outer and inner iterations. However, as the results of numerical experiments and the presented analysis have shown, convergence rate of this algorithm in the transient calculations is not satisfactory. Modified source iteration method with improved characteristics is presented. Results of the executed analysis and numerical experiments show, that presented method is 10-30 times faster than source iteration method. Such essential increase of the proposed method efficiency is due to faster converging iteration process and analytical presentation of the Neumann series sum for the inhomogeneous equation solution. This method is useful for various techniques of space approximation and permits to use acceleration techniques proved for static calculations