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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2017  DIRECT NUMERICAL SIMULATION OF A SHOCK WAVE PROPAGATING IN A HETEROGENEOUS MIXTURE OF TWO GASES
Yu. V. Yanilkin, L. G. Korolyova VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 1. P. 316.
The problem of a shock wave propagating in a heterogeneous mixture of two gases is given in 1D, 2D, and 3D formulations and results of simulations by the EGAK code in Eulerian variables (as well as in Lagrangian variables in a 1D case) are presented. It is demonstrated that the 3D simulation, where the distribution of components represents the reality to a higher extent, gives the shock wave propagation velocity close to the analytical solution. Key words: shock wave, heterogeneous gas mixture, numerical simulation, the EGAK code.
 A MODEL OF MEDIUM DISPERSION AT A LIQUIDGAS INTERFACE M. S. Samigulin, P. A. Kucherova, A. L. Yolkina, I. Yu. Tagirova, Yu. F. Danilov, N. V. Nevmerzhitsky VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 1. P. 1729.
An approach to the numerical simulation of the medium dispersion process at a liquidgas interface owing to KelvinHelmholtz and RayleighTaylor instabilities is described. A subgrid model of dispersion based on the analytical dependence of the perturbation amplitude on the conditions at the interface forms the basis for this approach. The model has been implemented in the LEGAK code for the numerical simulation of the dispersed medium dynamics, in which the carrying component dynamics is described in continuum (Eulerian) approximation and the disperse component dynamics  in discrete approximation. The code capabilities to simulate the generation and dynamics of gasdroplet mixtures are demonstrated by the example of describing results of experiments with the explosioninduced surface dispersion of a water layer and liquid acceleration by the compressed gas. Key words: numerical simulation, LEGAK code, dispersion, KelvinHelmholtz instability, RayleighTaylor instability, dynamics of disperse media.
 ON THE CONSTRUCTION OF A MONOTONE DIFFERENCE APPROXIMATION SCHEME FOR THE P_{1}EQUATION SYSTEM A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 1. P. 3045.
In a nonstationary radiation transport problem, the P_{1}approximation leads to a hyperbolic system of equations and its solution causes significant difficulties of constructing a monotone difference scheme of the second approximation order. In a multidimensional case, one fails to construct a monotone scheme even of the first order of approximation for hyperbolic equation systems. The difficulties of constructing monotone schemes for the P_{1}approximation can be explained by the fact that the method of spherical harmonics has the wave effect and may give negative solutions in curved an multidimensional geometries for any P_{n}expansion. The second approximation order and an improved monotone behavior can be achieved by replacing the monotonicity preservation requirement by the requirement of a reduced full variation in nonlinear TVDschemes. The objective of work was to study possible variants of constructing monotone difference approximation schemes for the P_{1}equation system by the example of two schemes. Key words: radiation transport, TVDreconstruction, P_{1}approximation.
 NUMERICAL STUDY OF ACCURACY AND SYMMETRY OF ANGULAR QUADRATURES USED TO APPROXIMATE THE 3D TRANSPORT EQUATION WITH THE METHOD OF DISCRETE ORDINATES FOR KOBAYASHI PROBLEMS M. P. Pepelyaev VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 1. P. 4659.
The paper offers the CB_{n} quadrature to approximate the transport equation in angular variables for the numerical solution with the method of discrete ordinates. This quadrature has the property of symmetry relative to all coordinate axes in contract to the ES_{n} quadrature, which provides symmetry in the XOY plane alone. The principal features of the ES_{n} and CB_{n} quadratures are considered by the example of solving 3D K., Kobayashi benchmarks. Key words: neutron transport equations, quadrature, approximation in angular variables, formulation of Kobayashi problems, benchmark results, simulations for convergence, asymmetry, integral density of neutron flux, indicating points.
 VERIFICATION OF MODELS OF UNSATURATED FLOW AND TRANSPORT IN UNSATURATED ZONE BY EXAMPLE OF CODE GeRa I. V. Kapyrin, V. V. Suskin, A. V. Rastorguev, K. D. Nikitin VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 1. P. 6075.
The main objective of the present work is the verification of a possibility to use the GeRa code to simulate the unsaturated flow and transport processes in unsaturated zone, i.,e. the verification of the corresponding models implemented in the code. Such problems are of most importance for the safety assessment of nearsurface disposals of radioactive wastes and the other nuclear and radiationdangerous objects. The paper presents the analytical and numerical models implemented in the GeRa code and describing the unsaturated flow and transport processes in unsaturated zone. A set of four verification tests is presented, which are the wellknown problems described in literature: the problem of a 1D unsaturated flow into dry soil (Selia test); the Oldenburg and Pruss problem of a capillary barrier; the problem of a 2D saturatedunsaturated flow and transport in heterogeneous unsaturation zone (a training problem for the VS2DT code); and the fullscale experiment on the unsaturated flow and mass transport in a region with drain. For each of the four problems a good qualitative agreement with analytical solutions and experimental data has been achieved and the comparison with results of the wellknown codes FEFLOW, HYDRUS1D, TOUGH2, VS2DT is presented. For the first time, the authors proposed and tested the numerical model of moisture transport using the piecewiselinear replenishment of the height of inflow in cells of computational grid. Key words: unsaturated flow, transport in unsaturated zone, verification, crossverification.
 A TECHNIQUE FOR CALCULATION OF TRANSMISSION GAIN OF RADIATION FROM THE CORE OF A BENDED ONEMODE FIBEROPTIC CHANNEL TO A RECEIVING FIBER OPTICS Yu. V. Malykh, V. V. Shubin VANT. Ser.: Mat. Mod. Fiz. Proc. 2017. No 1. P. 7686.
The paper presents a technique for the calculation of the transmission gain of radiation from the core of a bended onemode optical fiber to a receiving optical fiber. The technique allows accounting the Gaussian beams interaction efficiency (overlap integrals), radiation transmission by all fiberoptic components, and radiation losses depending on the bend length. The developed technique was used to calculate the transmission gain depending on the bend angle and the extraction coefficient for the SMF28 type optical fiber. The calculated results are compared with experimental data. Key words: bended onemode optical fiber, Gaussian beams, radius of mode spot, gain of radiation transmission through a lateral surface.
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