Issue N^{o} 3, 1990 
NUMERICAL GASDYNAMIC SIMULATION OF STRONG EXPLOSIONS IN EXPONENTIAL ATMOSPHERE
V.A. Zhmaylo, V.V. Zmushko, F.A. Pletenev, I.D. Sofronov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 39.
Numerical research on 2D problem of single explosion and 3D problem of two explosions at the same height in exponential atmosphere is described. The research was carried out within dasdynamic models with numerical approaches and within a modified method of infinitely thin shock layer. The computational results produced with different models both for 2D and 3D problems are compared.

PRINCIPLE OF MULTIPLICATION AND IDENTIFICATION OF THE MAIN PART OF THE MAPPING WHEN SOLVING NUMERICALLY THE STIFF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS N.Yu. Bakaev, V.N. Mikhailov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 1014.
A new approach to efficient numerical solution of stiff systems of nonlinear differential equations is suggested. A principle of multiplication and identification of the main part of the mapping that predetermines this stiff system formulated in this work lies in the basis of this approach.

SOLUTION APPROXIMATION FOR LAGRANGIAN BALLISTIC PROBLEM A.V. Zabrodin, N.N. Chentsov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 1517.
A classical problem of two flyingaway flat pistons separated with a volume of highlycompressed ideal gas with γ isentrope index is under consideration. Approximated formulas to find final energy of light pistons and gas velocity distribution as functions of Eulerian and Lagrangian coordinates are suggested; their relation with Sedov similarity solutions for flat cylindrical and spherical flows is shown. Computational difficulties for the ballistic problem with difference methods at γ ≈ 1 are analyzed; the volume of the model is estimated from below.

NUMERICAL SOLUTION OF 3D KINETIC EQUAITON IN COORDINATE SYSTEMS OF SPHERICAL AND CYLINDRICAL TYPES S.B. Serov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 1821.
Algorithms of numerical solution of 3D kinetic equation written in spherical and cylindrical coordinate systems and in a fixed basis momentum space Ω are described.

METHODS OF INCOMPLETE FACTORIZATION. PART 3. THEORY AND EXPERIMENTS V.I. Ilin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 2227.
The article is the finalizing one in a series of three devoted to methods of incomplete factorization to solve mesh linear equations. It discusses the issues of theoretical substantiation of methods, in particular the issues of no degeneracy of matrices, of the iteration processes convergence, of the evaluation of the iteration convergence velocity. The analysis of experimental data is provided and practical recommendations on implementation of various algorithms are given.

MATHEMATICAL SIMULATION OF NONUNIDIMENSIONAL NONSTATIONARY GAS FLOWS IN POWER UNITS Yu.A. Skvortsov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 2831.
A method of numerical simulation of nonunidimensional nonstationary flows of incompressible nonviscous gas in the airgas channel of power units based on implementation of direct replacement of local approximating functions into the integral form of the preservation equations for the element of the computational domain is described. The performance of the method is shown using the computational example of 2D nonstationary gas flow in axisymmetric ring channel of variable area.

COMPUTATIONS ON STATIONARY SUBSONIC VORTEX FLOWS OF THE IDEAL GAS IN AXISYMMETRIC CHANELS OF COMPLEX GEOMETRIES O.B. Khayrullina VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 3239.
A finitedifference method to construct stationary subsonic flows of the ideal gas in axisymmetric simplyconnected channels of complex geometries is developed. The method is based on implementation of nonorthogonal optimum curvilinear meshes and allows calculating vortex flows with closedloop lines of the flow. The results of numerical computations are provided to demonstrate the performance of the method. It is shown that in case of a large variation range of the Mach number when calculating subsonic flows we need to account for the compressibility of the gas.

FOURIERSPLINE APPROXIMATIONS OF QUASISTATIC ELECTROMAGNETIC FIELD WITH LOCALLY NONUNIFORM DISTRIBUTION OF SOURCES A.M. Afonin, A.Yu. Pautkin, A.S. Roshal VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 4043.
A new efficient method for calculations on quasistationary electromagnetic field created by a bunch of charged particles that occupies a relatively small part of the area under investigation is proposed. To do the computations of the potentials and the fields, we used the method of partition followed by Fourier series expansion by two coordinates and implementation of splineapproximation by the third one. An analytical solution of auxiliary tasks followed by joining numerical and analytical solutions at the boundary of the bunch is used in the areas not occupied by the bunch. The method has high accuracy and is costeffective as it does not use finitedifference approximation of derivatives and the computational grid is introduced only in the area of the bunch. The results of comparison between the analytical and numerical solutions for several benchmark problems are provided.

