Abstract
The objective is to analyze the neutron diffusion benchmark developed by the Atomic Energy Research community for verification of best-estimate neutronics codes. The 3D benchmark of Schulz models a VVER-1000 core in steady state. The assemblies are homogeneous, represented by given diffusion theory parameters. There are seven material compositions including four enrichments, burnable absorber, control rods and a reflector. The finite element method on tetrahedron computational grids is used to solve the three-dimensional neutron problem. The software has been developed using the engineering and scientific library FEniCS. The matrix spectral problem is solved using a scalable and flexible toolkit SLEPc. The solution accuracy of the benchmark is analyzed by condensing the computational grid and varying the degree of the finite elements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Duderstadt, J.J., Hamilton, L.J.: Nuclear Reactor Analysis. Wiley, Hoboken (1976)
Stacey, W.M.: Nuclear Reactor Physics. Wiley, Hoboken (2007)
Hetrick, D.L.: Dynamics of Nuclear Reactors. University of Chicago Press, Chicago (1971)
Marchuk, G.I., Lebedev, V.I.: Numerical Methods in the Theory of Neutron Transport. Harwood Academic Pub, Newark (1986)
Lewis, E.E., Miller, W.F.: Computational Methods of Neutron Transport. American Nuclear Society, Philadelphia (1993)
Avvakumov, A.V., Vabishchevich, P.N., Vasilev, A.O., Strizhov, V.F.: Spectral properties of dynamic processes in a nuclear reactor. Ann. Nucl. Energy 99, 68–79 (2017)
Schulz, G.: Solution of a 3D VVER-1000 benchmark. In: Proceedings of 6th Symposium of AER, Kikkonummi, Finland (1996)
Brenner, S.C., Scott, R.: The Mathematical Theory of Finite Element Methods. Springer, New York (2008). https://doi.org/10.1007/978-0-387-75934-0
Logg, A., Mardal, K.A., Wells, G.: Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-23099-8
Campos, C., Roman, J.E., Romero, E., Tomas, A.: SLEPc Users Manual (2013). http://slepc.upv.es/documentation/manual.htm
Kolev, N.P., Lenain, R., Fedon-Magnaud, C.: Solutions of the AER 3D benchmark for VVER-1000 by CRONOS. In: Proceedings of 7th Symposium of AER on VVER Reactor Physics and Safety, Hoernitz, Germany (1997)
Acknowledgments
The research was supported by the Government of the Russian Federation (project 14.Y26.31.0013).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Avvakumov, A.V., Vabishchevich, P.N., Vasilev, A.O., Strizhov, V.F. (2018). Solution of the 3D Neutron Diffusion Benchmark by FEM. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_47
Download citation
DOI: https://doi.org/10.1007/978-3-319-73441-5_47
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73440-8
Online ISBN: 978-3-319-73441-5
eBook Packages: Computer ScienceComputer Science (R0)