Issue N^{o} 12, 1995 
A METHOD FOR NUMERICAL SIMULATION OF 2D TIMEDEPENDENT FLOWS IN POLYDISPERSE MEDIA
M. S. Samigulin, Yu. V. Yanilkin, E. S. Gavrilova, A. A. Shanin VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 38.
A method is discribed for numerical simulation of 2D timedependent flows in polydisperse media using the model of interpenetrating continua. The system of differential equations is numerically integrated on a fixed arbitrary quadrangular grid. The motion of interfaces and that of the boundaries of domains containing the fractions of dispersion phase are computed with a special algorithm preventing numerical diffusion. The algorithm allows to model the flows where the carrier phase consists of several materials differing in physical properties and the interfaces are highly distorted. To demonstrate the method capabilities, the simulation results are presented for the experiments with shock waves in dustgas (mono and polydisperse) media.

KINETICSTATIC MODEL FOR THE STRESS RELAXATION V. A. Bychencov, K. E. Vasilchenko, A. A. Gornovoi VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 912.
A computational model is presented for the elasticplastic flow in terms of relaxation kinetics for shear stresses in a solid body and destruction kinetics. For the submicrosecond of lifetime a dilatone model of kinetic strength theory is used obtained from statistic theory. The same approach is used to the simulation of spalling distruction and the relaxation of compressing stresses. The Lagrangian numerical method is developed for dynamic applications. The computational results for the attenuation of the clastic precursor in steel and cylindrical steel shell motion are compared with the experiment.

DEUTERIUM THERMON UCLEAR COMBUSTION WAVE IN A MAGNETIZED PLASMA CHANNEL E. A. Zabrodina, N. A. Krasnoborov, M. D. Churazov, О. A. Vinokurov, N. A. Ryabikina VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 1318.
The results of some set calculations and estimations were considered for the thermonuclear deuterium (D_{0,9}^{3}He_{0,1}) burning in magnetized plasma channel. It was concluded that there is the necessity of inserting the kinetic transfer of the charged particles. In the case ρ_{0} ≈ 30 g/cm^{3}, R_{0} ≈ 0,01 cm, m_{об} ≈ 3g/cm it was obtained the velocity of the burning wave D ≈ 1,16 ⋅ 10^{9}cm/s. The conditions of the thermonuclear deuterium experiments ( Е_{O} ≈ 300 MJ) were estimated for the modernized big accelerators RHIC (BNL) or LHC (Cern).

SPALL FRACTURE COMPUTER SIMULATION I. R. Trunin, B. L. Glushak, S. A. Novikov VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 1924.
Results of numerical simulations for spall fracture of natural uranium under highrate deformation in expansion counterwaves. Spall fracture process is described using kinetic micromechanical model with internal parameters treating the fracturing as continuous emergence and increase of defects followed by coupling find macrofissure formation. Specific parameters values for kinetic model are given. The comparison with experimental data shows that computational results agree with principal laws of spall fracturing for metals.

THE COMPUTATIONAL METHOD FOR CURRENTS EXCITED IN WIRE ANTENNAS UNDER THE EFFECT OF PULSE ELECTROMAGNETIC FIELDS A. I. Golubev, M. D. Kamchibekov, V. A. Terekhin VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 2532.
A method is presented to evaluate the current excited by a plane electromagnetic wave on a thin cylindrical wire in a nonconducting medium. The method relies upon the solution of Poclington equation in the time representation that is reduced, through special replacement, to a system of equations, like telegraph equations, but with nonlocal inductance. The finitedifference method is presented for the resulting equations. Its performance is illustrated by one problem treating the electromagnet is pulse effect on a thin linear antenna for various ratios between the pulse duration and antenna length.

RAYLEIGH TAYLOR INSTABILITY IN STRONG MEDIA S. M. Bakhrakh, N. P. Kovalev VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 3337.
The analytical study results are presented for RayleighTaylor instability in elastic and viscous media. These results are suggested for testing numerical methods. Two applications are emphasized. The evolution of sinusoidal perturbations of the interface between an elastic medium and perfect gas under the constant acceleration g directed towards solid body. In this case (unlike the gases) there exists a critical perturbation wavelength λ _{k}. The exponential, amplitude growth occurs only for the perturbations with the wavelength λ > λ _{k}. For the pulse acceleration the interface fluctuates with the period defined as the shear module and density function. A useful test is the evolution of the perturbed interface between viscous fluid and a gas under pulse acceleration. In this case, as opposed to inviscid gases, the exponential factor appears decreasing the amplitude growth rate. This solution is interesting in that it can be used for the evaluation of approximation viscosity in numerical methods for gasdynamic (inviscid) flows.

