Advertisement

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

  • A. ElshinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)

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.

Keywords

Neutron Flux Trial Function Adjoint Equation Reactor Core Cell Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bell, G.J., Glasstone, S.: Nuclear Reactor Theory. Atomizdat, Moscow (1974). in RussianGoogle Scholar
  2. 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. 3.
    Elshin, A.: Obtaining finite difference equations for a heterogeneous reactor with spatial kinetics. AtomnayaEnergiya 103(4), 222–232 (2007)Google Scholar
  4. 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. 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. 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. 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. 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. 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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Alexandrov Research Institute of TechnologySosnovy BorRussia

Personalised recommendations