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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2009  VISCOSITY AND DISPERSION EFFECT ON THE RAREFACTION SHOCK EMERGENCE AT A POINT ENERGY RELEASE FRONT RUNNING WITH A GIVEN MASS VELOCITY
Yu. A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 320.
Considered here are the properties of rarefaction shock emergence at such a front running with a given mass velocity lower than mass velocity of sound in front of the shock. Criteria for rarefaction shock emergence have been established for three cases: 1) with smeared running energy release; 2) when viscosity shock on rarefaction is used for smearing; 3) when the shock is smeared by approximation dispersion, which occurs when one uses a cross difference scheme having the second order of approximation uncertainty. The mass velocity of sound behind the shock is higher than mass velocity of the shock for the rarefaction shocks for the first two cases. The third case allows the rarefaction shocks satisfying the following conditions: 1) mass velocity of sound behind the shock is lower than mass velocity of the shock; 2) the parameters of admissible rarefaction shock satisfy an additional ratio (apart from three RankineHugoniot conditions), which has an explicit form. It is shown that all the considered possible rarefaction shocks are evolutionary. Key words: normal detonation, running energy release, selfsimilar solution, rarefaction shock, admissive jumps, evolution jumps, viscosity, dispersion.
 THE APPLICATION OF THE TVDAPPROACH TO THE HEAT TRANSFER EQUATION IN THE PiAPPROXIMATION A. S. Vershinskaya, A. D. Gadzhiev, S. A. Grabovenskaya, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 2136.
Considered here is application of TVDreconstruction to construct positive and second order scheme to solve the heat transfer equations in P1 approximation. Numerical results for test problems are provided. Key words: heat transfer, P1approximation.
 THE APPLICATION OF THE TVDAPPROACH TO THE DSnAPPROXIMATION OF HEAT TRANSFER EQUATIONS A. D. Gadzhiev, V. V. Zavialov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 3748.
Described here are two TVDbased schemes for implicit finitedifference equations approximating the nonlinear system of timedependent differential equations. The system consists of spectral integrodifferential kinetic equation of photon transfer and energy equation. The suggested schemes allow sweep algorithm to be used. Numerical results for test problems are provided for onedimensional geometry. Key words: heat transfer, approach.
 FINAL ELEMENT METHOD NUMERICAL SCHEMES ON “RARE”MESHES D. T. Chekmarev VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 4954.
Considered here is the problem of variationaldifference and finiteelement schemes in which the cells (finite elements) do not occupy the whole domain but with gaps. Given here are the examples of 2D and 3D schemes which are essentially more effective in comparison with traditional ones. Key words: finiteelement method, variationaldifference method, efficiency of numerical schemes.
 USE OF GRAPHIC ARITHMETIC ACCELERATORS FOR MOLECULAR DYNAMICS COMPUTATIONS USING MD SOFTWARE B. L. Voronin, A. M. Erofeev, S. V. Kopkin, I. A. Kryuchkov, A. S. Rybkin, S. A. Stepanenko, V. V. Yuzhakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 5561.
Applicability of computers with hybrid architecture to solve molecular dynamics problems is studied. Such computers have multiplepurpose processors and graphic arithmetic accelerators NVIDIA 8800GTX. The paper analyzes the original algorithm and explains the way of dividing a code into fragments and measuring the runtimes of the code, as a whole and its separate fragments using multiplepurpose processors and arithmetic accelerators. The paper shows that it is possible to use computers with hybrid architecture to solve MD problems. The MD software adaptation has been performed. A hybrid computer allows reduction of the computational process duration (Morse potential) by a factor of 4.10, 2.67, and 1.49, as compared to one core, two cores and four cores, respectively. The computational process duration (Ackland potential) is reduced by a factor of 6.64, 3.26, and 1.98 owing to a hybrid computer, as compared to one core, two cores and four cores, respectively. Key words: graphic arithmetic accelerator, processor, program code, performance, molecular dynamics.
 APPLICATION OF GRAPHIC ARITHMETIC ACCELERATORS IN METHODOLOGICAL MONTECARLO TRANSPORT SIMULATIONS I. A. Kryuchkov, S. P. Ognev, A. S. Rybkin, S. A. Stepanenko, V. V. Yuzhakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 6268.
The appropriateness of a hybridarchitecture computer for speeding up MonteCarlo simulations of eigenvalue problems is considered. A methodological program for neutron multiplication time constant calculations using the relaxation method has been used. This program is close in its nature to energy release simulation programs. The program was modified and used on a hybridarchitecture computer with a MIMD (universal processor) and SIMD (graphic arithmetic accelerator  GAA) component, which allowed performing test simulations with one and two GAA, as well as with universal processor and GAA used in parallel. These data demonstrate good prospects of MIMD and SIMD components (not only NVIDIA GeForce 8800GTX, but also AMD FireStream 9170, IBM PowerXCellSi (eDP) and other hybrid processors being developed) as applied to MonteCarlo transport simulations. Key words: graphic arithmetic accelerator, GPU, processor, transport equation, Monte Carlo method.
 SupRROS TECHNOLOGY FORSUPPORT OF RESEARCH REACTOR OPERATION: COMPUTING TOOLS, TECHNICAL APPROACHES AND IMPLEMENTATION EXAMPLE Yu. E. Vaneev, N. Yu. Marikhin VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 6978.
Described here are the features of the modern development and application technology of the computing tools for support of research reactor operation. The examples of development and application are given in the framework of the software technology  the simulator of SM reactor core. Key words: research reactors, operation monitoring, computational tools, development technology, precision program, paralleling of computations, core simulator, simulation.
 EXACT FORMULAS FOR EXACT AND ROSSELAND AVERAGING OF POLYNOMIALS A. E. Dubinov VANT. Ser.: Mat. Mod. Fiz. Proc. 2009. No 2. P. 7981.
The explicit formulas for Planck and Rosseland averages of polynomials are given. The integrals of the formulas are expressed in terms of finite sums of the poly logarithms. The point values obtained for the mean may be used in mathematical programs for the transport and radiation absorption factors in laboratory and astrophysics plasma. Key words: polynomial, average, Planck weight function, Rosseland weight function.
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