EXACT SOLUTIONS FOR THE SYSTEM OF EQUATIONS IN RADIATION GASDYNAMICS A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 3847.
The paper is devoted to the problem of finding analytical solutions for system of equations in radiation gasdynamics, the complexity of which is defined first of all by (he necessity to account a great number of physical processes. Exact solutions of multidimensional gasdynamic equations with account to spectrum radiation transfer in anisotropic, scattering medium are obtained using specially chosen absorption and scattering coefficients. Tests are developed based on these solutions which allow to analyze the solutions in radiation gasdynamics in different approximations.

"TWOSTREAM" VISCOUS FLOW COMPUTATION TECHNIQUE FOR NONEQUILIBRIUM PLASMA IN MAGNETIC FIELD E.M. Antonenko, V. P. Bashurin, G. V. Dolgoleva, V. A. Zhmailo VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 4853.
The system of equations for “twostream” onedimensional flow of rarefied plasma, in magnetic field is presented. Numerical technique is described to calculate these equations. An example is given to illustrate this technique capabilities, namely, sector computation of point explosion in exponential atmosphere with magnetic field.

THE ACCELERATION OF CONVERGENCE OF ITERATIVE PRO C2SS AT CONSTRUCTING BLOCKREGULAR GRIDS O. B. Khairullina VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 5459.
Paper in details describes the acceleration of iterative: procedures with the purpose of fast stabilization of grid, testing on series of test problems of algorithm and program MOPS2a, which permits to design blockregular optimum curvilinear grids in twodimensional simplyconnected and multiconnected domains of simple and difficult topology, having smoothness of coordinate lines on boundaries of joinings of blocks.

ANALYTICAL PROBLEM SOLUTION FOR THE CURRENT INDUCED ON THIN INFINITE CONDUCTOR UNDER THE INFLUENCE OF LONGITUDINAL PULSE ELECTRICAL FIELD A. I. Golubev, V. A. Terekhin VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 6064.
Green function for current induced by pulse electromagnetic field on thin infinite conductor in nonconducting medium is obtained. Approximalion formula for this function is given which has sufficient accuracy for applications in the entire range of argument variations. The dependence of amplitude current values on conductor orientation with respect to electromagnetic wave front plane is qualitatively investigated.

NUMERICAL EVALUATION OF THE EXPLOSIVE BURST TYPE UNDER HEAT EFFECTS S. V. Bazhenov, A. A. Bazin, V. V. Gorev, T. V. Korolkova, B. N. Krasnov, S. V. Tsykin, Yu. D. Chernyshev VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 6571.
The 1D numerical method is presented for the chemical kinetics, neat conduction and gas dynamics equations specially dealing with thermal initiation of condensed explosive. The method property is that it has two grids one of them being reconfigurable. The method capabilities are demonstrated by two applications treating the history of a thermal explosive model. It is shown how the detonation is affected by the abnormal growth of the explosive conductivity in compression waves generated by the flame.

TVD METHOD ON ADAPTIVELY EMBEDDED GRIDS IN SUPERSONIC GASDYNAMIC APPLICATIONS A. N. Gilmanov, N. A. Kulachkova VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 7278.
An approach is proposed combining the finitedifference TVD method and adaptively embedded grids for 2D computations of supersonic inviscid gas flows over targets. The computational data are compared with known exact solutions. This combined approach is shown to be an efficient method for complex gasdynamic applications with large gradients of functions to be found and allows to obtain the solutions with relatively low processor tune cost.

NUMERICAL TECHNIQUE FOR I D TWOTEMPERATURE GAS DYNAMICS INCLUDING PONDEROMOTIVE FORCE AND HEAT CONDUCTION RESTRICTION EFFECT S. G. Garanin, Yu. F. Kiryanov, G. G. Kochemasov VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 7986.
Numerical technique is developed for solving onedimensional problem on interaction of powerful laser radiation with plasma in twotemperature gasdynamics approximation with account to energy transfer at the expense of heat conduction, ponderomotive force and heat conduction restriction effect It is shown that the chosen difference scheme describes well known analytical results with satisfactory accuracy.

RIGHTHANDSIDEITERATIVE METHOD FOR THE SYSTEM OF GROUP MESH MULTIDIMENSIONAL TIMEDEPENDENT DIFFUSION EQUATIONS L. P. Fedotova, R. M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 8790.
A new method iterative over the righthand side is generated for the system of group mesh equations for multidimensional diffusion. The method relies on the introduction of special algebraic systems at the timesteps to relate the solution of the energy group with the solution in all remaining groups and subsequently use these systems for the evaluation of parameters for a process iterative over the righthand side. The systems are generated from the source mesh diffusion equations. The multidimensional analog of the limit run coefficient is used. It is shown that the use of the suggested iterative method demonstrates a. very high efficiency.

