A modal multidimensional kinetics method using pseudo-harmonics

Modal methods for the neutron diffusion equation using different spatial modes

“…This occurs, for instance, in the out-of-phase oscillations observed in Boiling Water Reactors (BWR) (March-Leuba & Blakeman, 1991;March-Leuba & Rey, 1993). The generalization of this approach is the modal method (Stacey, 1969;Miró et al, 2002;de Lima et al, 2009;Avvakumov et al, 2017a) that expands the time-dependent flux as a sum of several spatial eigenfunctions of the initial configuration of the reactor. These spatial modes can be also updated along the transient (Miró et al, 2002).…”

“…Moreover, Avvakumov et al in (Avvakumov et al, 2017b) have formulated a new spectral problem, the δ-modes, which is connected to the self-adjoint part of operator representing neutron absorptiongeneration to make an a priori estimate of neutron flux dynamics. Finally, de Lima et al (de Lima et al, 2009) have proposed to use the pseudo-harmonics that are the eigenfunctions associated with the leakage and removal operator of each energy group, which are the solutions of a self-adjoint eigenvalue problem.…”