Issue 1/2010

ABSTRACTS:

UDK 519.6
ARTIFICIAL VISCOSITY ARRAY FOR 2D LAGRANGIAN  GAS DYNAMICS TO REDUCE THE "ENTROPY TRACE" IN NUMERICAL SIMULATIONS А. М. Stenin, Е. А. Solovieva // P. 3

The artificial diffusions of mass, momentum and total energy are artificially added to the system of gas dynamics equations which describes 2D flows in Eulerian coordinates. The formulae for artificial mass diffusion rate are obtained after passing on to Lagrangian coordinates, as well as the formulae for artificial viscosities in motion and energy equations. The artificial viscosity in motion equation is the tensor proportional to the rate-of-strain deviator. 
Results of test computations demonstrate the new viscosity system efficiency in reducing the entropy trace during the numerical simulation of Lagrangian gas dynamics.
Key words: Lagrangian gas dynamics, artificial viscosity, tensor viscosity, entropy trace, Noh problem, Zaltsmann problem.

UDK 533.9
SPLITTING SCHEME FOR NUMERICAL SIMULATION OF COLLISIONLESS RELATIVISTIC PLASMA DYNAMICS А. I. Golubev, Т. G. Sysoeva // P. 19

Considered here is the generalization of splitting scheme of the set of Vlasov–Maxwell equations that has been suggested earlier in the case of relativistic plasma. Formally, it is of the same type as in the case of non-relativistic plasma but numerical implementation of single steps is much complicated.
The accuracy analysis of the method of characteristics interpolating the distribution function of relativistic electrons in terms of cubic spline is carried out in numerical computation
of the most complicated splitting scheme steps accounting for the influence of electromagnetic field components. The analysis results showed that this method gives the accuracy of conservation laws for kinetic equations acceptable for applications.
Key words: Vlasov-Maxwell equation, electron distribution function, characteristic method, cubic interpolating spline.

UDK 519.6:536.71
QUASI-DIFFUSION METHOD APPLICATION FOR RADIATION TRANSFER PROBLEMS N. G. Karlykhanov // P. 32

The quasi-diffusion approach was first used to solve the problem of scattering integral iteration speedup in neutron transfer problems. In foreign literature this approach is known as Eddington Factor. Given here is the analysis of quasi-diffusion method as applied to the radiation transfer problems using spectral-kinetic scenario. Several questions arise when actually using the method given: if there is the necessity for quasi-diffusion coefficient iterations, what is the degree of convergence of this process; what is the computational accuracy of the said coefficients, if there is the possibility to use simple difference schemes of the first order of accuracy for the radiation transfer equation using kinetic scenario. The author tried to obtain the answers when analyzing the numerical computation results of the problems specially chosen.
Key words: radiation transfer, quasi-diffusion.

UDK 519.6
ABOUT THE APPLICATION OF RAIBIKI METHOD TO THE SOLUTION OF THE SYSTEM OF RADIATION TRANSFER EQUATIONS USING BOUNDARY CONDITION ITERATIONS Е. V. Groshev // P. 39

Suggested here is Raibiki method algorithm using boundary condition iterations combined with the simplicity of kinetic equation iteration for time-dependent spectral spherically symmetrical problems of radiation transfer. The entire system is divided into mathematical subdomains and after simple iterating for kinetic equation with spectral intensity values used as incoming flux for the corresponding mathematical subdomains, radiation transfer problem is solved (using Raibiki method).
Key words: system of radiation transfer equations, Raibiki method, boundary condition iterations, Raibiki method algorithm in boundary condition iterations.

UDK 539.122:518.5
WEIGHTING FACTOR AND SELECTION METHODS. SIMULATION OF COHERENT SCATTERING OF PHOTONS D. G. Modestov // P. 48

Weighting methods are the important part of statistical simulation methods. The analysis of weighting factor with statistical expectation being proportional to the distribution density of the random value specified is common to all the methods. However, it is not always possible to find the density. Particularly, it happens when selection methods are used with unnormalized distribution density. The work suggests using certain conditional random value with statistical expectation being equal to the density function for the arbitrary parameter. This approach is precise (as opposed to the use of approximate value of normalization factor), but at the same time it does not require additional computational efforts and is easily implemented for the arbitrary selection algorithm. The method is implemented for the simulation of coherent scattering of photons and compared to the other methods.
Key words: transport equation, scattering of photons, statistical simulation, upgrading method.

UDK 539.122:518.5
COMPUTATION OF NEUTRON DISTRIBUTION DENSITY AT ELASTIC SCATTERING D. G. Modestov // P. 55

The distribution density is not often directly used to solve the problems using statistical simulation methods. The sample design, for which the density use is not required, is quite sufficient. However, the use of distribution density can be useful for computational efficiency improving, or for estimation of development which is impossible by other means. In particular, it is also important for neutron transfer simulation accounting for the motion of medium structure elements, for example atoms. This account is more important for elastic scattering simulation. However, distribution density of scattering angle cosine is often defined in the center-of-mass system. Given here is the computational algorithm for the distribution density in the arbitrary reference system and use case.
Key words: transport equation, scattering of neutrons, statistical simulation, upgrading methods.

UDK 519.6
INITIAL DATA PROCESSING OF 2D SolidEditor AND 2D-IDC PROBLEMS P. V. Cherenkov, О. N. Borisenko, М. V. Cherenkova, V. I. Tarasov, К. К. Olesnitskaya, T. Yu. Bakanova, М. G. Kuznetsov, D. А. Shutov, А. S. Sergeeva // P. 59

The article deals with the technology of initial data processing of 2D SolidEditor and 2D-IDC mathematical physics problems developed in mathematical department of RFNC-VNIIEF. The technology is maximum unified for all the methods of mathematical department of RFNC-VNIIEF which allows efficient information sharing between the programs implementing these methods. SolidEditor allows setting, analysis and editing of physical and mathematical scenarios which make initial data processing easier for the series problems. 2D-IDC code is used for initial data computation (grid and grid values distribution).
Key words: SolidEditor editor, Open CASCADE library, user interface, problem geometrical modeling, initialization stage, physical and mathematical scenarios specification, 2D-IDC code, initial data computation.

UDK 519.6
RADIATION SOURCE MOTION RECOVERY ACCORDING TO THE SEQUENCE OF TELEVISION IMAGES USING QUASIOPTIMAL FILTRATION V. М. Ponyatskii // P. 68

Considered here is the quasioptimal filtration-based approach to estimate the radiation source motion against the noise background over a series of video frames. A continuous and discrete algorithm is developed to estimate center coordinates of the radiation source and its rotation frequency and radius, as well as the brightness level and radius of its image. The algorithms are simulated in the Matlab environment.
Key words: video frames, image, signal, parameters, noise, model, estimation.

UDK 519.6
SOFTWARE-HARDWARE SYSTEM OF TIME SYNCHRONIZATION IN ISOLATED LOCAL NETWORKS А. P. Chukhontsev, V. А. Pervov, А. N. Davydov, М. Yu. Оsipov // P. 82

Considered here is the system of synchronization for isolated local networks. The system provides system time synchronization of internal time server of local network with wired broadcasting reference value. It provides the universal and actual time to manage the interacting processes in the local network, that is monitoring and management of the networks, time constraint of numerous local network events, comparable analysis of these events, early network problems detection.
The operation principle of the system is based on decoding of wire radio channel standard time signal sequence, microcontroller processing, interaction with time server of system clock updating and reference time transmission in the local network to synchronize the other network components.
Key words: hardware-software complex, isolated networks, time server, time synchronization, system clock update, wired broadcasting, galvanic isolation, radio signal decoding, microcontroller.