MODIFICATION OF PARABOLIC GRID GENERATOR V. A. Mikhalin VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 9194.
One of the more efficient generators of grids for timedependent gas dynamics is the parabolic generator allowing to construct regular grids in domains with complex boundaries and demonstrating a relatively high speed. The grid is generated in two steps: algebraic predictor and parabolic corrector steps. The first step uses predefined values of grid node coordinates on the domain boundaries. However for complex configurations, fixing the grid nodes on the outer boundaries may lead to strong deformation of cells inside the domain or even to their degeneration. This paper proposes a modified algorithm where the predictor step does not fix grids nodes on the outer boundary specified by the reference nodes and local polynomials. The paper contains the polynomial descriptions and the examples of grids generated in the course of computations of flows over aircrafts and aerody namic interference.

THE DEVELOPMENT OF SMALL PERTURBATION METHOD AND STUDY RESULTS FOR THE STABILITY OF HYDROSTATIC EQUILIBRIUM OF TWO GASES IN THE GRAVITY FIELD G. A. Grishina VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 95102.
A brief presentation is given for the general approach to small perturbation method. The solution for the disturbed problem is represented as Taylor series from the variations of initialboundary conditions of the undisturbed problem. The differential equations are given for the evaluation on the first and second derivatives of this series. The problem for the stability investigation of the equilibrium in the gravity field of two contacting gases is solved analytically. The solution found from the sum of two variations shows how the sinusoidal boundary shape changes with time and jets form when the upper medium is heavier than the lower one. The problem is given as an example of how to account approximation in the investigations of flow stability with the small perturbation method.

THE EVALUATION OF EXTERNAL TEMPERATURE EFFECTS FROM TEMPERATURE SPECTRUM V. V. Bashurov, A. M. Kononov VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 103105.
The simplest twoparameter model is considered for the body healing under the external temperature effect. The notion of temperature spectrum is introduced as the maximum body heating dependence from the parameter determining its thermoinertial characteristics. The approximate solution is given for the problem of finding the external temperature from the specified temperature spectrum. It. is proved that in the class of nonnegative monotonically increasing functions this problem reduces to the conversion of the Laplace transform for the specified function.

ALGORITHM OF NONLINEAR LEASTSQUARES METHOD WITH SIMPLE LIMITATIONS ON VARIABLES Y. P. Romanikhin VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 106110.
Implementation of the nonlinear leastsquares method with apriori twosided limitations on variables is given. The optimization GaussNewton scheme was used. The linear equation systems which appeared m the problem were solved using orthogonal matrix transformations which allowed to considerably reduce requirements to information representation accuracy. It is shown that imposing twosided limitations on the parameters of the approximating function is a rather powerful stabilizing factor extending the convergence domain of the nonlinear leastsquares method based on the GaussNewton method.

COMPUTATION OF THE LINEAR HEAT CONDUCTION PROBLEM ON DISTRIBUTED MEMORY COMPUTERS (MP3, DELTA) A. N. Bykov, B. L. Voronin VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 111113.
One of the schemes is considered for parallel computation of 3D linear heat conduction problem on a distributed memory computer based on the wellknown method of splitting over spatial variables. Results of paralleling efficiency measurement, are given which were obtained at, (he problem computation on computer systems: Delta of Intel Corporation and MP3 developed at VNIIEF.

NUMERICAL SIMULATION OF TWODIMENSIONAL CRYSTAL DEFORMATION AND FRACTURE V. K. Golubev, A. A. Selezcnev VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 114116.
By using the method of molecular dynamics, numerical simulation of deformation and fracture of the twodimensional argon crystal under conditions of uniaxial tension and onedimensional deformation of tension and compression was carried out. The diagrams of loading force and temperature for the perfect and faulty crystals under tension and compression were received. Some characteristic features of deformation and fracture were obtained.

ON ESTIMATION OF RESIDUAL VELOCITY AT TARGET PIERCING BY A PENETRATOR M. P. Kuzhel VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 12. P. 117118.
A technique for estimation of penetrator residual velocity at, piercing a target is suggested which is based on derivation of the balance equation using mechanical energy equivalent. Such an approach allows to take into account the processes accompanying penetrator penetration into a target more accurately as compared to known approaches.

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