Optimization of an Algorithm for Search for the Solution of the System of Equations in the Nuclear Reactor Fuel Rod Mechanics Problem
https://doi.org/10.1134/S2304487X21010053
Abstract
An essential part of the simulation of the behavior of a fuel rod for fast-neutron and thermal-neutron nuclear reactors is finding the stress–strain state of the fuel pellet and the fuel rod cladding in addition to the thermal problem. The system of equations that describes the fuel rod mechanical behavior includes not only the elastic strain, thermal strain, and radiation swelling strain but also thermal and radiation creep strain that makes the system of equations nonlinear with respect to the interlayer and axial pressure variables. The solution of that kind of equations demands effective iteration methods. In this work, the algorithm for search for the solution of the system of nonlinear equations of nuclear fuel rod mechanics has been advanced by replacing the Gauss elimination method with the sweep method adapted to the matrix type of the linearized system. Optimization gives substantial acceleration in finding the solution of the system of linear equations that is raised in the problem: the discretization computational time at 10 and 20 layers decreases by one and two orders of magnitude, respectively. As a result, the time of finding the solution of the nonlinear system of equations by the Newton method for 10 and 20 layers decreases by a factor of 1.3 and 2, respectively.
About the Author
A. P. Dolgodvorov
Nuclear Safety Institute, Russian Academy of Sciences
Russian Federation
Russian Federation
115191
Moscow
References
1. Kalitkin N. N. Chislenniye metody [Numerical methods]. Moscow, “Nauka”, 1978.
2. Samarskiy A. A., Gulin A. V. Chislenniye metody [Numerical methods]. Moscow, “Nauka”, 1989.
3. Boldyrev A. V., Chernov S. Yu., Dolgodvorov A. P., Dolinsky I. O., Ozrin V. D., Tarasov V. I. BERKUT – Best Estimate Code for Modelling of Fast Reactor Fuel Rod Behaviour under Normal and Accidental Conditions. Proc. Int. Conf. on Fast Reactors and Related Fuel Cycles (FR17), Paper IAEA-CN-245-363, Ekaterinburg, 2017.
4. Ikonen T., Loukusa H., Syrjälahti E., Valtavirta V., Leppänen J., Tulkki V. Module for thermomechanical modeling of LWR fuel in multiphysics simulations. Annals of Nuclear Energy, 2015, vol. 84, pp. 111–121.
5. Loukusa H., Valtavirta V. FINIX – Fuel behavior model and interface for multiphysics applications – Code documentation for version 0.17.12 RESEARCH REPORT VTT-R-06793-17.
6. Boldyrev A. V., Belikova G. V., Veprev D. P., etc. Usovershenstvovannaya versia tvelnogo koda BERKUT, modeliruyushchego povedenie v bystryh reactorah tvela s nitridnym i oxidnym toplivom. Uchebnaya versiya 1.0 BERKUT-U/E1.0 [Advanced version of the fuel performance code BERKUT modeling fuel rod behavior in fast-neutron reactors with the nitride and oxide fuel. Training version 1.0 BERKUT-U/E1.0]. Textbook, 3<sup>rd</sup> edition, revised and expanded, Moscow, 2020.
Review
For citations:
Dolgodvorov A.P. Optimization of an Algorithm for Search for the Solution of the System of Equations in the Nuclear Reactor Fuel Rod Mechanics Problem. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(1):41-46. (In Russ.) https://doi.org/10.1134/S2304487X21010053
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