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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2016  INVESTIGATION OF THE ITERATION CONVERGENCE RATE OF THE VDEPF METHOD USED FOR JOINTLY SOLVING THE ENERGY AND RADIATION TRANSPORT EQUATIONS
A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 316.
The application of implicit schemes for the mathematical modeling of the thermal radiation transport requires studying the convergence problem of the iterative process of solving a system of photon and energy transport equations. The paper considered some modifications to the method of identifying a diagonal element in the corrector form for iteratively solving a nonlinear system consisting of the photon transport equation and energy transport equation. The iteration convergence rate is theoretically investigated. Key words: radiation transport, iteration convergence rate.
 NONSTATIONARY PROBLEMS FOR TESTING ELASTOPLASTICITY CODES A. A. Krayukhin, V. A. Svidinskii, A. L. Stadnik, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 1730.
The paper describes three nonstationary test problems for the verification of elastoplasticity codes. The first problem consists in finding the velocity of a moving longitudinal wave in elastic media of different configurations, such as an unbounded medium, a plate, and a bar. The second one is the problem of accelerating a system of elastic components by a pressure pulse, or an impactor. Its analytical solution has been found for the system of three components in the form of bars, or plates. In the third problem a plane elastoplastic wave propagates in an unbounded medium. The problem has been analytically studied in details. Results of numerical simulations with the EGAK code are presented for the problems above. Key words: verification, test problems, d’Alembert method, longitudinal wave, the EGAK code, elastoplastic wave.
 APPLICATION OF THE ALGORITHM OF CORRECTING A GRID WITH RESPECT TO THE SURFACE OF REVOLUTION O. V. Ushakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 3137.
The paper considers the application of the algorithm of correcting a grid with respect to the surface of revolution generated by the revolution through 180° around its axis of a plane curve generator consisting of straightline segments, arcs of circles, and ellipses. The algorithm is used during the global reconstruction, or optimization of structured grids. Key words: grids, boundary nodes, correction, surfaces of revolution.
 3D NUMERICAL SIMULATION OF THE VORTEX RING GENERATION DUE TO A RISING THERMAL IN ATMOSPHERE O. G. Sin’kova, V. P. Statsenko, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 3847.
The generation of a vortex ring due to a rising atmospheric thermal (light cloud) in the earth gravity field is studied numerically. 3D simulations were carried out with the EGAK code. Results of these simulations are compared with the approximate analytical solutions for the motion of a buoyant vortex ring verified using the existing experimental data. Key words: buoyant volume, field of gravity, vortex ring, turbulence, numerical simulation.
 DIRECT NUMERICAL SIMULATION OF NEARWALL TURBULENCE IN PLANE CHANNEL IN A WIDE RANGE OF REYNOLDS NUMBERS D. G. Asfandiyarov, S. A. Finogenov, V. M. Goloviznin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 4858.
The paper presents direct numerical simulation results for the nearwall turbulence in a plane channel obtained using computational grids of 4 x 10^{6} to 34 x 10^{6} cells for Reynolds numbers 5 600, 13 750, 21 900. Simulations were carried out using the modified CABARET scheme. The choice of geometrical sizes for the computational domain and computational grids is justified based on the analysis of correlation dependences and spectral characteristics of flow. The simulation results were used to obtain standard parameters of the turbulent flow in plane channel, namely, the averaged velocity profile, components of turbulent stress tensor, contributions from the molecular and turbulent components of viscosity tensor, and the channel resistance coefficient. It is shown that they are in a good agreement with the data calculated for a similar problem using the pseudospectral scheme. All simulations were carried out on supercomputer "Lomonosov". Key words: direct numerical simulation, scheme CABARET, turbulent flow in plane channel, viscous incompressible fluid.
 NUMERICAL SIMULATION OF IMPACTS OF STEEL IMPACTORS AND ALUMINUM TARGETS AT A VELOCITY OF 6.2 KM/S USING SPH CODE OF LOGOS SOFTWARE PACKAGE I. V. Kovalenko, N. A. Zhavoronkova, E. I. Lipenkova, Yu. N. Bukharev VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 5965.
The paper describes several problems of a highspeed impact and presents results of the 3D simulation for these problems using the SPH code of LOGOS software package developed at FSUE "RFNCVNIIEF" (Sarov, N.Novgorod region). The work objective was to obtain verification data for the conditions of interaction at a velocity of 6.2 km/s between a discshaped target made of aluminum alloy AMg6 and an impactor (a sphere, or a disc) made of steel EP637 by comparing results of simulations with the earlier published data of experiments and results of simulations using other codes. Stability of the numerical simulation results obtained for the problems of impacting an Al disk by a steel spherical impactor and their satisfactory agreement with the available experimental and earlier calculated data have been demonstrated. For the shockwave phase of a planar impact of two discs, there have been found noticeable oscillations of pressure and mass velocity relative to the expected analytical values, which can be lowered, in particular, by optimizing the artificial viscosity parameters in the computational algorithm. Key words: numerical simulation, highspeed impact, SPH code, LOGOS software package, impactor, target.
 GEOMETRICAL INTEGRATION OF 3D ISOBARIC FLOW EQUATIONS OF AN IDEAL INCOMPRESSIBLE FLUID V. E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 6674.
A geometrical method is used to integrate equations describing 3D isobaric flows of an ideal incompressible fluid. An equivalent system of external equations is matched with the system of differential equations. It is shown that the original differential system integrability is conditioned by expansibility of the corresponding external forms and full integrability of the distribution associated with these forms. As a result, a general solution to the 3D isobaric flow equations has been found and the geometrical cause of integrability of these equations has been identified. The same is valid for 2D equations also, however, the integration of 2D equations is trivial and not considered in the paper. Some other authors have already found the general solution to isobaric equations using traditional methods and, therefore, the integration method described here is of interest from viewpoint of methodology. Key words: ideal incompressible fluid, isobaric flows, differential forms, associated distribution, full integrability, a general solution to isobaric flow equations.
 MATHEMATICAL MODEL OF URANIUM HEXAFLUORIDE DESUBLIMATION A. A. Orlov, A. F. Tsimbalyuk, R. V. Malyugin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 2. P. 7583.
The paper presents a nonstationary mathematical model of the UF_{6} desublimation in a vertical storage vessel regarding the convection and UF_{6} desublimation on a bottom wall, as well as the ellipticity of the upper and lower walls of the vessel. Simulation results are presented for the linear desublimation rate, thickness of a solid layer, temperature distribution in the vessel walldesublimate layer system, and dynamics of filling out the 2,5 m^{3} cylindrical vessel with solid UF_{6} as functions of time. Key words: uranium hexafluoride, desublimation, mathematical model, heatandmass transport, nonstationary process, gas dynamics, Stephen problem, a mobile grid, SIMPLE algorithm, iterationinterpolation method.
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