Open AccessComparison of the operation of the equations of the surface harmonics method and the finite difference method in the test problem
Author(s) -
A. V. El’shin,
A. U. Koreshkova,
A. K. Makovets
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1689/1/012007
Subject(s) - finite difference method , finite difference , homogenization (climate) , mathematics , piecewise , mathematical analysis , finite difference coefficient , diffusion equation , finite element method , harmonics , mixed finite element method , physics , biodiversity , ecology , economy , quantum mechanics , voltage , economics , biology , service (business) , thermodynamics
Currently, one of the main methods of neutron-physical calculation of the reactor is the homogenization method, in which after obtaining effective small-group characteristics of cells, the heterogeneous core, in fact, turns into a piecewise homogeneous one. To find the distribution of neutrons in such a zone, the diffusion equation is solved by finite-difference (or nodal) methods. One of the methods justifying this approach is the surface harmonics method (SHM), which in the initial period of its development acted as a justification and refinement of the homogenization method. In the simplest versions of the SHM, the resulting finite-difference equations are reduced to a form similar to the finite-difference approximation of the diffusion equation. It is interesting to compare in the simplest cases the advantages and disadvantages of a simple finite-difference approximation of the diffusion equation and the finite-difference equations obtained using SHM. An analytical comparison is made using the example of two-dimensional geometry. To do this, the paper briefly describes how to obtain equations in SHM.