Spectral properties of dynamic processes in a nuclear reactor

State change modal method for numerical simulation of dynamic processes in a nuclear reactor

“…Similar calculations of the eigenvalues for the VVER-1000 test problem without delayed neutrons can be found in Avvakumov et al (2017). The results of solving the spectral problem (23) for the first eigenvalues α n = λ (α) n , n = 1, 2, ..., N , N = 10 on different computational grids using Table 2, 3.…”

“…In our study (see Avvakumov et al (2017Avvakumov et al ( , 2016) we focus on the use of welldesigned algorithms and relevant free software. To solve spectral problems with non-symmetrical matrices we use the SLEPc (Scalable Library for Eigenvalue Problem Computations, http://slepc.upv.es/).…”

Modal methods for the neutron diffusion equation using different spatial modes

“…Different spectral problems can be associated with the neutron diffusion equation (Velarde et al, 1978;Ronen et al, 1976;Avvakumov et al, 2017b). The λ-modes, obtained by dividing the fission terms by a positive number, λ, have been efficiently computed (Verdú et al, 1994;Vidal-Ferrandiz et al, 2014).…”

“…Recently, several techniques have been proposed for their computation in (Carreño et al, 2017). 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.…”

Spatial modes for the neutron diffusion equation and their computation

“…The γ-modes were presented in (Ronen et al, 1976) and (Velarde et al, 1978), but as far as the authors know, there is not a lot of work devoted to this kind of modes. Recently, (Avvakumov et al, 2017) a new spectral problem has been formulated (δ-modes), which is connected to self-adjoint part of operator of neutron absorption-generation to make an a priori estimate of neutron flux dynamics.…”