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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 3, 2010  APPLICATION OF THE TVDAPPROACH TO SOLVE THE THERMAL RADIATION TRANSPORT EQUATION WITH QUASIDIFFUSION METHOD
A. D. Gadzhiev, S. A. Grabovenskaya, V. V. Zavyalov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 314.
A nonlinear TVDtype scheme of the second order of approximation used to solve the thermal radiation transport equation with the quasidiffusion method is described. The numerical simulation results for some test problems are also given. Key words: TVDscheme, quasidiffusion method.
 DIAGONAL ELEMENT SINGLINGOUT SCHEMES USED TO SPEED UP ITERATIONS DURING THE THERMAL RADIATION TRANSPORT EQUATION SOLUTION IN DIFFUSION APPROXIMATIONS A. D. Gadzhiev, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 1527.
The paper describes the numerical schemes of singling out a diagonal element used to speed up iterations during the thermal radiation transport equation solution in diffusion approximations. The principal idea of such methods can be implemented in three stages: For each computational grid cell, the energy equation is solved first and then the diagonal element singlingout schemes are used to find the temperature value via the density of radiation. The temperature value is used to calculate the Planck function value. The new values of density and radiation flux are found with the sweep method using the known righthand part of equation. Key words: acceleration of iterations, thermal radiation transport.
 DS_{n}SCHEME OF CHARACTERISTIC TUBES FOR THE TRANSPORT EQUATION IN CYLINDRICAL COORDINATES A. I. Bochkov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 2837.
A characteristic scheme has been developed to solve the transport equation written in cylindrical coordinates. The scheme includes two stages. In the first stage an ordinary differential particle balance equation is built in a computational grid cell and used to find the total flux of particles on the nonexposed surface of the cell. In the second stage of the DS_{n}type scheme the outgoing particle flux is distributed over the nonexposed cell`s faces. Key words: transport equation, difference scheme, DS_{n}method, DS_{n}scheme of characteristic tubes.
 SPECIFIC FEATURES OF THE DETONATION COMPUTATIONS WITH THE DICTATED WAVE FRONT VELOCITY USING EULERIAN GRIDS Yu. A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 3845.
The paper analyzes results of 1D hydrodynamic computations of the normal detonation using Eulerian grids. A significant effect of a slightly violated (sim1%) conservation of the total energy on the detonation computation accuracy is shown. A selfsimilar solution with regard to the negative total energy disbalance with the given velocity of the energy release front has been built. There is a good agreement between the results of computations with nonconservative schemes and the selfsimilar solution features. It has been shown that with the higher accuracy methods used to recalculate the hydrodynamic quantity values from a Lagrangian grid to the Eulerian one a significantly reduced amount of calculations with the accuracy preserved is possible. Key words: gas dynamics in Eulerian variables, detonation, numerical methods, selfsimilar solutions, test problems, conservativeness, computation accuracy, nonconservation of total energy.
 2D SCALAR ARTIFICIAL VISCOSITY OF EGAK TECHNIQUE IN SPHERICAL SYSTEMS Yu. V. Yanilkin, O. O. Toporova VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 4654.
The paper considers the problem of a spherically converging shell with a light gas inside it. It is shown that the artificial viscosity type is of a great importance for the numerical solution of this problem. The classic von NeumannRichtmyer viscosity may give a large error on spherical grids, because it does not take into account the uniform material compression under the spherical convergence conditions. Application of the viscosity earlier proposed by the authors allowed a significant reduction of the error. Key words: gas dynamics, artificial viscosity, 2D flows, difference scheme.
 KINETICS OF THE EXPLOSIVE TRANSFORMATION INITIATION OWING TO FRICTION UNDER LOWVELOCITY IMPACTS WITHIN D TECHNIQUE M. E. Martynova  ,   ,  Yu. D. Chernyshev 
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 5564.
One of the possible explosive transformation initiation mechanisms under lowvelocity impacts is considered. It is based on the surface explosive heating caused by rubbing against the surrounding materials. The implementation of kinetics equations within D technique is presented. The algorithm of accounting for the forces of friction occurring on the interfaces during the interaction of an explosive with the surrounding materials is described. The paper gives results of the numerical simulation with the described kinetics for experiments of the Stiven Test type. Key words: D technique, lowvelocity impacts, Stiven Test, friction coefficient, initiation of explosive transformations.
 VERIFICATION OF THE COMPUTATIONAL MODEL OF THE IMPURITY TRANSPORT WITH CONVECTION BY THE EXAMPLE OF CRYSTALLIZATION OF TWOMATERIAL PbSn MELTS S. M. Ganina, V. P. Ginkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 6572.
A computational algorithm has been developed for the impurity segregation during crystallization of twomaterial melts characterized by largesize twophase areas. The calculation of convection in a porous medium takes into account an additional resistance to flow similar to Darcy law. The liquidus point linearly depends on the concentration of impurity in a liquid phase. The proposed model has been implemented in GIGAN2D program complex. Two benchmarks have been run to verify the model: one of them simulated the crystallization of Sn with 10% Pb concentration and another simulated the melting process of Pb with 18% Sn concentration. Key words: promising materials, intermetallides, directed crystallization, melting, twophase transient area, benchmark, segregation, mathematical modeling, impurity transport with convection, moving interfaces, computational algorithm.
 AN UPDATED MANYPARTICLE POTENTIAL ALGORITHM FOR THE MD SIMULATION USING GRAPHIC ARITHMETIC ACCELERATOR S. V. Kopkin, I. A. Kryuchkov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 7382.
The paper describes main stages of adapting the algorithm of calculating the values of MEAM potential in MD complex to a hybrid computer system. The information about the speedup gained with a varying number of computing devices is presented. Test computations have been carried out and confirm the validity of results. Key words: arithmetic accelerator, molecular dynamics, potential, MEAM, speedup, hybrid computer system.
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