A Newton-Krylov Solution to the Coupled Neutronics-Porous Medium Equations.

Newton-Krylov;Multi-Physics;Nuclear Engineering and Radiological Sciences;Engineering;Nuclear Engineering & Radiological Sciences

Ward, Andrew M.Xu, Yunlin ;

University of Michigan

关键词: Newton-Krylov;    Multi-Physics;    Nuclear Engineering and Radiological Sciences;    Engineering;    Nuclear Engineering & Radiological Sciences;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/91609/wardam_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The solution of the coupled field equations for nuclear reactor analysis has typically been performed by solving separately the individual field equations and transferring information between fields. This has generally been referred to as ;;operating splitting” and has been applied to a wide range of reactor steady-state and transient problems. Although this approach has generally been successful, it has been computationally inefficient and imposed some limitations on the range of problems considered. The research here investigated fully implicit methods which do not split the coupled field operators and the solution of the coupled equations using Neutron-Krylov methods. The focus of the work here was on the solution of the coupled neutron and temperature/fluid field equations for the specific application to the high temperature gas reactor. The solution of the neutron field equations was restricted to the steady-state multi-group neutron diffusion equations and the temperature fluid solution for the gas reactor involved the solution of the solid energy, fluid energy, and the single phase mass-momentum equations. In the research performed here, several Newton-Krylov solution approaches have been employed to improve the behavior and performance of the coupled neutronics / porous medium equations as implemented in the PARCS/AGREE code system. The Exact and Inexact Newton;;s method were employed first, using an analytical Jacobian, followed by a finite difference based Jacobian, and lastly a Jacobian-Free method was employed for the thermal-fluids. Results in the thermal fluids indicate that the Exact Newton;;s method outperformed the other methods, including the current operator split solution. Finite difference Jacobian and Jacobian-Free were slighty slower than the current solution, though fewer outer iterations were required. In the coupled solution, the exact Newton method performed the best. The finite difference Jacobian with optimized perturbation integrated into the GMRES solve also performed very well, which represented the best iterative solution to the coupled problem. Future analysis will consider the transient problem.