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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2016  ON CORRECTNESS OF VISCOELASTOPLASTICITY MODELS WITH NONNEWTONIAN VISCOSITY
M. A. Guseva, V. N. Sofronov VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 315.
Problems arising in the numerical implementation of viscoelastoplasticity models are considered. In this type of models, von Mises model has been taken for a plastic component and nonNewtonian medium has been taken for a viscous component, for which the viscosity coefficient depends not only on the thermodynamic parameters, but on the reduced velocity of shear strains as well. An attempt has been made to give an answer to the question concerning the extent of arbitrariness of such dependence. The thermodynamic research of correctness is based on constructing the plastic and viscous dissipation functions. There is a common requirement of convexity of these functions relative to fluxes. The conditions (limits on the model parameters), under which the viscous dissipation function is strictly convex for the given form of viscosity, have been identified. For the plastic potential, this requirement is always met, if an ideal plasticity model is used. The condition of evolutionary development (correctness of the Cauchy problem for appropriate differential equations) has been found, this condition coincides with the requirement of convexity of the viscous dissipation function. The conditions (limits on the model parameters and parameters of shock waves) under which the solution for the given form of viscosity exists in the form of a stationary wave have been identified. It is shown that the requirement of convexity of the viscous dissipation function is also a sufficient condition of the structure existence. The viscoelastoplastic model has been used for the numerical simulation of Barker experiments, in which the shock wave front structure has been identified using the laser interferometry method. Two parameter sets of the viscosity model (both with the met and not met requirement of convexity of the dissipation function) have been used to take into account the viscousity properties of a given material. In the first case, a good agreement of the calculated and experimental results is observed. In the second case, there is no passage to the limit with the computational grid refinement Δm > 0 and the shock wave front structure does not agree with that obtained experimentally. So, the results allow concluding that the model parameters should ensure that the dissipation function convexity requirement is met. Key words: viscoelastoplasticity models, nonNewtonian models of viscosity, dissipation functions, condition of evolutionary development, steadystate structures.
 AN ALGORITHM OF CORRECTING A GRID WITH RESPECT TO THE SURFACE OF REVOLUTION O. V. Ushakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 1627.
The paper presents an algorithm of correcting positions of boundary nodes of a structured grid with respect to the surface of revolution generated by the revolution through 180° around its axis of a plane generator of curve consisting of line segments, arcs of circles and ellipses. This correcting algorithm supplements the algorithm of globally reconstructing grids at surfaces of revolution and allows moving boundary nodes during the reconstruction of grids directly over surfaces of revolution, rather than over linear surfaces of cell faces of the original grid. The algorithm can be used independently to correct the grid which nodes moved away from the surface of revolution. The algorithm implementation in software systems used for the global reconstruction of 3D space grids and in individual codes in Fortran and C++ used to correct grids with respect to the surface of revolution allowed significantly improving the efficiency of simulation of multimaterial media. Key words: grids, boundary nodes, surfaces of revolution, projection.
 NUCLEATION OF SPALL IN THE ALUMINIUM WEDGE SAMPLE UNDER THE SLIDING DETONATION LOADING: EXPERIMENTAL STUDY AND NUMERICAL SIMULATION O. B. Drennov, A. G. Ioilev, S. S. Sokolov, V. N. Sofronov, A. L. Stadnik, T. I. Chaika, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 2836.
Experiments on loading Vshape aluminum samples by sliding detonation in a thin layer of high explosive (HE) were performed. Each experiment implements the conditions of spall initiation and development in the twodimensional stressstrained state of material. The obtained experimental data were used to validate the kinetic models of the material damage initiation and development and the damaged material behavior which had been implemented in the TIM and EGAK codes. The validation test results are in a good agreement with experimental data on the length of spall fracture and thickness of spall layer. Key words: detonation, shock wave, spall, fissure, stress, strain, plasticity, hardening, softening, viscosity, damage, fracture, validation, the TIM code, the EGAK code.
 USE OF THE METHOD OF GENERATIONS FOR CONSISTENT SIMULATIONS OF STEADYSTATE CHARACTERISTICS D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 3747.
