Issue N^{o} 4, 1993 
SATURN PARALLELIZATION ALGORITHM FOR 3D TRANSPORT EQUATION
A.V. Alekseev, R.M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 37.
A parallelization algorithm is presented for numerical kinetic solution of 3D multigroup transport equation using difference schemes that are typically characterized by a family of planes crossing the symmetry axis and dividing the spatial body into volume sectors. The specific feature of the algorithm is that it can be parallelized into relatively large number symmetric (similar in terms of computational cost) processes which insures an efficient leading of all processing elements. The parallelization relies upon the concept of sequential processes loading. The paper contains analytical estimates for the parallelization algorithm. Numerical studies on 10processors Elbrus2 multiprocessor showed that this algorithm allows to reduce considerably the computation time when the problem is solved numerically while demonstrating a relatively low overhead and efficient usage of computer resources.

A SUCCESSIVE CONSTRUCTION OF THE SOLUTION IN THE PROBLEM OF THE STRATIFIED SHELL SYSTEM CONVERGENCE G.V. Dolgoleva, A.V. Zabrodin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 814.
The paper gives a solution construction (successively considering Impact domains) in the stratified shell system dynamics problems. General rules, showing stratified shell system dynamics with regard for example, to HIF targets are found. The knowledge of the stratified system dynamics dependence on multiple specifying parameters (geometry, material, number of layers and energy release method selection) allows the optimization of such constructions. The consideration uses the hydrodynamic approach.

THE DISCRETE PHOTONS METHOD. 2. REGULAR AND NONRECRJLAR SETS OF DISCRETE DIRECTIONS, NUMERICAL RESULTS FOR TEST PROBLEMS A.M. Bujko, Yu.A. Demeatyev, R.F. Mashinin, I.D. Sofronov, E.N. Tikhomirova, E.G. Vasina VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 1521.
The method is intended to solve threedimensional timedependent radiant heat transfer problems. Approximate equations describe locally thermodynamically equilibrium radiation with account of material absorption and Isotropic scattering. Spatial cubooctahedron mesh and two sets of discrete directions are used. Two test problems numerical solutions are given. The problem concerning plane wave travelling with constant speed was solved using regular set of 14 directions correlated with cubooctahedron cells. The numerical results are in good agreement with analytical solution of the problem for radiant heat conduction equation. The problem of radiation transfer within a spheric cavity puts high requirements to angular description accuracy. With regular discrete directions set the numerical solution reveals strong ray effects. With specially precalculated view factors using nonregular set of directions aimed at boundary cells the solution is free from ray effects.

A CONJUGATECONSISTENT DS_{n}METHOD FOR SOLVING MULTIDIMENSIONAL NEUTRON TRANSPORT EQUATIONS IN CURVILINEAR COORDINATES S.B. Serоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 2228.
A conjugateconsistent version of the DS_{n}method for solving multidimensional kinetic equation in curvilinear coordinate is proposed. In case of curvilinear geometries conjugateconsistent DS_{n}method shows some advantages not typical of classical DS_{n}method by Carlson.

MULTIGROUP INTERACTION CHARACTERISTICS SETTING FOR PLANE NEUTRON SHIELDING CALCULATION V.P. Gоrelоv, G.G. Farafоntov VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 2933.
The setting procedure is proposed for multigroup characteristics of neutron integration with layer material in a specific plane shielding. Resonance effects and their spaceangular function are approximately described.

SPACIAL AVERAGING IN MATHEMATICAL MODELS OF POLYPHASE MEDIA WITH SMALL VOLUME CONCENTRATION OF THE CONDENSED PHASES Yu.M. Kоvalev VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 3439.
The mathematical model of flows polyphase media with small volume concentration of the condensed phase is proposed. The equations relating the derivatives of the averaged over the phase parameter to the averaged derivative of the corresponding microparameter are obtained for the spacial averaging.

EXPLICIT ITERATIVE DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS V.T. Zhukov VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 4046.
The modifications of special explicit iterative difference scheme with Chebyshev parameters for parabolic equations are constructed. Properties of these schemes are investigated and comparison with traditional schemes is carried out.

GENERATING ADAPTIVE AND SURFACE GRIDS S.A. Ivanenко VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 4753.
Adaptive grid generation algorithm is considered. It is based on the variational method for quasiuniform grid generation on the adapted function value surface. Computational results to illustrate method capabilities are presented.

ASYMPTOTIC (WITH LARGE REYNOLDS NUMBERS) EQUATIONS FOR FAST OSCILLATINCFLOW OF MULTICOMPONENT VISCOUS GAS WITH 1D OSCILLATIONAVERAGED FARAMETERS Yu.A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 5461.
The paper gives a very general definition of "physically observable" 1D symmetry for fastoscillating solutions and their mathematical description. "Onedimensional" equations are presented resulting from the consistency analysis of previously obtained 3D equations for multicomponent viscous compressible fastoscillating gas flow after substitution of "physically 1D" solutions into them. In original NavierStokes equations the component pressures are assumed to be identical. Heat conduction molecular diffusion and chemical reactions are neglected. The component equations of state are arbitrary. The equivalent divergent form of the closed asymptotic equation system of "1D" fastoscillating flow for multicomponent gas is considered.

THREAD DYNAMICS IN THE BODIES BRAKING PROBLEM V.A. Svidinsку VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 6268.
Within the flexible linearelastic thread model the problem of high velocity solid body braking by attaching primary motionless textile tapes is raised. For this problem basic shock effects in a thread are considered. Characteristic features of wave adiabats are noted. The Riemann problem and the "piston" problem for a finite thread are solved. It is possible to apply textile tapes used in parachute constructing for creating given conditions for braking of bodies with initial velocities to 1000 m/s.

EGAK  PACKAGE FOR 2D FLOW CALCULATIONS IN A MULTICOMPONENT MEDIUM Yu.V. Yanilkin, N.P. Kovalev, A.A. Shanin, E.S.Gavrilova, E.V. Gubkov, N.S. Dibirova, O.A. Dibirov, G.V. Zharova, A.I. Kalmanovich, I.N. Pavlusha, M.S. Samigulin, G.P. Simonov, O.G. Sinkova, M.G. Sotnikova. V.I. Tarasov, T.A. Toropova VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 6975.
A program package for 2D flow calculations in a multicomponent medium showing severe deformation of contact boundaries is presented. The method of concentrations is used to localize the contact boundaries. Calculations of broad class continuum mechanics problems are given.

TIMEDEPENDENT ION MOTION THROUGH SOLID BODY G.H. Pоtetyunko VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 4. P. 7679.
The motion of a broad ion beam through a flat target is considered, using a timedependent definition and smallangle approximation for ion energy, which is in the maximum of material electron deceleration potential and somewhat, lower, where electronic constant dominates the ion deceleration. Analytical solution is obtained using the approximation based on the unique ion energy dependence on ion penetration depth. A method of possible problem solution is discussed for low ion energies, where elastic component dominates the deceleration. For plane geometry, the solution of propagation theory problem is shown to be analytically dependent on μ = cost γ before the first derivative of depth distribution function, which indicates that the unity instead of μ is reasonable in smallangle approximation.

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