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.
Highlights
The coarse-mesh finite difference (CMFD) scheme, originally developed by Smith [1,2], is being widely used for accelerating neutron transport calculations
It is shown that the use of different transport solvers in Fourier analysis can have some effect on the prediction of the convergence rate
The remainder of this paper is organized as follows: Section 2 presents the Fourier analysis of the CMFD schemes, such as CMFD, partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD), for both fixed-source problems and k-eigenvalue problems
Summary
The coarse-mesh finite difference (CMFD) scheme, originally developed by Smith [1,2], is being widely used for accelerating neutron transport calculations. Fourier analysis and numerical results are presented to show that odCMFD can become unstable and even fail at a relatively large optical thickness because of insufficient diffusion. The linear prolongation-based CMFD (lpCMFD) scheme is the latest development in the CMFD family [8] It replaces the conventional flat flux ratio-based scaling approach in the standard CMFD method with a linear interpolation of the scalar flux differences at the coarse-mesh cell edges between the high-order transport and low-order diffusion calculations. The remainder of this paper is organized as follows: Section 2 presents the Fourier analysis of the CMFD schemes, such as CMFD, pCMFD, odCMFD, and lpCMFD, for both fixed-source problems and k-eigenvalue problems. A brief summary of the CMFD algorithm and formulation is presented in Appendix A
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
