Neutron transport criticality calculations using a parallel monolithic multilevel Schwarz preconditioner together with a nonlinear diffusion acceleration method

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

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A flexible nonlinear diffusion acceleration method for the S transport equations discretized with discontinuous finite elements

Journal of Computational Physics ◽

10.1016/j.jcp.2017.01.070 ◽

2017 ◽

Vol 338 ◽

pp. 107-136 ◽

Cited By ~ 9

Author(s):

Sebastian Schunert ◽

Yaqi Wang ◽

Frederick Gleicher ◽

Javier Ortensi ◽

Benjamin Baker ◽

...

Keyword(s):

Finite Elements ◽

Nonlinear Diffusion ◽

Transport Equations ◽

Discontinuous Finite Elements ◽

Acceleration Method

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Implementation and performance study of lpCMFD acceleration method for multi-energy group k-eigenvalue neutron transport problem in hexagonal geometry

Annals of Nuclear Energy ◽

10.1016/j.anucene.2019.107220 ◽

2020 ◽

Vol 139 ◽

pp. 107220 ◽

Cited By ~ 1

Author(s):

Yimeng Chan ◽

Sicong Xiao

Keyword(s):

Neutron Transport ◽

Transport Problem ◽

Performance Study ◽

Energy Group ◽

Acceleration Method ◽

And Performance

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COMPARISON OF CHEBYSHEV AND ANDERSON ACCELERATIONS FOR THE NEUTRON TRANSPORT EQUATION

EPJ Web of Conferences ◽

10.1051/epjconf/202124703001 ◽

2021 ◽

Vol 247 ◽

pp. 03001

Author(s):

Ansar Calloo ◽

Romain Le Tellier ◽

David Couyras

Keyword(s):

Eigenvalue Problem ◽

Transport Equation ◽

Fundamental Mode ◽

Iteration Method ◽

Neutron Transport ◽

Neutron Transport Equation ◽

Reactor Physics ◽

Nonlinear Methods ◽

Power Iteration ◽

Acceleration Method

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.

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