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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2018  METHODOLOGICAL ISSUES OF SIMULATING TRANSIENT PROCESSES IN SEMICONDUCTORS
M. V. Gorbatenko, S. S. D’yakov, D. V. Opasin, B. N. Shamrayev VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 4. P. 318.
The paper considers difference schemes for solving the continuity equations of charge carriers in semiconductors to select a costeffective scheme for solving multidimensional problems of the radiation effect on semiconductors. A modification to the classic ShockleyHallReed kinetics is described, which provides the charge conservation during recombination. The calculated results are compared with analytical estimates and experimental data on the (p–n)junction breakdown. Key words: charge carrier statistics, drift, diffusion, recombination kinetics, (p–n)junction breakdown.
 CONSTRUCTING A SCHEME TO SOLVE THE NUCLEI KINETICS PROBLEM D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 4. P. 1928.
The nuclei kinetics problem is the Cauchy problem for a system of differential equations in which the righthand sides, in a simplest case, are the functional on the transport equation solution. The resultant equation system is rigid. It is usually solved with the specialized methods using the behavior specifics of the given system physical characteristics. A most common approach is the use of the firstorder scheme, although it seems a higher order of accuracy could allow reducing the labor input. However, the analysis has demonstrated that, in general, the construction of scheme above the second order of accuracy is impossible. Results of simulations for a methodological problem are presented as an example and they demonstrate that even such schemes allow significantly decreasing the amount of calculations for solving problems, which are not too extremal. Key words: nuclei kinetics, numerical schemes, Cauchy problem, an integration scheme, the particle transport equation, the method of generations.
 THE GRID EFFECTS IN THE NUMERICAL SIMULATION OF THERMAL RADIATION A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 4. P. 2945.
One of the most difficult problems to solve in the transport theory is the radiation transport equation. The difficulty of solving this equation is mainly due to a significant nonlinearity of all quantities of interest and large dimensions of space under consideration. Effects not associated with the physics of simulated process occur in the numerical simulation of the heat flux transport equations and makes it difficult to achieve a proper understanding of these phenomena. The description of the grid effects and examples of model problems, which simulation clearly demonstrate these effects, are given. Key words: radiation transport, numerical simulation.
 NUMERICAL IMPLEMENTATION OF A 3D THERMALHYDRAULIC MODEL USING THE IMMERSED BOUNDARY METHOD IN THE "KORSAR/CFD" CODE Yu. V. Yudov, S. S. Chepilko, I. G. Danilov VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 4. P. 4656.
A numerical implementation of a CFD module based on the immersed boundary method included in the KORSAR/CFD code using the semiimplicit scheme is described. The KORSAR/CFD code has been developed from the KORSAR/GP thermalhydraulic system code certified by the ROSTECHNADZOR (Federal Environmental, Industrial and Nuclear Supervision Service of Russia) in 2009 for the numerical safety analysis of VVER reactors. The CFD module is intended for representing threedimensional effects in the reactor lower plenum and used in spatial simulations of coupled thermalhydraulic (in the subchannel analysis approach) and neutronic processes in the reactor core during asymmetrical loop operation. The module is based on the immersed boundary method and Cartesian cut cell approach. To improve the numerical scheme stability, small cutcells are merged with appropriate large neighboring cells. The diffusion and convection terms in conservation equations are approximated on the collocated grid with the second order accuracy using the central difference scheme and the bounded continuously differentiable SDPUSC1 scheme, respectively. The time integration of the conservation equations is implicitly performed by the secondorder KimChoi scheme. The Poisson equation for pressure is solved with the geometric multigrid method. Results of testing the method on the Karman vortex street problem, where a uniform laminar stream flows over a circular cylinder, are presented. Key words: CFDmodule, immersed boundary method, multigrid method, Karman vortex street.
 MPI+OpenMP PARALLEL IMPLEMENTATION OF THE CONJUGATE GRADIENT METHOD WITH FACTORIZED EXPLICIT PRECONDITIONINGS I. E. Kaporin, O. Yu. Milyukova VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 4. P. 5769.
For the preconditioning of a symmetric positive definite sparse matrix, its approximate inverse is considered in the form of a product of an upper triangular sparse matrix by its transpose. Several choices of sparsity structure for the preconditioners are considered and analyzed. Parallel implementation of the corresponding linear solvers within the MPI+OpenMP framework is proposed. Comparative timing results are presented based on preconditioned conjugate gradient solution of test problems from the University of Florida sparse matrix collection using MPI, or MPI+OpenMP algorithms. The comparison also includes the point Jacobi preconditioning and the Block Incomplete Inverse preconditioning with the 2nd order Cholesky factorization within the blocks. Key words: sparse matrices, conjugate gradient method, explicit preconditioning, incomplete inverse triangular factorization, parallel computing.
 MODULE OF GEOMETRIC CORE GeoCore IN "3DRND" PROGRAM PACKAGE D. V. Loginov VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 4. P. 7075.
The problem of constructing a grid on a surface of revolution deformed by another surface of revolution is considered. To solve it, a nonstationary algorithm of constructing grids in regions with moving deformable boundaries is suggested. This algorithm includes three stages: a preparatory stage followed by deformation and optimization stages. In the preparatory stage, the deforming body shape (whether a cone, a cylinder, or a sphere) is identified and the coordinate system transformations are performed. In the deformation stage, the deforming body puts pressure on the surface of revolution and the deformation step is selected. Nodes subjected to deformation are displaced with respect to the selected step and projected to the deforming surface (body). In the optimization stage, the deformed grid quality is improved. The main criteria for the assessment of the grid quality are nondegeneracy, smoothness, and similarity to uniform and orthogonal grids. The deformation and optimization stages are repeated till the achievement of the required deformation, with the deforming body occupying the specified position inside the deformed region. The algorithm is implemented in a C++ software system. Key words: structured grid, axially symmetric region, deformed grid, optimal grid, moving grid.
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