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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2013  DISPERSION AND VISCOSITY IMPACT ON EXPANSION SHOCKS PARAMETERS FOR GENERAL NONCONVEX EQUATION OF STATE
Yu. A. Bondarenko, V. N. Sofronof, Yu. E. Dudnik VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 317.
The admissibility conditions of expansion shocks were obtained in the case of general equation of state with nonconvex insentropy with normal dispersion as a main process smearing the jump out, and with no viscosity. They differ from admissibility condition of shocks at the defining role of viscosity. For Bizarrium problem with nonconvex equation of state the exact disperse solution is given for the disperse condition of expansion shocks admissibility differing from the viscous exact solution with admissibility viscous condition of expansion shocks obtained by O. Heuz´e, S. Jaouen, H. Jourdren. The computations showed that grid refinement numerical solutions approximate the viscous exact solution when using the dominating expansion viscosity, and in case of its absence the solutions approximate the disperse exact solution. It may be concluded that the selection problem of the only and “correct” expansion shock in gas dynamics computations should be solved at the level of physical models selection in terms of the main physical processes to be omitted for the ideal gas dynamics equations. Key words: expansion shocks, admissibility conditions, viscosity, dispersion, selfsimilar solution, numerical convergence.
 ANALYSIS OF THE ORDER OF NUMERICAL CONVERGENCE OF THE TVDSCHEME FOR SOLVING THE HEAT TRANSFER EQUATION IN THE P_{1}APPROXIMATION A. S. Vershinskaya, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 1833.
We study the order of numerical convergence of two nonlinear difference schemes proposed for solving the heat transfer equation in the P1approximation. The first scheme is based on a sweep monotonic scheme with firstorder invariants. The second scheme is built by TVDreconstruction of the first scheme using a corresponding monotonic limiter and is formally considered to have the second order of approximation. Key words: heat transfer, TVDscheme P_{1}approximation.
 MONTECARLO SIMULATION OF INELASTIC SLOW NEUTRON SCATTERING A. N. Ivanov, N. V. Ivanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 3444.
The problem of chemical bonds is considered in slow neutron transfer. The efficient method is suggested to simulate the slow neutron paths using MonteCarlo method. The accuracy of the method suggested is shown with numerical computations of critical assemblies. Key words: MonteCarlo method, slow neutrons, inelastic scattering.
 SIMPLIFIED SOLUTIONS OF FLECK PROBLEMS V. V. Zavyalov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 4552.
Analytical solutions for a steady system of equations were given for a spectrum radiation transfer with Fleck conditions. The comparison with numerical computations is given. The temperature of material obtained from numerical computations showed a good agreement with analytic formulae. Key words: radiation transfer, Fleck problem.
 ANALYTICAL SOLUTION FOR TEMPERATURE FIELD IN RECTANGULAR PLATE WITH ALTERNATING INTERNAL SOURCE USING RAPID DECOMPOSITIONS A. D. Chernyshov, A. N. Marchenko, V. V. Goryainov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 5358.
The approximate explicit analytical solution is obtained using rapid decompositions. It is shown that the solution is radically changed at a certain critical value of the parameter defining the heat release and proportional to temperature. The curves were obtained for distribution of temperature and heat flows. Key words: analytical solution, temperature, internal selfheating, rectangular shape, rapid decompositions.
 SIMPLE ITERATION METHOD WITH STOCHASTIC RIGHT MEMBER D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 5968.
The root of nonlinear equation system should be determined for a number of practical problems; the statistical simulation methods are used for the right members of these equations. The simplest algorithm based on the substitution of a function value for a random value due to a stationary Markovian chain simulation in the simple iteration method, is of little use for applications for two main reasons: shifting of mathematical expectation and no reliable criterion of iteration extinction. Thus, the solution scheme is suggested in terms of a nonstationary Markovian chain which has no disadvantages. The application results of the scheme to solution of two simple methodic problems are given. Circuit parameter effect is estimated in terms of these results. Key words: stochastic simulation methods, MonteCarlo method, numerical methods, simple iteration method, successive approximations method, Markovian chain.
 2D GAS DYNAMIC D TECHNIQUE USING HYBRID COMPUTATION SYSTEM A. A. Chuprakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 6977.
Software implementation method of difference equations of 2D gas dynamics is suggested using the hybrid computation system with arithmetical accelerators. The problems of parallelization efficiency using several accelerators are studied, the MPI and CUDAbased scheme of sharing between the generalpurpose processor core and arithmetical accelerators is described. Key words: arithmetical accelerators, GPU, CUDA, MPI, D technique.
 COMPARATIVE ANALYSIS OF LIQUID WATER FINE STRUCTURE I. N. Svistunov, A. S. Kolokol, I. V. Pyshin, A. L. Shimkevich VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 1. P. 7884.
There exists a great number of water computer models; here the choice of the model is due to the set object of study. None of them is absolutely preferable. A comparative analysis of three widelyused water models is given: threepoint SPCE, fourpoint TIP4PEW and fivepoint TIP5PEW. The molecular dynamics study of water was carried out at standard conditions using these models. Unlike the system static pressure it is found that the system temperature fluctuations observed in the numerical experiment are not sensitive to the size of molecular dynamics cells. Thus, the minimization technique of static pressure in system was developed to be used for specification of the cell size. The pair functions of particle radial distribution were obtained and verified for each model, and the shots of molecular configurations of hydrogen bonds in molecular dynamics cell were studied. The average number of hydrogen bonds per water molecule was determined, the donoracceptor characteristics for the networks of liquid water molecule hydrogen bonds was obtained. A conclusion was made concerning the applicability of the models. Key words: molecular dynamics, liquid water, computer models, radial distribution function, hydrogen bond.
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