Skip to main content
SpringerLink
Log in

Finite Difference Equations for Neutron Flux and Importance Distribution in 3D Heterogeneous Reactor

  • Conference paper
  • First Online:
Finite Difference Methods,Theory and Applications (FDM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9045))

Included in the following conference series:

  • 2567 Accesses

Abstract

This paper describes an application of the surface harmonics method to derivation of few-group finite difference equations for neutron flux distribution in a 3D triangular-lattice reactor model. The Boltzmann neutron transport equation is used as the original equation. Few-group finite difference equations are derived, which describe the neutron importance distribution (the multiplication factor in the homogeneous eigenvalue problem) in the reactor core. The derived finite difference equations remain adjoint to each other like the original equation of neutron transport and its adjoint equation. Non-diffusion approximations apply to calculation of a whole reactor core if we increase the number of trial functions for describing the neutron flux distribution in each cell and the size of the matrices of the few-group coefficients for finite difference equations.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bell, G.J., Glasstone, S.: Nuclear Reactor Theory. Atomizdat, Moscow (1974). in Russian

    Google Scholar 

  2. Elshin, A.: The evolution of the surface harmonic method to derive equations for a distribution of neutrons and their importance in a heterogeneous reactor. In: Proceeding of International Topical Meeting on Mathematics and Computations, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France (2005)

    Google Scholar 

  3. Elshin, A.: Obtaining finite difference equations for a heterogeneous reactor with spatial kinetics. AtomnayaEnergiya 103(4), 222–232 (2007)

    Google Scholar 

  4. Corn, G.G., Corn, T.: Mathematical handbook for scientists and engineers. McGraw-Hill Book Company, Inc., New York, Toronto, London (1961)

    Google Scholar 

  5. Laletin, N.I.: Basic principles for developing equations for heterogeneous reactors a modification of the homogeneous method. Nucl. Sci. Eng. 85, 133–138 (1983)

    Google Scholar 

  6. Laletin, N.I., Elshin, A.V.: System of refined finite difference equations for 3D heterogeneous reactor model. Atomnaya Energiya 60(2), 96–99 (1986). (in Russian)

    Google Scholar 

  7. Boyarinov, V.F.: 3D equations of heterogeneous reactors in the method of surface harmonics with one unknown quantity per cell-group. Atomnaya Energiya 72(2), 227–231 (1992). (in Russian)

    Google Scholar 

  8. Elshin, A.V., Abdullayev, A.M.: On reciprocity relations and high order approximations in the surface harmonics method. Proceeding of XXIII inter-departmental meeting: Neutronic problems of nuclear power plants with closed fuel cycle (Neutronics-2012), in two volumes. Obninsk, IPPE. 2, pp. 515–521 (2013) (in Russian)

    Google Scholar 

  9. Methods for calculation of thermal neutron fields in reactor lattices (ed. by Ya. V. Shevelev, PhD), Moscow, Atomizdat, 216–239 (1974)(in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Alexandrov Research Institute of Technology, Sosnovy Bor, Russia

    A. Elshin

Authors
  1. A. Elshin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Elshin .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Sofia, Bulgaria

    Ivan Dimov

  2. Institue of Mathematics and MTA-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Elshin, A. (2015). Finite Difference Equations for Neutron Flux and Importance Distribution in 3D Heterogeneous Reactor. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-20239-6_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation