Scientific Papers

1. T.I. Serezhnikova, A.F. Sidorov and O.V. Ushakova, On One Method of Construction of Optimal Curvilinear Grids and Its Applications. Soviet Journal of Numerical Analysis and Mathematical Modelling, Vol.4, N2. 1989, pp.137-155.

2. S.A. Ivanenko and A.F. Sidorov, On the Development in Russia of the Research in the Field of Grid Generation and Its Applications, Numerical Grid Generation in Computational Field Simulation. Proc. Of the 5th Inter. Conf., held at Mississippi State University, April 1-5, 1996, Mississippi, pp.1111-1121.

3. O.B. Khairullina, Method of Constructing Block Regular Optimal Grids in Two-dimensional Multiply-connected Domains of Complex Geometries, Rus. J. Numer. Anal. Math. modell., 1996, V. 11, N.4, pp. 343-358.

4. O.V.Ushakova, Algorithm of Two-Dimensional Grid Generation, Numerical Grid Generation in Computational Field Simulation. Proc. Of the 5th Inter. Conf., held at Mississippi State University, April 1-5, 1996, Mississippi, pp.37-47.

5. O.B. Khairullina, To the Calculation of Flow of Gas in Channels of Complex Configurations, Prikladnaya Mechanica i Tecnicheskaya Fizika, 37, (2), 1996, pp. 103-108.

Foreign Collaborators

Dr. Bh.K.Soni

Mississippi State University

National Science Foundation

Engineerirng Research Center for Computational Field Simulation

№-0336 Numerical Simulation of Unsteady Viscous Gas Dynamics Problems

Full Title:	Numerical Simulation of Unsteady Viscous Gas Dynamics Problems on Multiprocessor Computer Systems
Technology Field(s):	PHY-NGD: Physics / Fluid Mechanics and Gas Dynamics INF-SOF: Information and Communications / Software

Contributors

Boris N Chetverushkin

Institute of Mathematical Modeling (IMM) 4a, Miusskaya sq., Moscow, 125047, Russia Phone: 7+095+9721159; 7+095+1554353 Fax: 7+095+9720723 chetver@imamod.msk.su

Present Status of Research

Brief Description of Research

A new approach to numerical simulation of gas dynamic flows based on solving a kinetically consistent system of difference equations (KCSDE) has been proposed. This system of equations can be interpreted as an approximation of the equations describing viscous flows, which is derived directly from the kinetic Boltzmann equation. The differential analogue to this system of difference equations, known as the quasi-gas dynamic system of equations, results in the same description of viscous flows as in the case of the Navier-Stokes equations. However, owing to additional regularizing terms, this system provides more effective solutions of gas dynamic problems. In particular, KCSDE are easily adapted to the architecture of massive parallel distributed memory computer systems and applied to unstructured meshes (triangle mesh, Dirichlet cells).

The Institute for Mathematical Modeling RAS has accumulated 15 years’ experience in work in this direction. In particular, some important results on simulation of unsteady oscillating viscous compressible gas flows, aeroelasticity, and aeroacoustics problems have been achieved. The latest results have been obtained with the help of a high performance multiprocessor computer systems.

Calculations of complex gas dynamic flows performed on the basis of the proposed numerical technique is in good agreement with the experimental data available.

Legal Aspects

There are no patents and licenses. There are papers published in Russian and foreign scientific journals. The works of Project participants have been presented at international conferences (ECCOMAS-94, -96, Parallel CFD-95, -97).

Special Facilities

Multiprocessor Computer System Parsytec CC-12 with total peak productivity of 3 Gflops.

Scientific Papers

T. Elizarova, B. Chetverushkin, and Yu. Sheretov, Quasi-gas dynamic equations and computer simulation of viscous gas flows, volume 414 of Lecture Notes in Physics. Proc. of the XIII International Conference of Numerical Methods in Fluid Dynamic. Rome, Italy, July 1992., pp. 421-425, Springer-Verlag, Heidelberg, 1992.

B. Chetverushkin, Solution of gas dynamic problems on massively parallel computer systems, Proc. of the II European Computational Fluid Dynamic Conference. Stuttgart, Germany, June 1994, pp. 456-460, John Wiley & Sons, Chichester, 1994.

I. Abalakin and B. Chetverushkin, Using kinetically consistent finite difference schemes for prediction of moderately rarefied gas flows, Proc. of the II European Computational Fluid Dynamic Conference. Stuttgart, Germany, June 1994, pp. 347-350, John Wiley & Sons, Chichester, 1994.

B.N. Chetverushkin, Kinetically consistent finite difference schemes and their Application to Transient Flow Prediction, in Proc.: Experimentation, Modeling and Computation in Flow, Turbulence and Combustion Vol.1, Ed. by J.A. Desideri, B.N. Chetverushkin, Y.A Kuznetsov, J Periaux and B. Stoufllet, pp. 211-220, John Wiley & Sons, Chichester, 1996.

I.V. Abalakin, M.A. Antonov, B.N. Chetverushkin and others, On the opportunity of parallel implementation of kinetically consistent finite difference schemes for gas dynamic flow simulation, Proc. of Parallel CFD-96, Capri, Italy, May 1996, Elsevier 1997, pp. 182-188.

A.N. Antonov, M.A. Antonov, B.N. Chetverushkin and others, High accuracy simulation of viscous unsteady flows, Proc of Parallel CFD-97, Manchester, England, May 1997.

Foreign Collaborators

Prof. D.Thess, Parsytec Computer GMBH, Germany.

№-0337 Numerical Modeling for Crystal Growth

Full Title:	Numerical Modeling for Crystal Growth
Technology Field(s):	MAT-CER: Materials / Ceramics INF-SOF: Information and Communications / Software

Contributors

Igor V Friazinov	Institute of Mathematical Modeling (IMM) 4a, Miusskaya sq., Moscow, 125047, Russia Phone: 7+095+2507890; 7+095+1554353; 7+095+2507939 Fax: 7+095+9720723 chur@imamod.ru
Marina P Marchenko	Institute of Mathematical Modeling (IMM) 4a, Miusskaya sq., Moscow, 125047, Russia Phone: 7+095+2507890; 7+095+1554353; 7+095+2507939 Fax: 7+095+9720723 chur@imamod.ru

Present Status of Research

Brief Description of Research

Mathematical models and numerical methods for solving non-stationary problems connected with crystal growth processes by Bridgman, THM and floating zone techniques (the last in microgravity) are developed. The Navier-Stoke equations in Boussinesq’s approximation, convective heat and multicomponent diffusion equations are solved in the melt. Phase interface positions are determined, the heat equation is considered in solid phases. The possibility of crystal growth in constant and rotating magnetic fields and also with an electric current through the melt are taken into account.

Heat exchange models by radiation were constructed. Radiation models involve many factors: light reflection between the material in the ampoule and the heater, the dependence of the quartz absorption coefficients on frequency and temperature, and geometric and physical system parameters. These factors for the quartz ampoule are taken into account in boundary temperature conditions. In the ampoule, emerging heat was represented by the source in the heat equation. A predetermined function of the temperature on the boundaries may also be considered on the external boundary. The Stefan conditions are taken into account at the interface, and either a fixed interface temperature is given or temperature continuity is given in the case of alloys. For concentrations, the mass balance conditions for each material and the equality of chemical potentials are considered.

The basis of the mathematical model derives from developments based on investigations and experiments by Brebrick. Chemical reactions are taken into account in the melt (the multicomponent melt consists of Hg, Cd, Te, HgTe, CdTe). The structure of the growing crystal is determined during the process.

For the growth of CdTe and CdHgTe, the functional relationships between concentrations and temperature were used at the interface. In the case of doped crystals, the relationship between concentrations in the solid and the melt is determined by finding the coefficient of equilibrium distribution of an impurity.

Numerical methods were developed solving the problems under consideration. The calculated region was transformed into an agglomeration of squares. Equations and boundary conditions were approximated using difference methods. The conservation property is fulfilled for the grid equations obtained. Monotone approximations with extended stencils were developed for convective terms. Numerical solutions do not indicate long wavelength spatial oscillations, and they are not periodic. Having operators with fixed signs leads to stability of the scheme. Methods for calculation of chemical reactions during Cd_xHg_1-xTe crystal growth were developed. A numerical method was developed for solving the system of concentration equations and for the definition of a moving phase interface.

The computer code KARMA1 was constructed for solving 2-D heat–mass transfer problems in a multicomponent melt. KARMA1 calculates transient crystal growth processes by calculating moving phase interface positions and the growing crystal structure. The calculations were performed for real experiments on the crystal growth of Cd_xHg_1-xTe and Ge-doped Ga to determine the structural dependence on input data (external heat conditions, melt structure, magnetic field parameters - frequency, amplitude).

Legal Aspects

Author's testimony N1512187 "Method MAHID crystal growth", author I.V.Friazinov and other. Numerical methods and some results of mathematical modeling were published.

Special Facilities None.

Scientific Papers

M.P Marchenko, I.V.Friazinov. Computer code KARMA1 for solving non-stationary problems of crystal growth in ampoules. J. Comput. Math. and Math. Phys. 1997. v.37. N8. p. 988-998.

Foreign Collaborators

Dr. Charles Neumeyer, PPPL, Princeton University, USA

№-0338 Thermohydraulic Calculations of the VVER - 1000 Reactor

Full Title:	The Development of Mathematical Models and a Program Package for the Thermohydraulic Calculations of the VVER - 1000 Reactor with Coated Particles as Fuel Elements
Technology Field(s):	FIR-MOD: Fission Reactors / Modelling

Contributors

Vladimir A Gasilov	Institute of Mathematical Modeling (IMM) 4a, Miusskaya sq., Moscow, 125047, Russia Phone: 7+095+2507939; 7+095+1554353 Fax: 7+095+9720723 gasilov#8@imamod.msk.su
Arthur R Avetissian	All-Russian Nuclear Power Engineering Research and Development Institute (Nuclear Power Eng Inst) 6a, Cosmonaut Volkov str., Moscow, 125171, Russia Phone: 7+095+1508285 Fax: 7+095+1508285 vniiam@dol.ru

Present Status of Research

Brief Description of Research

At present, VNIIAM and the I.V. Kurchatov Institute of Atomic Energy are working on a joint project to create the VVER-1000 reactor core, which utilizes coated particles as fuel elements. The ultimate goal of the study is the development of a system of very high safety. To solve the problem of constructing the extremely safe VVER reactor, it was proposed to use microfuel elements produced via ceramic cladding technology. The fuel elements for high temperature reactors are spherical pellets consisting of a uranium dioxide or plutonium dioxide core coated with a multilayer shell (pyrolytic graphite, silicon carbide etc.). The diameter of the coated fuel pellet is about 1 mm. These claddings effectively retain accumulated radioactivity at temperatures up to 2000 °C. Operational experience with ceramic claddings has shown that they provide unique safety features for any type of accident. Therefore, it is interesting to consider the combination of high-temperature reactor technology and the technology of light water reactors. The application of coated particles will essentially increase safety, first of all, by increasing stability against severe accidents, such as those at Chernobyl or Three-Mile Island.

The preliminary studies on the project were carried out at VNIIAM. They showed that it is possible to use the coated particles without any change in reactor design, including their application in operating NPP's with VVER. However, now it is quite important to carry out a detailed numerical investigation of the thermohydraulic processes (e.g. natural and forced convection) in the reactor core in both normal and in emergency situations, taking into account the real three-dimensional reactor geometry and heterogeneous phase transitions. The numerical models required for such investigations were developed mutually at IMM and VNIIAM.

The aim of the submitted project is the development of a three-dimensional version of the two-phase thermohydraulic numerical model and appropriate software for numerical investigations of normal and emergency situations in the VVER-1000 reactor core with coated particles.

Legal Aspects

The four patents related to the project were submitted by the VNIIAM specialists in 1995.

Special Facilities None in this research.

Scientific Papers

Grishanin E.I., Denisiv E.E., Lyubin A.Ya., Falkovskii L.N. The development of a mathematical model for calculation of heat-carrier parameters in fuel containers with coated particles. Tyajeloye Mashinostroyeniye (Moscow, Russia), 1995, N.9, pp. 11-20.

Boldarev A.S., Gasilov V.A., Zaichik L.I., Olkhovskaya O.G. Eulerian Modeling of Spontaneously Condensing Steam Flows. In: Proc. of the Int. Symp. on the Physics of Heat Transfer in Boiling and Condensation (21-24 May 1997, Moscow, Russia), pp. 221-225.

Foreign Collaborators

FRAMATOME (France).

№-0339 Influence of Admixtures on Radiation Heat Exchange in the Atmosphere

Full Title:	Influence of Admixtures on Radiation Heat Exchange in the Atmosphere
Technology Field(s):	INF-SOF: Information and Communications / Software OBS-NAT: Other Basic Sciences / Natural Resources and Earth Sciences

Contributors

V Ya Gol'din	Institute of Mathematical Modeling (IMM) 4a, Miusskaya sq., Moscow, 125047, Russia Phone: 7+095+2509803; 7+095+1554353; 7+095+9721159 Fax: 7+095+9720723 chur@imamod.ru
A V Shilkov	Institute of Mathematical Modeling (IMM) 4a, Miusskaya sq., Moscow, 125047, Russia Phone: 7+095+2509803; 7+095+1554353 Fax: 7+095+9720723 chur@imamod.ru

Present Status of Research

Brief Description of Research

The research group is currently working on project 115 - 95 of ISTC "ATRAD" for creating a mathematical model of heat exchange between solar and heat radiation and the Earth’s atmosphere. The mathematical model is extensively based on the new mathematical methods (method of Lebesgue averaging, method of quasi-diffusion) which make it possible to calculate effectively and accurately the radiation transport equation, taking into account a very large number of absorption lines, scattering anisotropy, large optical thicknesses, and reflection from the Earth’s surface. A database "ATRAD" (originating from the data base "HITRAN") is being created as a part of the model for accumulating all the data on light absorption and scattering coefficients, scattering indices, and reflection coefficients. The method is comparable in accuracy to the "line - by - line" method but is considerably more efficient, so that it will be possible to study the influence of different admixtures on radiation heat exchange and climate.

We hope, that, because of the efficiency of the proposed method, it will be possible to combine it with gas dynamics calculations using the methods available in a number of research centers. This will make it possible to create a more reliable mathematical tool for climate forecast.

Legal Aspects

There are no patents.

Special Facilities

The "HITRAN" data base was used.

Scientific Papers

A.V. Shilkov, Methods of Averaging of Cross - Sections and the Energy Spectrum in Neutron Transport Problems, Mathematical Modeling, 1991, v. 3, No 2, pp. 63-81, (in Russian).

A.V.Shilkov. Generalized Multigroup Approximation and Lebesque Averaging Method in Particle Transport Problems, // Transp. Theory and Stat. Physics, (1994), v.23, N6, p. 781-814.

A.V. Shilkov, I.L. Tsvetkova, S.V. Shilkova. "ATRAD" System for Atmosphere Radiation Calculations: Lebesgue Averaging of Spectra and Absorption Cross - Sections. - Mathematical Modeling, 1997, v.9, No 6, pp. 3-24, (in Russian).

E.N. Aristova, V.Ya. Gol'din. Method of Strong Scattering Anisotropy Consideration in Transport Equation. - Mathematical Modeling, 1997, v. 9, No 6, pp. 39 -52, (in Russian).

Foreign Collaborators

Dr. Walter Joss, High Magnetic Field Grenoble, France

№ -0145 Complex Method of Structure, Composition, and Interface Investigation for Very Thin Films

Full Title:	A Complex Method of Structure, Composition, and Interface Investigation for Very Thin Films and Multilayers
Technology Field(s):	PHY-SSP: Physics / Solid State Physics

Contributors

V V Afrosimov

A.F.Ioffe Physico-Technical Institute (Ioffe Inst) 26, Polytechnicheskaya str., St Petersburg, 194021, Russia Phone: 7+812+2479946 Fax: 7+812+2476096 afros@acl.ioffe.rssi.ru

