A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Dean Wang and Zuolong Zhu
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Dean Wang: Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH 43210, USA
Zuolong Zhu: Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH 43210, USA

Energies, 2021, vol. 14, issue 2, 1-18

Abstract: 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.

Keywords: neutron transport; Fourier analysis; SOR; CMFD; pCMFD; odCMFD; lpCMFD (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
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