МЕТОД ПОВЕРХНОСТНЫХ ГАРМОНИК ДЛЯ НЕЙТРОННО-ФИЗИЧЕСКОГО РАСЧЕТА ТРЕХМЕРНОГО ГЕТЕРОГЕННОГО РЕАКТОРА С НЕСИММЕТРИЧНЫМИ ЯЧЕЙКАМИ

Abstract

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.