Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems

  • A. V. Avvakumov
  • V. F. Strizhov
  • P. N. Vabishchevich
  • A. O. VasilevEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


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.


Time step selection Parabolic equation Approximation error Neutron diffusion 



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.


  1. 1.
    Samarskii, A.A., Matus, P.P., Vabishchevich, P.N.: Difference Schemes with Operator Factors. Kluwer, Dordrecht (2002)CrossRefGoogle Scholar
  2. 2.
    Ascher, U.M.: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial Mathematics, Philadelphia (1998)CrossRefGoogle Scholar
  3. 3.
    Vabishchevich, P.N.: A priori estimation of a time step for numerically solving parabolic problems. Math. Model. Anal. 20(1), 94–111 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Avvakumov, A.V., et al.: Numerical modeling of neutron diffusion non-stationary problems. Matematicheskoe Modelirovanie 29(7), 44–62 (2017)MathSciNetGoogle Scholar
  5. 5.
    Chao, Y.A., Shatilla, Y.A.: Conformal mapping and hexagonal nodal methods-II: Implementation in the ANC-H Code. Nucl. Sci. Eng. 121, 210–225 (1995)CrossRefGoogle Scholar
  6. 6.
    Avvakumov, A.V., et al.: Spectral properties of dynamic processes in a nuclear reactor. Ann. Nucl. Energy 99, 68–79 (2017)CrossRefGoogle Scholar
  7. 7.
    Avvakumov, A.V., Strizhov, V.F., Vabishchevich, P.N., Vasilev, A.O.: Algorithms for numerical simulation of non-stationary neutron diffusion problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2016. LNCS, pp. 212–219. Springer, Cham (2017). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • A. V. Avvakumov
    • 1
  • V. F. Strizhov
    • 2
  • P. N. Vabishchevich
    • 2
    • 3
  • A. O. Vasilev
    • 3
    Email author
  1. 1.National Research Center Kurchatov InstituteMoscowRussia
  2. 2.Nuclear Safety Institute of RASMoscowRussia
  3. 3.North-Eastern Federal UniversityYakutskRussia

Personalised recommendations