2017 journal article

Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems

JOURNAL OF COMPUTATIONAL PHYSICS, 346, 278–294.

co-author countries: United States of America πŸ‡ΊπŸ‡Έ
author keywords: Multigroup neutron diffusion equations; Iteration methods; Eigenvalue problems; Fourier analysis
Source: Web Of Science
Added: August 6, 2018

We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.