Implementation of a Newton-Krylov Iterative Method to Address Strong Non-Linear Feedback Effects in FORMOSA-B BWR Core Simulator
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Date
2002-12-31
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Abstract
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. The Newton's method provides the solver with a higher-than-linear convergence rate, assuming that a good initial estimate of the unknowns is provided. Within each Newton iteration, an appropriately preconditioned BICGSTAB method is utilized for solving the linearized system of equations. Taking advantage of the higher convergence rate provided by the Newton's method 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, observed when performing calculations on 200 loading patterns (LPs) using an 800 assembly BWR/6 core model, 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 has also been initiated in this research. Results from this study indicate that further reduction in the execution time can likely be obtained through the implementation of an inexact Newton's method. In general, the inexact Newton-BICGSTAB solver can provide speedups of 1.73 to 2.10 with respect to the traditional solver. As a specific example, an inexact Newton-BICGSTAB solver, in which the Jacobian coefficient matrix is approximated and a hybrid Chord-Shamanskii scheme is used to fix the frequency of the Jacobian matrix updates, can provide 2.10 and 2.27 overall and solver portion speedups, respectively. For this particular problem where a single LP of an 800 assembly BWR/6 core model is examined, the speedups gained by utilizing the traditional (BICGSTAB) solver and by utilizing the exact Newton-BICGSTAB solver are 1.63 and 1.76, respectively. This means that the inexact Newton-BICGSTAB solver provides additional speedups of 29% and 19% to the traditional (BICGSTAB) solver and the exact Newton-BICGSTAB solver, respectively.
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Neutron diffusion equation, BWR, BICGSTAB, Newton-Krylov
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Degree
PhD
Discipline
Nuclear Engineering