MULTIDIMENSIONAL COMPUTATIONS OF STRONG EXPLOSIONS IN EXPONENTIAL ATMOSPHERE B.L. Voronin, V.A. Zhmaylo, A.G. Kozub, S.I. Skrypnik, I.D. Sofronov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 4450.
The computational results on the problem of two strong explosions of the same yield simultaneously in the exponential atmospheres at the same height at a certain distance from each other are described. 2D and 3D options of the problem (depending on the distance) are considered. The computations were carried out using RAMZES software package based on EulerianLagrangian computational method for multidimensional nonstationary gasdynamic problems. A distribution pattern of gasdynamic parameters in the area covered with a shock wave was produced, as well as its development with time. There was noted the preservation of the 3D character of the perturbed area shape in the respective computations at all the time range of the computation starting with the collision moment of the shock waves spread from the blasts.

A PROBLEM ON FLYING THE PISTON WITH A CHARGE OF EXPLOSIVES OF CONICAL SHAPE A.V. Zabrodin, L.A. Pliner VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 5155.
The explosive in the problem under consideration is initiated by the contact with the impactor that flies at a constant velocity. Specific features of the ongoing processes are reproduced in the numerical experiment. A formula for approximated estimation from above of the velocity of piston flying that gives good agreement with computational data is produced.

STABILITY OF DIFFERENCE SCHEMES FOR PARABOLICAL EQUATIONS IN ARBITRARY NORMS. PART 3. N.Yu. Bakaev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 5661.
A stability theory of additive difference schemes in Banach spaces is described. The produced estimations of stability are the generalization of the results produced by the author on the stability of nonsplit difference schemes. And the components of the initial operator splitting are not supposed to be commutating, but we need them to be close to the commutating in the sense specified in the paper. The results of the work can be applied to the additive schemes both with constant and with alternating transition operator. Stability estimations for additive schemes with perturbed operators are constructed.

COMPUTATIONS ON THE EQUATIONS OF STATE FOR THE ALUMINUM IN HIGHTEMPERATURE RANGE ON THE BASIS OF THE MODIFIED HARTREEFOCKSLATTER MODEL A.F. Nikiforov, V.G. Novikov, S.K. Trukhanov, V.B. Uvarov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 6274.
The tables of pressure, internal energy and average ionization degree are provided for aluminum in a wide range of temperature and density variation (4 eV ≤4 keV; 0.01 ≤ ρ≤ 100 g/cm^{3}) when calculated using the modified HartreeFockSlatter model. The produced data were analyzed, Hugoniots for uniform and porous aluminum were constructed, and the results were compared with experimental data and computation results by other authors. The work is the first one in the series of efforts on functional completion of the THERMOS data base developed in the M.V. Keldysh Institute of Applied Mathematics of the Academy of Science of the USSR.

CENTRAL PART OF THE SOFTWARE OF THE FILM PREPARATION SYSTEM AT THE NONHOMOGENEOUS COMPUTER SYSTEM A.A. Solonenkov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 7578.
General description of the central part of the software of the film preparation system at the nonhomogeneous computer system is provided. Graphic data are collected within centralized system output. The archive structure of the system is described. A microfilming device is used for the output of vector images on the film.

LINGO PACKAGE TO WORK WITH EXTERNAL DATA L.V. Nesterenko, D.M. Obuvalin, S.V. Sivolgin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 7983.
A technology to work with external storage located at the same conceptual level with widely spread imperative programming language is described. From the user’s point of view it has independent properties from the language used and from the operational environment. LINGO complex comprises four basic components: a compiler of declarative statements; precompiler(s) of the access operators of the programming language(s); an executive system and an administrator. User’s interface of LINGO system is represented by data access language, which is submerged into the user’s programming language and is processed by the precompiler. The executive system and the administrator are hidden from the level of the applied programming. They are meant for the data access, dynamic connection of the declarers with the copies of data, program operation synchronization with the data being separated.

IMPLEMENTATION OF NUMEICAL  ANALYTICAL METHODS FOR THE GAS SEEPAGE INTO THE VACUUM I.A. Bashkirtsev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 3. P. 8489.
A problem of gas seepage into the vacuum in case of spherical and cylindrical symmetry is considered. The convergence rate of characteristic series was experimentally studied there. Acceleration methods for convergence of series were implemented; the values of gas dynamic parameters were produced with high accuracy both for the case of the cavity implosion and for the case of the gas seepage from the ball (cyllinder). The provided results can be used as references when solving gas dynamic problems with difference methods.

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