Calculation of multiple eigenvalues of the neutron diffusion equation discretized with a parallelized finite volume method

Abstract

The spatial distribution of the neutron flux within the core of nuclear reactors is a key factor in nuclear safety. The easiest and fastest way to determine it is by solving the eigenvalue problem of the neutron diffusion equation, which only contains spatial derivatives. The approximation of these derivatives is performed by discretizing the geometry and using numerical methods. In this work, the authors used a finite volume method based on a polynomial expansion of the neutron flux. Once these terms are discretized, a set of matrix equations is obtained, which constitutes the eigenvalue problem. A very effective class of methods for the solution of eigenvalue problems are those based on projection onto a low-dimensional subspace, such as Krylov subspaces. Thus, the SLEPc library was used for solving the eigenvalue problem by means of the Krylov-Schur method, which also uses projection methods of PETSc for solving linear systems. This work includes a complete sensitivity analysis of different issues: mesh, polynomial terms, linear systems solvers and parallelization.