Variable time-step modal methods to integrate the time-dependent neutron diffusion equation

Abstract

The time-dependent neutron diffusion equation can describe the power evolution inside a nuclear reactor core. One approach to integrate this time-dependent equation is the modal method. This methodology is based on assuming that the solution can be decomposed as a finite sum of time-dependent amplitudes multiplied by shape functions (obtained by solving a partial eigenvalue problem), which are updated along the transient. In this work, different controls, that adapt the time-step according to the state of the transient, are implemented. Several benchmark problems show the competitiveness of the methodology.