Present Status of Research

Brief Description of Research

The method of investigation of films and multilayers with thicknesses from 1 to 100 nm, using a 50–500 keV light ion (H⁺, He⁺) beam as a probe, is developed. It provides the possibility of establishing film thicknesses with an accuracy of about 5%, composition with an accuracy of ~3%, the crystalline structure perfection, and the position of impurity (implanted) atoms in the host lattice. The method also makes it possible to study the quality of interfaces and to define block misorientation angles with an accuracy of ~0.1°. The advantage of this method, in comparison with the traditional Rutherford backscattering one, is the high depth resolution, which makes it possible to obtain the above-described information for films with the thicknesses of a few nm. The information about the object under investigation is derived from the energy spectra of the backscattered ions and the spectra of ion-induced X-ray emission (mainly in the 500–5000 keV quanta energy region). The backscattered ion spectra are measured with the help of an electrostatic analyzer, which allows one to perform non-damaging investigations with high depth resolution (~0.5 nm) for the near-surface region. The survey channels are based on unique semiconductor detectors, having an energy resolution of ~3 keV (an approximately 5 nm depth resolution at the surface) and placed on backscattering angles of 120° and 175°.

This unique X-ray detector makes possible highly efficient measurements of quanta with energies beginning from 500 keV (K-line of oxygen). The measurements of X-ray spectra in the aligned regime allows one to investigate the structural perfection of sublattices formed by separate elements in multielement single crystal samples. A combination of modeling and spectra treatment computer programs, taking into account the specific character of middle-energy ion scattering and aimed at the distinct interpretation of the experimental results, was carried out. The experimental testing of possible applications for the existing channeling theory to the above-mentioned energy region was performed.

During the past three years, the following objects have been investigated: HTSC films, substrates and interface layers, HTSC single crystals, defects of single crystals appearing in the implantation process, the distribution of implanted ions, initial stages of HTSC film growth, and others.

Scientific Papers

V.V. Afrosimov, G.O. Dzjuba et al., Behavior of Bi-Sr-Ca-Cu-O Thin Films on Si, SiC, and MgO Substrates during Annealing at Various Temperatures, Supercond. Phys. Chem. Technol., 1991, vol. 4, no. 9, pp. 1674–1684.

V.V. Afrosimov, G.O. Dzjuba et al., Channeling of Medium-Energy Protons in a YBa₂Cu₃O_7-x Single Crystal, Tech. Phys., 1996, vol. 41, no. 12, pp. 1240–1246.

Foreign Collaborators

Dr. J. Leotin, Centre National de la Recherche Scietifique, Delegation Regionale Midi-Pyrenees, Service National des Champs Magnetiques Pulses, Toulouse, France.

№ -0123 Microscopic X-Ray Fluorescent Tomography Based on X-Ray Optics

Full Title:	Development of Methods and Devices for Microscopic X-Ray Fluorescent Tomography Based on the Use of X-Ray Optics
Technology Field(s):	PHY-OPL: Physics / Optics and Lasers CHE-RAD: Chemistry / Photo and Radiation Chemistry

Contributors

Vasily A Shelokov

CCB "ALMAZ" (ALMAZ) 80, Leningradskii pr., Moscow, 111024, Russia Phone: 7+095+1759410; 7+095+2619581 Fax: 7+095+1585671; 7+095+2619581

Present Status of Research

Brief Description of Research

It is proposed to elaborate nondestructive methods for 3D reconstruction of the distribution of some admixture in a sample on the basis of processing X-ray fluorescent signals obtained by scanning on the sample with a focused X-ray beam. This includes methods which exclude the necessity of rotating the sample. The admixture may have a continuous distribution in the sample or be in the form of a set of particles or clusters.

At present, some models of X-ray fluorescent signal formation have been created for various types of objects including objects containing spatially distributed nonhomogeneities. Some approaches have been worked out for solving the corresponding inverse problems (see [5]–[8]).

The possibility for nondestructive analysis of nearsurface layers will be achieved for bulk samples, to which traditional tomographic methods cannot be applied.

Local nondestructive analysis of small concentrations of an admixture and exclusion of mechanical movement (rotation) of the investigated sample for 3D reconstruction of its interior structure will also be achieved.