A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

Abstract

Coarse-mesh finite difference (CMFD) method is a widely used numerical acceleration method. However, the stability of CMFD method is not good for the problems with optically thick regions. In this paper, a stability rule named the “sign preservation rule” in the field of numerical heat transfer is extended to the scheme of CMFD. It is required that the disturbance of neutron current is positively correlated with that of the negative value of flux gradient. A necessary condition for stability of the CMFD method is derived, an adaptive diffusion coefficient equation is proposed to improve the stability of CMFD method, and the corresponding revised CMFD method is called the rCMFD method. With a few modifications of the code, the rCMFD method was implemented in the hexagonal-Z nodal SN (discrete-ordinates) solver in the NECP-SARAX code system. The rCMFD method and other similar acceleration methods were tested by three fast reactor problems which were obtained by modifying the hexagonal pitches of a benchmark problem. The numerical results indicated that the rCMFD method showed better stability than the traditional CMFD method and the artificially diffusive CMFD (adCMFD) method and a better convergence rate than the adCMFD method and the optimally diffusive CMFD (odCMFD) method for these fast reactor problems.

Acceleration performance results of the SN nodal transport solvers in MOSASAUR code system for lead-based reactor cores

“…In MOSASAUR, two SN nodal transport solvers have been integrated: one (Tri-solver) based on triangular prism meshes and another (Hex-solver) based on a hexagonal prism meshes. The SN nodal method (Lu and Wu, 2007;Xu et al, 2022a) begins its derivation from the multigroup SN form of the neutron transport equation. For instance, in the context of the most common eigenvalue problems, the equation takes the following form as shown in Eq.…”

“…However, the traditional CMFD method has poor convergence stability, and in recent years, many improved CMFD methods have emerged. Besides the traditional CMFD method, we have implemented the adCMFD (Jarrett et al, 2016) method, the odCMFD (Zhu et al, 2016) method and the rCMFD (Xu et al, 2022c) method.…”

“…To enhance the efficiency of reactor core transport calculations using SNM, two approaches can be adopted. Firstly, the number of iterative iterations can be reduced through the application of coarse-mesh finite difference (CMFD) acceleration or similar techniques (Xu et al, 2018;Xu et al, 2020;Xu et al, 2022a). Secondly, the calculation time for each iteration can be minimized by utilizing parallel computing (Xu et al, 2020;Xu et al, 2022b;Qiao et al, 2021).…”

NHAPMAD: Novel hybrid approaches for privacy‐preserved multiple attacks detection

“…The AFLOA 39 facilitates an advanced evaluation and selection process by enabling a LO, enabling more accurate identification and analysis of the key features while considering the complex relationships within the dataset. By incorporating the LO $$$ \beta \cdot {\nabla}^2C $$$, the algorithm effectively accounts for spatial changes and fluctuations in the concentration gradients of the numerical features, enabling a more comprehensive understanding of the underlying data dynamics.…”