Series: Nuclear and Reactor Constants

since 1971

Русский (РФ)

ISSN 2414-1038 (online)

DOI: 10.55176/2414-1038-2019-4-107-117

Authors & Affiliations

Elshin A.V.1,2, Agalina P.V.2
1 Alexandrov Research Institute of Technoloqy, Sosnovy Bor, Russia
2 Institute of Nuclear Power Engineering (branch) of Peter the Great Saint-Petersburg Polytechnic University, Sosnovy Bor, Russia

Elshin A.V. – Senior Researcher, Head of Department, Dr. Sci. (Tech.), Aleksandrov Science and Research Institute of Technology, Institute of Nuclear Power Engineering (branch) of Peter the Great Saint-Petersburg Polytechnic University. Contacts: 72, Koporskoe shosse, Sosnovy Bor, Leningrad region, Russia, 188540. Tel.: +7 (921) 438-48-55; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..
Agalina P.V. – student, Institute of Nuclear Power Engineering (branch) of Peter the Great Saint-Petersburg Polytechnic University.


The paper addresses the application of the surface harmonics method to building a system of finite difference equations for describing the neutron field of a 3D heterogeneous reactor. The reactor is comprised of cells shaped as right-angled parallelepipeds with non-symmetric contents. Neutrons distribution in the cells is presented as a linear combination of trial functions that satisfy the neutron transport equation and some non-uniform boundary conditions allowing to consider the influence of the cell environment on the neutron distribution within the cell. Even given non-symmetric cells, we can build a system of equations (by sewing the neutron distribution in adjacent cells on joint faces), which, if diffusion approximation is used on the cell faces, are similar in appearance to the finite difference approximation of a group-diffusion equation (using a different method to obtain coefficients of equations, with complete matrices of group neutron diffusion coefficients). Finite-difference equations can also be defined by considering the additional neutron distribution components in cells (trial functions), which are necessary for valid transition to particular cases: two-dimensional and one-dimensional geometry. Due to cell asymmetry, additional components are introduced in equations and formulas for equation coefficients are corrected (correction is similar to the introduction of "discontinuity coefficients" used in foreign codes). As it is shown, the system of equations allows us to avoid using the diffusion approximation in reactor calculations since we can now sew together not only the neutron current density and neutron flux but also higher angular momenta at boundaries of cells without changing the form of equations (increasing the dimension of coefficient matrices and dimension of required vectors). Numerical results are presented on an example of 1D single-velocity test problems.

surface harmonics method, 3D heterogeneous reactor model, finite difference equations, non-symmetric unit cells, avoidance of diffusion approximation

Article Text (PDF, in Russian)


UDC 621.039.51

Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2019, issue 4, 4:11