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 space-time-dependent multigroup neutron dynamics equations. The spatial aspect of the problem was formulated as an array of finite elements by using a two-dimensional rectangular coordinate system subdivided into contiguous triangular elements. Within each element and within each neutron group, the flux was represented by a linear polynomial. Numerical experiments using a computer program developed during the course of the investigation demonstrated that the method is straightforward to implement and that it produces stable calculations for a wide range of time steps. The stability of the method has been tested for sinusoidal, ramp, and step-changed reactivity insertions. The results show that the TSM outperforms most alternating direction implicit methods in the sense that a similar degree of accuracy can be achieved with larger time steps using the same number of nodes. System condition number calculations 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 matrices during the time-dependent calculations