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Since 1978
Published in Sarov (Arzamas-16), Nizhegorodskaya oblast |
RUSSIAN FEDERAL
NUCLEAR CENTER -
ALL-RUSSIAN RESEARCH INSTITUTE
OF EXPERIMENTAL PHYSICS |
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 Русский |  English
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Issue No 4, 2012 |
A POLINOMIAL APPROXIMATION METHOD FOR THE STEP OPERATOR OF THE HEAT CONDUCTIVITY EQUATION
O. M. Kozyrev, V. P. Litvinov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 3-12.
Given here is for solving the boundary-value problems of the heat conductivity equation. The method is based on constructing a difference step operator in the form of an operator polynomial. The operator polynomial is constructed in the space of Fourier images using Chebyshev and Lanczos polynomials. The solution algorithm represents explicit stepwise calculations and is implemented in the form of {it predictor-corrector} scheme. The method is easy to implement and can be efficiently parallelized. The method is described by the example of Cauchy problem for the linear heat conductivity equation. Results of numerical solutions for some well-known test problems are presented.
Key words: heat conductivity equation, Fourier image, Chebyshev and Lanczos polynomial.
| | A PENOMENOLOGICAL MODEL OF THE DAMAGE EVOLUTION KINETICS IN SOLIDS UNDER PULSE IMPACTS S. S. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 13-26.
A phenomenological model of kinetics describing the origination and evolution of damages in solid materials under the effect of pulse loadings and compaction of fractured materials under the effect of compression forces is presented. A continual-kinetic approach was used to construct the model, in which fracturing is simulated as the process of accumulating damages under the effect of tensile stresses and shear strains. Results of the numerical simulation of fracture in wedge-like uranium samples and a flat aluminum sample are given along with comparison between the calculated results and experimental data.
Key words: phenomenological model, origination and evolution of damages, fracture due to shear strains and tensile stresses, compacting, validation simulations.
| | NUMERICAL STUDY OF ENERGETIC PARAMETERS OF A SUPERSONIC CHEMICAL OXYGEN-IODINE LASER WITH FLOW MIXING VARIATIONS Yu. N. Deryugin, B. A. Vyskubenko, D. K. Zelenskiy, S. P. Il`in, Yu. V. Kolobyanin, E. A. Kudryashov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 27-38.
The paper presents a mathematical model and a 3D computational technique for studying the structure of non-equilibrium flows and determining the energy characteristics of a chemical oxygen-iodine laser. The mathematical model includes the main kinetic processes in an active medium of the laser and the processes of generating laser radiation both in stable and unstable resonators. A 3D computational technique is based on solving both complete and parabolic Navier-Stokes equations and allows describing non-equilibrium fluxes of subsonic and supersonic flows (including those in the resonator area), and supersonic flow mixing, as well as determining the energy parameters of the laser.
The energy parameters of a supersonic oxygen-iodine laser with mixing devices of various types have been studied numerically. For each type of mixing device, there have been identified optimum conditions with respect to geometry and composition of the injected gas under which maximum values of the laser energy parameters can be implemented. It is demonstrated that all the studied configurations of mixing devices are acceptable and allow achieving high enough energy parameters of the laser. Maximum values of parameters - radiation power ≈ 99 kW, specific energy rejection 300 J/g, chemical efficiency 35% - have been achieved for a nozzle unit with a three-row tube injector and this result is in a good agreement with the achieved results of experiments.
Key words: chemical oxygen-iodine laser, mathematical model, computational technique, radiation generation parameters, chemical efficiency.
| | ESTIMATION OF THE EFFICIENCY OF CODES FOR STIFF DIFFERENTIAL EQUATION SYSTEMS IN PROBLEMS OF COMBUSTION PHYSICS V. K. Ryabinin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 39-47.
The efficiency of three codes, which are the integrators of ordinary differential equation systems of a high degree of mathematical stiffness, has been studied. Such equations occur during the description of kinetics of branched chain reactions typical for the combustion processes and explosive transformations. The integrators have been tested by the example of three model problems, which are specific to the gaseous combustion physics.
Key words: mathematical simulation, combustion, chemical kinetics, stiff differential equations, software testing.
| | SYSTEMS FOR COMPUTER SIMULATION OF HIGH-ENERGY NUCLEAR REACTIONS AND PREPARATION OF ACTIVATION NUCLEAR DATA A. A. Andrianov, Yu. A. Korovin, I. S. Kuptsov, A. A. Natalenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 48-59.
The paper describes integrated software systems IViS SMPI and InIS HAND developed by the authors to improve the effectiveness of fundamental and application studies in the field of constant supply for the simulation of advanced nuclear power reactors. The algorithm of acquiring nucleophysical data using the developed software, which is based on the advanced methods of the multiple-criteria decision-making theory, is described.
Key words: models of high-energy nuclear reactions, software systems, interactive media, methods of multiple-criteria decision-making theory, factorial analysis, estimated nucleophysical data.
| | NUMERICAL SIMULATION OF UNSTEADY-STATE HEAT-AND-MASS TRANSPORT PROCESSES IN A GAS-WATER-OIL MIXTURE MOOVING THROUGH THE CENTRIFUGAL ELECTRICAL PUMP PASSAGE V. M. Konyukhov, I. V. Konyukhov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 60-69.
A mathematical model of transient thermohydrodynamic processes taking place in a multiple-stage immersion centrifugal electrical pump during the replacement of water by a three-phase mixture in the stage of putting a production oil well into operation has been constructed. A numerical model and a corresponding software complex have been developed. The specific features of water replacement by a water-oil-gas mixture in the pump passages and variations in the performance characteristics of the pump stages have been studied on the base of computational experiments.
Key words: mathematical support, software complex, numerical simulation, multiphase fluxes, oil stratum, producing well, centrifugal electrical pump, data bank.
| | THE EFFECT OF MICROVOLUME PARAMETERS OF VLSI CIRCUIT COMPONENTS ON THE ENERGY OUTPUT DUE TO THE IMPACT OF PROTONS A. V. Afonin, L. A. Grishantseva, V. A. Polunin, A. I. Chumakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 70-73.
Reduction of active dimensions of components in integrated circuits leads to a higher sensitivity to local radiation effects caused by nuclear particles. The paper describes efforts on the numerical simulation by GEANT4 code of the energy output processes under the effect of 15 ÷ 1 000 MeV protons in VLSI circuit components with a variety of their shapes and scales in the standard environment. The results obtained for sensitive areas of micron scales demonstrate that the energy output maximum in a microvolume weakly depends on the charge accumulation conditions; account for particles generated outside the sensitive volume provides an almost 3 times increase of the probability of energy output; a maximum value of energy output actually remains unchanged with proton energies above 50 MeV.
Key words: proton radiation, integrated circuit, energy output, charge collection effect, GEANT4 numerical code.
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