ISSUES OF ATOMIC SCIENCE AND TECHNOLOGY
Series: Mathematical simulation of physical processes

Year 2011 2010 2009
Issue 1-2-3-4 1-2-3-4 1-2-3-4

2009
ISSUE 2

ABSTRACTS:

UDK 517.9:533.7:536.46
VISCOSITY AND DISPERSION EFFECT ON THE RAREFACTION SHOCK EMERGENCE AT A POINT ENERGY RELEASE FRONT RUNNING WITH A GIVEN MASS VELOCITY / Yu. A. Bondarenko // P. 3

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. and 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 Rankine-Hugoniot conditions), which has an explicit form.

It is shown that all the considered possible rarefaction shocks are evolutionary.
Key words: normal detonation, moving energy release, self-similar solution, rarefaction shock, admissible shocks, viscosity, variance.

UDK 519.6
THE APPLICATION OF THE TVD-APPROACH TO THE HEAT TRANSFER EQUATION IN THE Ð1-APPROXIMATION / A. S. Vershinskaya,  A. D. Gadzhiyev,  S. A. Grabovenskaya, À. À. Shestakov // P. 21

Considered here is application of TVD reconstruction to construct positive and second order scheme to solve the heat transfer equations in Ð1-approximation. Numerical results for test problems are provided.
Key words: heat radiation transfer, P1-approximation.

UDK 519.6
THE APPLICATION OF THE TVD-APPROACH TO THE DSn-APPROXIMATION OF HEAT TRANSFER EQUATIONS / A. D. Gadzhiev,  V. V. Zavialov,  À. À. Shestakov // P. 37

Described here are two TVD-based schemes for implicit finite-difference equations approximating the non-linear system of time-dependent differential equations. The system consists of spectral integro-differential 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 one-dimensional geometry.
Key words: heat radiation transfer, TVD-approach.

UDK 519.6
FINAL ELEMENT METHOD NUMERICAL SCHEMES ON “RARE” MESHES / D. T. Ñhekmarev // P. 49

Considered here is the problem of  variational-difference and finite-element 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: final element method, variational-difference method, numerical scheme efficiency.

UDK 519.6
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 // P. 55

Applicability of computers with hybrid architecture to solve molecular dynamics problems is studied. Such computers have multiple-purpose 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 multiple-purpose 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.

UDK 519.6
APPLICATION OF GRAPHIC ARITHMETIC ACCELERATORS IN METHODOLOGICAL MONTE-CARLO TRANSPORT SIMULATIONS / I. A. Kryuchkov, S. P. Ognev, A. S. Rybkin, S. A. Stepanenko, V. V. Yuzhakov // P. 62

The appropriateness of a hybrid-architecture computer for speeding up Monte-Carlo 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 hybrid-architecture 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 PowerXCell (eDP) and other hybrid processors being developed) as applied to Monte-Carlo transport simulations.
Key words: graphic arithmetic accelerator, GPU, processor, transport equation, Monte-Carlo method.

UDK 621.039.5
SUPRROS TECHNOLOGY FOR SUPPORT OF RESEARCH REACTOR OPERATION: COMPUTING TOOLS, TECHNICAL APPROACHES AND IMPLEMENTATION EXAMPLE / Yu. E.Vaneev,  N. Yu. Marikhin // P. 69

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 reactor, support, computing tools, development technique, high-precision program, parallelizing, core simulator, simulation.

UDK 519.6
EXACT  FORMULAS FOR PLANCK AND ROSSELAND AVERAGING OF POLYNOMIALS / Dubinov A. E. // P. 79

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 polylogarithms. 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.

Year 2011 2010 2009
Issue 1-2-3-4 1-2-3-4 1-2-3-4