Issue N^{o} 2, 1991 
DESCRIPTION OF A TEST SET FOR 2D PROCEDURES AND PROGRAMS IN GAS DYNAMICS. PT. 1
Yu. A. Bondarenko, B. L. Vоrоnin, V. I. Delоv, E. N. Zubоv, N. P. Kоvalуоv, S. S. Sокоlоv, V. E. Shmarulin VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 39.
A problem set is proposed designed for testing 2D procedures and programs in gas dynamics. The authors kept in mind that a test problem must have properties similar to those of most typical actual problems. It is desired for the test problem to have an exact solution. The set consists of 15 tests. This part contains the first seven tests while the others are presented in part 2.

DESCRIPTION OF A TEST SET FOR 2D PROCEDURES AND PROGRAMS IN GAS DYNAMICS. PT. 2 Yu. A. Вondarenko, B. L. Vоrоnin, V. I. Delоv, E. N. Zubоv, N. P. Kоvalуоv, S. S. Sокоlоv, V. E. Shmarulin VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 1014.
A problem set is proposed designed for testing 2D procedures and programs in gas dynamics. The authors kept in mind that a test problem must have properties similar to those of most typical actual problems. It is desired for the test problem to have an exact solution. The set consists of 15 tests. The first seven are described in part 1 while this part contains the others.

WIDE RANGE TABULAR EQUATION OF STATE FOR WATER A. T. Sapozhniкоv, G. V. Kovalenko, P. D. Gershchuk, E. E. Mironоva VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 1519.
Results of the GLOBUS tabular equation of state are given for describing thermodynamic water and vapor properties in a wide temperature and density range. Thermal pressure and energy components are represented by tables on a uniform logarithmic mesh with a bicubic interpolation between the nodes. Potential pressure is given by a cubic spline on a cubic spline on a uniform density mesh for densities less than normal one and on a uniform logarithmic mesh for densities greater than normal one. The equation of state describes experimental data for water and porous ice shock compression, thermal expansion and vaporization along with predicted results for the ThomasFermi model with quantum and exchange corrections. Thermodynamic water properties are taken for densities and temperatures ranging from 0,001 to 64 g/сm^{3} and from 300 К to 10^{6} К respectively. An extrapolation beyond the table is provided. The GLOBUS may be used in continuum dynamics programs.

A STABILITY IN BAMACH NORMS OF DIFFERENCE SCHEMES APPROXIMATING PARABOLIC DIFFERENTIAL EQUATIONS ON A GRID, UNIFORM IN EVOLUTION VARIABLE N. Yu. Bакaуev, V. V. Vyazankin VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 2024.
Stability estimated in Banach norms are obtained for difference schemes constructed within the RungeKutta method on nonuniform grids (close, in a sense, to uniform ones).

TRANSITION TO A MULTIGROUP APPROXIMATION IN TAKING INTO ACCOUNT DIRECTED MEDIUM NUCLEI MOTION IN A BALL AND IN A ROTATING SOLID G. A. Gоnchaгоv, V. P. Gorelov, G. G. Farafontov VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 2529.
One of possible way for taking into account a directed medium nuklei motion using a multigroup approximation is studied. Formulas are derived for computing neutron interaction group characteristics and multigroup equations are written for a ball and a rotating solid. The approach developed is characterised by group shape dependencies on the direction of a neutron impacting a moving target.

ANALYTICAL INTEGRATION OF A TRANSPORT EQUATION OVER THE FREE PATH LENGTH S. N. Sheludкo VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 3033.
Partial analytical integration of von Neumann series describing a transport equation solution is performed (over all free path lengths). Computations were carried out for, problems with infinite uniform media, point, threadlike, and plane sources. A timeindependent case is considered. The formulas obtained may be used to derive local estimates of the Monte Carlo method for the problems related to a deep penetration of radiation into materials.

A GENERALFURPOSE PULSE ANALYZER PROGRAM FOR INVESTIGATIONS IN NUCLEAR PHYSICS N. N. Zalуalov, M. M. Leplyavkina, M. S. Dudоrоv, Yu. I. Vinogradov VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 3437.
Multichannel computer and KAMAKhardware based analyzers are widely uaed for investigations in nuclear physics. Most of implemented analyzer programs are oriented to a fixed recorder system structure and perform within a specific experiment. For a broad range of multiparameter experiments, the general purpose pulse analyzer program provides a flexible organization of spectrometry measurements based on KAMAKhardware. The program tuning to a specific configuration of a measurement KAMAK system, structure definition of data to be accumulated and experiment monitoring are performed in an interactive mode. The program includes service capabilities for data set control, spectrometry data visualization, its simplest preprocessing and holding it on external magnetic media, along with facilities for measurement process automatization. The program is written in Assembler language and executes on the SM and Electronica60 computers under OS RAFOS or RT11.

