E. N. Aristova

Boundary conditions implementation in bicompact schemes for the linear transport equation

Boundary conditions implementation in previously proposed bicompact schemes is studied. These schemes are constructed by the method of lines for a linear transport equation. These schemes are conservative, monotonic, and economical and can be solved by running calculation method. Methods are proposed for the boundary conditions implementation in bicompact schemes that ensure their high accuracy by using A- and L-stable diagonally implicit Runge-Kutta schemes with the third-order approximation for the time integration of the transport equation.

Efficiency of quasi-diffusion method for calculating critical parameters of a fast reactor

The efficiency of different implementations of the iterative process for solving a multigroup system of transport equations on the basis of the quasi-diffusion method is considered. Computations are performed for a two-dimensional model of the core of the BN-800 reactor working in the selfadjustable neutron-nuclear regime (SANNR). The results of this work make it possible to develop efficient methods for simulating the nonstationary behavior of fast reactors in the SANNR in any multidimensional geometry.

Bicompact Schemes for an Inhomogeneous Linear Transport Equation

The bicompact finite-difference schemes constructed for a homogeneous linear transport equation for the case of the inhomogeneous transport equation are generalized. The equation describes the transport of particles or radiation in media. Using the method of lines, the bicompact scheme is constructed for the initial unknown function and the complementary unknown mesh function defined as the integral average of the initial function with respect to space cells. The comparison of the calculation results of the proposed method and the conservative-characteristic method is carried out. The latter can be assigned to the class of bicompact finite-difference schemes; however, this method is based on the idea of the redistribution of incoming fluxes from illuminated edges to unilluminated edges.

Implementation of the quasi-diffusion method for calculating the critical parameters of a fast neutron reactor in 3D hexagonal geometry

A numerical technique for solving a multigroup neutron transport equation with quasi-diffusion aimed at determining critical parameters of fast reactors capable of long-term operation in a self-adjustable neutron nuclear mode (SANNM) is described. The method for solving a multigroup neutron transport equation is based on the Gol’din quasi-diffusion method. The conservative-characteristic method for solving the transport equation which was proposed earlier is extended to the case of three-dimensional (3D) hexagonal geometry. Approximation of quasi-diffusion equations is suggested. The effective algorithm is constructed based on all reactor arrangement symmetries possible in the case of the reactor operation in a self-adjustable mode. The calculations are performed for a 3D model of the active zone of the BN-800 type reactor capable of operation in SANNM. The results of the study can be used for dynamic simulation of active zones in fast reactors.

Low-cost calculation of multigroup neutron transport equation for the recalculation of spectrum-averaged cross sections

The procedures of the recalculation of the multigroup equation of neutron transport in the two-dimensional r-z geometry based on the quasi-diffusion method are described. The quasi-diffusion method allows a considerable reduction of the required iterations of the source and increases accuracy of the calculation. The procedure is demonstrated on the calculation results of a two-dimensional model of the active zone of the BN-800 reactor working in the self-controlled neutron-nuclear mode.

Monotonization of a highly accurate bicompact scheme for a stationary multidimensional transport equation

A variant of a hybrid scheme for solving the nonhomogeneous stationary transport equation is constructed. A bicompact scheme of the fourth order approximation over all space variables and the first order approximation scheme from a set of short characteristic methods with interpolation over illuminated faces are chosen as a base. It is shown that the chosen first order approximation scheme is a scheme with minimal dissipation. A monotonic scheme is constructed by a continuous and homogeneous procedure in all the mesh cells by keeping the fourth approximation order in domains where the solution is smooth and maintaining a high level of accuracy in the domain of the discontinuity. The logical simplicity and homogeneity of the suggested algorithm make this method well fitted for supercomputer calculations.

Bicompact schemes for an inhomogeneous linear transport equation in the case of a large optical depth

B.V. Rogov’s compact difference schemes are considered, which are constructed for an inhomogeneous linear transport equation inherent in the description of the transport problems of radiation or particles in a medium. The transition from a multigroup description of the energy dependence of the transport equation solution to the Lebesgue averaging method implies a strong expansion in the range of the absorption coefficient variation, especially in the direction of its increase. This paper proposes a new method for the solution of the monotonization of problems with a large optical depth, which significantly improves the accuracy of the solution in the case of its nondifferentiability, with an accuracy close to that of conservative characteristic schemes.

Project of the active zone for the BN-800 type reactor operating without a reactivity margin under minimal control over a long period of time

Parameters are suggested for the active zone (AZ) and control of a BN-800 type reactor with uranium-plutonium oxide fuel and primary sodium, which ensure the establishment of a self-adjusting neutron nuclear mode of second type (SANNM-2). In the SANNM-2 the reactor operates without a reactivity margin and fuel replacement in a mode close to the equilibrium one over a long period of time. This significantly improves the reactor’s safety and efficiency. Mathematical modeling of the AZ for the BN-800 type reactor is performed within the framework of a one-and-a-half-dimensional dynamical model based on the quasidiffusion transfer equation.

Second-order short characteristic method for solving the transport equation on a tetrahedron mesh

In this paper the second order approximation method on unstructured tetrahedral mesh for solving the transport equation with the help of short characteristics is constructed. The second-order interpolating polynomial is constructed from the values at the vertices of an illuminated face with the use of the values of the integrals of the required function along the edges of the same face. The value at the unilluminated vertex is obtained by integrating along the backward characteristic interval inside the tetrahedron from the interpolated value on the illuminated face. The accuracy of the method depends on the interpolation accuracy and on the source integration along the interval of the characteristic. In the case of piecewise constant approximation of the source part, the method is of the second order, assuming the solution to be sufficiently smooth. On test problems it is shown that the convergence rate of the method is slightly smaller than two in the case of smooth solutions, while this rate is smaller than one for nondifferentiable solution.

Lebesgue averaging method in serial computations of atmospheric radiation

The Lebesgue averaging method was applied to the numerical simulation of the radiative transfer equation. It was found that the method ensures good accuracy, while the amount of computations with respect to the energy variable is reduced by more than three orders of magnitude. “Fast” simplified techniques for the Lebesgue processing of photon absorption cross sections in serial computations of atmospheric radiation were examined. Attention was given to the convenience of using the techniques, including by experienced users.