This article describes a computer program for visualization of the process of solving the diffusion equation by the source iteration method. This method is used in the overwhelming majority of software systems for calculation of VVER and RBMK reactors. This program allows you to visually demonstrate the process of obtaining the neutron field micro-and macrostructure (macrofield) in course of the iterative solution of the equation. Visualization of the iterative process allowed us to establish the fact of the rapid appearance of the microstructure of the solution at the first iterations and the slow appearance of the macrofield of the neutron flux density. This fact made it possible to propose a new approach for solving the diffusion equation, namely, to extract the low-frequency component from the initial data of macroscopic interaction cross sections using digital filtering methods; then initially perform the calculation with filtered macroconstants on a coarse grid, and finally on a fine grid. The studies have shown that the calculation of reactor is accelerated several times even on a one-dimensional model, which means that when solving a three-dimensional problem, the solution speed will increase by orders of magnitude. This is important when solving optimization problems and «online» calculating emergency situations.

No abstract