Skip to main content
SpringerLink
Log in

Perturbation Theory in the Method of Characteristics

  • Published:
Atomic Energy Aims and scope

First-order perturbation theory for the multiplication coeffi cient based on the method of characteristics in the form used in the MCCG3D code is presented. Finite-difference analogs of the perturbation theory formulas are derived using the difference scheme of the MCCG3D code. Test calculations were performed. It is shown that the results obtained by perturbation theory and direct calculations converge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. I. Marchuk, Method for Calculating Nuclear Reactors, Gosatomizdat, Moscow (1961).

    Google Scholar 

  2. A. S. Seregin and T. S. Kislitsyna, Synopsis of the Program System TRIGEX–CONSYST–BNAB-90, Preprint FEI-2655 (1997).

    Google Scholar 

  3. I. Kodeli, “Multidimensional deterministic nuclear data sensitivity and uncertainty code system: Method and application,” Nucl. Sci. Eng., 138, No. 1, 45–66 (2001).

    Article  Google Scholar 

  4. M. Williams and B. Rearden, “SCALE-6 Sensitivity/Uncertainty Methods and Covariance Data,” Nucl. Data Sheets, 109, No. 12, 2796–2800 (2008).

    Article  ADS  Google Scholar 

  5. B. Rearden and M. Jessee (eds.), SCALE Code System, Vers. 6.2.2, ORNL/TM-2005/39 (2017).

  6. I. R. Suslov, “Method of characteristics in regions with complex geometry,” At. Energ., 65, No. 1, 57–58 (1988).

    Article  Google Scholar 

  7. A. Marin-Lafl eche, M. Smith, and Ch. Lee, “PROTEUS-MOC: a 3D deterministic solver incorporating 2D method of characteristics,” in: Int. Conf. Mathematics and Computation Methods Applied to Nuclear Science and Engineering, Sun Valley, Idaho, May 5–9, 2013, ID 7525.

  8. W. Boyd, K. Smith, B. Forget, and A. Siegel, “Parallel performance results for the OpenMOC method of characteristics code on multi-core platforms,” in: Int. Conf. PHYSOR 2014, Japan, Sept. 28 – Oct. 3, 2014, ID 1104798.

  9. I. R. Suslov, “Improvements in the long characteristics method and their effi ciency for deep penetration problems,” Prog. Nucl. Energy, 39, No. 2, 223–242 (2001).

    Article  Google Scholar 

  10. H. Greenspan, C. Kelber, and D. Okrent, Computing Methods in Reactor Physics, Gordon & Breach Sci. Pub. Ltd, New York (1968).

    MATH  Google Scholar 

  11. I. V. Tormyshev and I. R. Suslov, “Conjugacy analysis of the fi nite difference equations of the method of characteristics on the basis of a linear algebraic formulation,” At. Energy, 122, No. 6, 369–376 (2017).

    Article  Google Scholar 

  12. Benchmark on the VENUS-2 MOX Core Measurements, OECD/NEA Rep. (2000).

Download references

Author information

Authors and Affiliations

  1. State Science Center of the Russian Federation – Leipunskii Institute for Physics and Power Engineering (IPPE), Obninsk, Russia

    I. R. Suslov & I. V. Tormyshev

Authors
  1. I. R. Suslov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. V. Tormyshev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Tormyshev.

Additional information

Translated from Atomnya Énergiya, Vol. 127, No. 4, pp. 229–232, October, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suslov, I.R., Tormyshev, I.V. Perturbation Theory in the Method of Characteristics. At Energy 127, 255–258 (2020). https://doi.org/10.1007/s10512-020-00619-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10512-020-00619-1

Search

Navigation