Abstract
This work focuses on the k-eigenvalue problem of the neutron transport equation. The variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method which has been widely applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, they are often compared to the unaccelerated power iteration. Hence, the goal of this paper is to apply the Anderson acceleration to the power iteration, and compare its performance to the Chebyshev acceleration.
Highlights
This work investigates the solution of the multigroup neutron transport equation with a discrete ordinates (Sn) method
The Chebyshev acceleration consists in applying power iteration method on a polynomial of H−1F such that the dominance ratio is as small as possible without changing the eigenvectors of the latter
The Chebyshev and Anderson acceleration methods were implemented in a mock-up in-house Sn code and several benchmarks have been considered
Summary
This work investigates the solution of the multigroup neutron transport equation with a discrete ordinates (Sn) method. The critical reactor core is obtained by establishing an equilibrium between fission sources and the removal term, without external sources, and is equivalent to solving for the largest eigenvalue keff such that (keff, ψ) is the solution to H−1F ψ = keffψ. In this case, the variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. The goal of this paper is to apply the Anderson acceleration method to the power iteration method, and to compare its performance to the Chebyshev acceleration method
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