Implementation of a Newton-Krylov iterative method to address strong non-linear feedback effects in FORMOSA-B BWR core simulator.

摘要

A Newton-BICGSTAB solver has been developed to reduce the CPU execution time of the FORMOSA-B boiling water reactor (BWR) core simulator. The new solver treats the strong non-linearities in the problem explicitly using the Newton's method, replacing the traditionally used nested iterative approach. Taking advantage of the higher convergence rate provided by the Newton's method, assuming that a good initial estimate of the unknowns is provided, and utilizing an efficient preconditioned BICGSTAB solver, we have developed a computationally efficient Newton-BICGSTAB solver to evaluate the three-dimensional, two-group neutron diffusion equations coupled with a two-phase flow model within a BWR core simulator.; The robustness of the solver has been tested against numerous BWR core configurations and consistent results have been observed each time. The best exact Newton-BICGSTAB solver performance provides an overall speedup of 2.07 to the core simulator, with reference to the traditional approach, i.e. outer (fission-source)-inner (red/black line SOR). When solving the same problem using the traditional approach but with the BICGSTAB solver as the inner iteration solver [traditional (BICGSTAB)], we observed a speedup of 1.85. This means that the Newton-BICGSTAB solver provides an additional 12% increase in the overall speedup over the traditional (BICGSTAB) solver. However, one needs to note that, on average, the exact Newton-BICGSTAB solver provides an overall speedup of around 1.70; whereas, on average, the traditional (BICGSTAB) provides an overall speedup of around 1.60.; An investigation on the feasibility of implementing an inexact Newton-BICGSTAB solver indicates that further reduction in the execution time can likely be obtained through this approach. This study shows that the inexact Newton-BICGSTAB solver can provide speedups of 1.73 to 2.10 with respect to the traditional solver.