AN INVESTIGATION OF THE TEMPORAL SUBDOMAIN METHOD FOR SOLVING THE FINITE-ELEMENT FORMULATION OF THE SPACE-TIME REACTOR KINETICS EQUATIONS

The temporal subdomain method (TSM), based on a spatial finite element formulation, is investigated as a method for the solution of the spac e-time-dependent multigroup neutron dynamics equations. The spatial as pect of the problem was formulated as an array of finite elements by u sing a two-dimensional rectangular coordinate system subdivided into c ontiguous triangular elements. Within each element and within each neu tron group, the flux was represented by a linear polynomial. Numerical experiments using a computer program developed during the course of t he investigation demonstrated that the method is straightforward to im plement and that it produces stable calculations for a wide range of t ime steps. The stability of the method has been tested for sinusoidal ramp, and step-change reactivity insertions. The results show that the TSM outperforms most alternating direction implicit methods in the se nse that a similar degree of accuracy can be achieved with larger time steps using the same number of nodes. System condition number calcula tions as a function of node number were also carried out for a series of static eigenvalue calculations to determine the likelihood of error propagation and the difficulty of inverting the global system matrice s during the time-dependent calculations.