The simulation of the steadystate characteristics of a critical system can be represented as the solution of the two problems simultaneously: the conditionally critical problem of identifying neutronphysical parameters and the problem of identifying the rest stationary parameters. With the use of a special technique to solve each of the two problems, there is a need to implement an iterative scheme to provide consistency of the obtained characteristics. Hence, there arise questions concerning the scheme convergence and errors in the results. If the method of generations is used to solve the given conventionally critical problem, inherent errors of the method emerge. It is possible to make them indefinitely small, however, with a significant increase in the labor intensity. And if simulations are carried out on multiprocessors, the contribution to the labor intensity of supporting procedures leveling some of these errors may exceed all the rest computational costs. The paper considers the features of the iterative operator used to solve the resultant equation system. It is shown that the scheme minimizing downtime of the method of generations can be constructed with some general assumptions concerning the properties of the system of interest, which allow achieving convergence of iterations. Simulations of the VVER1000 reactor in its steady state are described for the demonstration purposes. Key words: numerical schemes, the simple iteration method, the method of generations, VVER1000.
 STUDYING THE STEADY CONDITIONS OF NATURAL CONVECTION IN A ROTATING SPHERICAL LAYER I. V. Bychin, A. V. Gorelikov, A. V. Ryakhovskii VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 4859.
Software has been developed for the numerical solution of hydrodynamics and heat transfer problems using GPU for simulations. The developed software has been used to study the conditions of natural convection in rotating spherical layers depending on the Ekman, Rayleigh, and Prandtl numbers, as well as on the initial distribution of temperatures. A family of quasistationary solutions differing in their flow structure has been obtained. There have been found the critical values of Ekman number with which the convection process breaks off. Key words: natural convection, computational fluid dynamics, spherical layer, GPU, OpenCL.
 MULTILEVEL ALGORITHMS OF DECOMPOSING A DATA GRAPH FOR PARALLEL SIMULATIONS ON A HETEROGENEOUS COMPUTER SYSTEM N. V. Starostin, M. A. Pankratova VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 6068.
The paper considers the urgent problem of architecturedependent decomposition that allows effectively planning a parallel job execution on a multiprocessor. “Planning” means decomposing the given parallel job for a required number of processors with regard to balance limitations and allocating the obtained portions of the job to the processors to minimize the cost of interprocessor communications. The procedure allows reducing the parallel code runtime. A mathematical formulation of the general problem of architecturedependent decomposition is given, its special cases are discussed, and two multilevel computational algorithms are presented. The first algorithm is based on recursively bisectioning the input problem data and the second one is based on sequentially relaxing the original data with further decomposing the data graph and solving the quadratic assignment problem. The algorithm execution results using test problems are compared with those obtained with the wellknown software products. Key words: architecturedependent decomposition, mapping, parallel code, supercomputer, multilevel algorithm.
 A METHOD FOR CALCULATION OF THE EFFICIENCY OF RADIATION TRANSFER FROM A LATERAL SURFACE OF A CURVED SINGLEMODE OPTICAL FIBER TO AN OPTICAL RECIEVER Yu. V. Malykh, V. V. Shubin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 1. P. 6979.
A method used to calculate parameters of the radiation transfer from a lateral surface of a curved singlemode optical fiber to an optical receiver is described. The major characteristic of the radiation output from optical fiber and the major parameter of its efficiency – the lateral radiation transfer coefficient, kt – are considered. The paper presents the developed optical circuit of radiation transfer from the bend of optical fiber and the order of calculating an optimal position of a receiving singlemode optical device. The paper describes the procedure of calculating the efficiency of matching parameters of the optical receiver and the singlemode fiber bend, as well as losses at the interfaces between various media and losses due to the absorption during the radiation transfer process. The radiation transfer efficiency results obtained with the presented computational method are compared to data of experiments. Key words: bend in a singlemode optical fiber, transition losses, radiation transfer simulation method, a computational method for the efficiency of radiation input to fiberoptic devices.
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