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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 3, 2017  CLOSING MODELS FOR LAGRANGIAN GAS DYNAMICS AND ELASTOPLASTICITY EQUATIONS IN MULTICOMPONENT CELLS. PART 1. ISOTROPIC MODELS
Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 3. P. 421.
This paper describes the first part of the work, which overviews models of closing the Lagrangian gas dynamics and elastoplasticity equations in multicomponent (mixed cells) containing two and more components. Part 1 describes isotropic models and gives a brief description of the methods based on these models, many of them have been implemented in the EGAK code. In view of a large number of various models and methods, results of testing them are presented in Part 2. Key words: multicomponent gas dynamics and elastoplasticity, difference scheme, mixed cell, closing models, the EGAK code.
 CLOSING MODELS FOR LAGRANGIAN GAS DYNAMICS AND ELASTOPLASTICITY EQUATIONS IN MULTICOMPONENT CELLS. PART 2. ANISOTROPIC MODELS Yu. V. Yanilkin, O. O. Toporova, V. Yu. Kolobyanin VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 3. P. 2238.
This paper continues describing the work presented in Part 1 written by one of the authors, which overviews isotropic models of closing the Lagragian gas dynamics and elastoplasticity equations in multicomponent (mixed cells). Part 2 contains the description of anisotropic closing models. It briefly describes the methods based on these models and implemented in the EGAK code. The paper also considers additional relations, which are necessary to simulate mixed cells. Test computation results are presented. Key words: multicomponent gas dynamics and elastoplasticity, difference scheme, mixed cell, closing models, test computations.
 SOLVING THE 2D THERMAL RADIATION TRANSPORT EQUATION IN THE MULTIGROUP QUASITRANSPORT APPROXIMATION D. A. Koshutin, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 3. P. 3950.
Solution of the spectral radiation transport equation is one of the challenging problems in the transport theory due to a high dimensionality of space. This is the reason for using different approximations, which allow reducing the given transport problem to a simpler problem. The paper describes the model for the heat transport simulation in the multigroup quasitransport approximation for a 2D geometry, which has been developed by introducing multiplying factors for path in the diffusion approximation. The model problem solution results are compared. Key words: radiation transport, quasitransport approximation.
 MATHEMATICAL MODELING OF UNSTEADY SEPARATION PROCESSES IN A CASCADE OF GAS CENTRIFUGES FOR SEPARATION OF KRYPTON ISOTOPES A. A. Orlov, A. A. Ushakov, V. P. Sovach VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 3. P. 5161.
Operation of a cascade of gas centrifuges is associated with unsteady separation processes. They lower the effectiveness of cascade and affect the final product quality. In this connection, the fullscale accounting of unsteady processes in the multicomponent isotope mixture separating stage has become an urgent problem. By present time, there have been developed mathematical models of unsteady separation processes with a restricted application area, i.e. the simulation is possible only for steady hydraulic parameters of a gas centrifuge cascade. Earlier, the paper authors developed a mathematical model of unsteady hydraulic processes in gas centrifuge cascades for the separation of multicomponent isotope mixtures and tested it for separation of Si, Xe, W, and Ni isotopes. It was demonstrated that the model properly described unsteady hydraulic processes. The present paper describes the development of a mathematical model of unsteady separation processes in a gas centrifuge cascade for the separation of multicomponent mixtures of isotopes. The model was verified by calculating parameters of unsteady separation processes in a model cascade of centrifuges for separating krypton isotopes. Comparison between the calculated parameters and data obtained by other authors demonstrates that the model properly describes unsteady separation processes in a cascade of gas centrifuges for the separation of multicomponent isotope mixtures. Key words: gas centrifuge, multicomponent mixture of isotopes, separating stage, isotope, hydraulics, separation, modeling, unsteady processes.
 TWOLEVEL PARALLELING OF EXPLICIT DIFFERENCE SCHEMES IN EGAK CODE V. Yu. Kolobyanin, A. A. Fedorov, N. P. Antipina VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 3. P. 6269.
The paper describes the twolevel paralleling (in shared memory and distributed memory) of explicit difference schemes in the EGAK code. The transfer from the onelevel paralleling model (in distributed memory) to the twolevel model is described. Results of numerical scalability tests are presented. Key words: the EGAK code, twolevel paralleling, paralleling efficiency, parallel computers.
 RAMZESKP CODE ON HYBRID PARALLEL COMPUTERS WITH GRAPHICS ACCELERATORS A. N. Bykov, D. G. Gordeyev, V. G. Kudelkin, E. A. Sizov, A. A. Fedorov VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 3. P. 7076.
The paper describes the RAMZESKP code (for gas dynamic equations with regard to heat conduction) for a hybridarchitecture parallel computer comprising generalpurpose processors and graphics accelerators. Program profiling and optimization results are presented. The paralleling efficiency values achieved by using a homogeneous multiprocessor (with generalpurpose processors only) and a hybrid computer to solve the same problems are given. Key words: RAMZESKP, graphics accelerators, arithmetic accelerators, acceleration, paralleling, MPI, efficiency, implicit gas dynamics, heat conduction.
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