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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2020  A DS_{n}SCHEME FOR THE 3D KINETIC TRANSPORT EQUATION IN SPHERICAL COORDINATES
A. I. Bochkov, V. V. Suchkova VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 315.
A scheme for the numerical solution of the 3D timedependent transport equation written in spherical coordinates is presented. The finitedifference approximation to the equation is performed on spatial 3D regular grids and constructed using a scheme with additional relations, and it is conservative. To solve the resultant system of grid equations, an algorithm has been developed, which is based on the sweep method. Results of the method testing on a model problem are given. Key words: 3D transport equation, spherical coordinate system, finitedifference approximation, a system of grid equations, a numerical solution algorithm.
 FULLY CONSERVATIVE SPHSYSTEMS IN GAS DYNAMICS AND A SCHEME FOR NUMERICALLY INTEGRATING THEM I. D. Blazhnov, M. N. Vishnyakova, S. N. Polishchuk, B. P. Tikhomirov VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 1632.
Fully conservative systems are identified among a set of ordinary differential equation systems of the smoothed particles hydrodynamics (SPH) method describing twodimensional axially symmetric flows. A fully conservative SPH system has been constructed with the variational method and is a "duplicate" of the known Brookshaw system for equations in cylindrical coordinates. A modified predictorcorrector method for the numerical integration of SPH systems, which is based on the fully conservative central difference scheme of Lagrangian fluid dynamics, is proposed and it is demonstrated how the method can be used to simulate 2D axially symmetric gas flows. Key words: SPHmethod, axially symmetric flows, the least action principle, Lagrangian fluid dynamics, central difference schemes, a modified predictorcorrector method, the problem of an intense explosion.
 NUMERICAL STUDY OF THE XRAY TRANSPORT IN VACUUM CAVITY V. V. Vatulin, K. A. Volkova, A. A. Kibkalo, P. I. Pevnaya, N. P. Pleteneva, R. M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 3344.
The problem of Xray transport in vacuum cavity of a target has been solved using techniques based on different physical models and mathematical methods: "vacuum" approximation with the use of angular visibility factors, diffusion approximation, multigroup kinetic approximation, and the Monte Carlo method. Key words: transport of Xrays, visibility factors, vacuum approximation, multigroup kinetic approximation, the Monte Carlo method, diffusion approximation.
 "LOGOS" SOFTWARE PACKAGE: SOLUTION OF NONLINEAR TRANSIENT PROBLEMS OF DEFORMABLE SOLID MECHANICS WITH REGARD TO CONTACT INTERACTIONS D. Yu. Dyanov, A. V. Kazantsev, S. V. Starodubov, K. V. Tsiberev, A. A. Chelakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 4559.
The paper describes the basic algorithms for the simulation of contact interactions implemented in the LOGOS software package for nonlinear transient problems in mechanics of a deformable solid. Methods used in LOGOS to determine the interaction forces on contact boundaries are described. Algorithms identifying points of force application are presented. Applicability of the described approaches is demonstrated by the example of verification problem solutions. Key words: LOGOS software package, a computational module for dynamic problems of deformable solid mechanics, contact interaction simulating algorithms, the penalty force method, Lagrangian method of multipliers.
 "LOGOS" SOFTWARE PACKAGE: FUNCTIONALITY FOR THE SIMULATION OF STATIC STRAINS IN LAMINAR COMPOSITES ON THE BASE OF A SHELL FINITE ELEMENT M. F. Abdullin, R. A. Barabanov, A. D. Kvaratskheliya, E. A. Filimonkin, M. V. Kitaev, A. V. Kornev, M. V. Nikitin, E. B. Saganov VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 6070.
The paper describes the LOGOS software package functionality implemented in 20172018 to extend the methods of simulating the static strain processes for thingwalled structures, including those made of laminar composites. These methods and algorithms are constructed on the base of a shell finite element. Successful implementation of the described functional capabilities is demonstrated by the example of solving static strain problems for structural components of aircrafts, including those made of composites. Key words: LOGOS software package, LOGOSSA module, stressstrain state, shell, a laminar composite, physical nonlinearity, geometrical nonlinearity.
 "LOGOS" SOFTWARE PACKAGE: A TECHNIQUE FOR THE SIMULATION OF A STRUCTURE RESPONSE UNDER THE EFFECT OF BROADBAND RANDOM VIBRATION A. Yu. Eremenko, S. S. Kosarim VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 7185.
The paper discusses the specific features of the technique for the simulation of a structure response under the effect of broadband random vibration implemented in the LOGOS software package. The derivation of relations for the calculation of the spectral response of a structure is described in details. The description of two implemented methods for the structure response integration with respect to frequency to obtain rootmeansquare deviations of resultant quantity values is given. The accuracy of the integration methods was compared by the example of the problem simulating the response to vibration of a container during its transportation. Conclusions on the applicability of the analyzed methods were made basing on the comparison results. Key words: broadband random vibration, random processes, normal distribution, spectral power density, modal analysis, a structure response under the effect of broadband random vibration.
 METHODOLOGICAL APPLICATION TESTS DEVELOPED AT RFNCVNIIEF FOR NUMERICALLY STUDYING PARAMETERS OF HPC SYSTEMS A. V. Alekseev, S. P. Belyaev, A. I. Bochkov, A. N. Bykov, M. V. Vetchinnikov, A. N. Zalyalov, A. A. Nuzhdin, S. P. Ognev, N. S. Samsonova, I. S. Sapronov, I. N. Chistyakova, T. V. Shemyakina, R. M. Shagaliev, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 2. P. 86100.
The paper considers the issues of testing highperformance computing systems for the numerical simulation of complex physical processes. Methodological application tests (miniapps) developed at RFNC VNIIEF are reviewed. A test package includes codes for the simulation of various physical processes: neutron transport simulations using difference methods (in kinetic and diffusion approximation) and the Monte Carlo method, gas dynamics, heat transfer, and molecular dynamics processes. These test codes are used to assess the efficiency of paralleling, real performance, and correctness of simulations by highperformance computing systems. The general functionality of test codes, as well as the specific features of algorithms and testing procedures for each code are considered. Key words: highperformance computing systems, numerical simulation of physical processes, a test program, miniapps, efficiency of paralleling, performance.
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