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Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

An automatic algorithm of time step control for solving the boundary value problems for nonstationary parabolic equations is presented. The solution is obtained using complete stable implicit schemes, and the time step is evaluated using of the explicit scheme solution. The time step evaluation formulas are derived using the estimation of the approximation error at next time step. Calculation results obtained for several neutron diffusion problems demonstrate reliability of the proposed algorithm for time step control.

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Acknowledgements

This work are supported A.V. Avvakumov and V.F. Strizhov by the Russian Foundation for Basic Research #16-08-01215, P.N. Vabishchevich by the grant of the Russian Federation Government #14.Y26.31.0013 and A.O. Vasilev by the Russian Foundation for Basic Research #18-31-00315.

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Authors and Affiliations

  1. National Research Center Kurchatov Institute, Moscow, Russia

    A. V. Avvakumov

  2. Nuclear Safety Institute of RAS, Moscow, Russia

    V. F. Strizhov & P. N. Vabishchevich

  3. North-Eastern Federal University, Yakutsk, Russia

    P. N. Vabishchevich & A. O. Vasilev

Authors
  1. A. V. Avvakumov
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  2. V. F. Strizhov
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  3. P. N. Vabishchevich
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  4. A. O. Vasilev
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Corresponding author

Correspondence to A. O. Vasilev .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Avvakumov, A.V., Strizhov, V.F., Vabishchevich, P.N., Vasilev, A.O. (2019). Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_14

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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