THE EQUATIONOFSTATE CENTER PROGRAM COMPLEX ON THE ES EVM V.A. Zherebtsov, V.P. Kоpуshev VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 3841.
General design and operation principles are described for the ZURSES Complex intended for investigating various equationof state. The Complex comprises a programset to implement various equationofstate models and to solve different problems including isolinez and adiabat tracings, thermodynamic quantity computations etc. using these equations. The programs are related to each other only through a single parameter organization way, so that Complex nonoriented programs may be also added. The Complex provides programming automatization tools to write new programs which makes their development easy.

NUMERICAL SIMULATION OF A MODERATELY UNDEREXPANDED SUPERSONIC B. Sh. Albasarоv, A. A. Вezruкоv VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 4250.
Modified highorder IVDtype schemes are used to give a formulation of problems, which adequately simulate a timedependent process of perfect gas supersonic jet formulation and a timeindependent flow from a sonic nozzle along with numerical methods. The transition of a lifted jump regular reflaction to an irregular one within the first jet "barrel" is studied as the jet noncomputability varies. A comparison with an experiment is carried out.

A PROCEDURE FOR COMPUTING CHARACTERISTICS OF AN ELECTROMAGNETIC FIELD EXCITED BY AN INTENSE GAMMA BEAM IN AIR G. G. Bliznуuk, A. V. Ivanоvsкy, A. A. Sоlоvуоv VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 5156.
A mathematical formulation and a numerical method are described for computing electromagnetic field parameters in the vicinity of a strong gamma quantum beam moving through the air. The field characteristics are derived from a 1D system of equations obtained with a running wave approximation. A system of ionization kinetics equations is solved to find a radiationinduced conduction in the medium. The sources, that is current density of charged particles produced by gamma quanta (electrons and positrons) and air ionization intensity are determined by solving equations with a selfconsistent field and a collision integral in the FockerPlank form. A numerical example is given.

A SEMIEMPIRICAL EQUATION OF STATE POR METALS WITH A VARIABLE NUCLEUS AND ELECTRON HEAT CAPACITY B. L. Glushak, L. P. Gudarenкo, Yu. M. Stуazhкin VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 5762.
For the equation of state presented the pressure and energy are splitted in potential, thermal grid and thermal electron components. Grid and electron heat capacities sire functions of density and temperature. Physical contents of some equation of state components is discussed. For copper, parameter values of heat components are given and potential pressure dependencies on density are defined. A comparison is carried out with experimental data obtained using absolute and relative methods.

A SPECTRAL RADIUS ESTIMATE FOR AN ARBITRARY MATRIX O. V. Diуanкоv VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 6366.
An estimate of a spectral radius for an arbitrary matrix is proved using a spectral radius of a symmetric one derived from a source matrix. Some examples are given of using this estimate when investigating one matrix type resulting from consideration of difference scheme issues in gas dynamics. The Godunov scheme stability was studied for a 2D case.

RECHARGE AND IONIZATION PROCESS SIMULATIONS IN INVESTIGATING THE STAGNATION OF AN IONIZED CLOUD BREAKING OUT INTO A RAREFIED MAGNETIZED PLASMA V. P. Bashurin, A. I. Gоlubev, S. V. Zhikhareva VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 6772.
The paper proposes a hybrid plasma model modification to take into account nonelastic particle collisions leading to changes of ion charge states. Particle recharge and ionization kinetics is described by a collision integral, quasilinear in distribution function, which was obtained using small ion velocity and energy change approximations for nonelastic collisions. A numerical solution of a kinetic equation for the plasma ion component is defined by a particle method including a way to account collisions specially developed based on splitting by physical processes. Numerical results are given for two test problems related to recharge kinetics in moving plane plasma flows.

AEROSOL TRANSPORT AND PRECIPITATION SIMULATION WITH THE MONTE CARLO METHOD N. V. Ivanоv, V. N. Pisкunоv VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 7378.
A turbulent diffusion semiempirical equation is used to consider the transport of aerosol particles in air. Velocity and diffusion coefficients are assumed to be only a function height. The Monte Carlo method is applied to numerically solve the diffusion equation with the attention focused on (Calculating the density of particle precipitation on an underlying surface. A source equation factorization is proposed, which allows to obtain a solution for a 3D problem by modelling a 1D diffusion process with height. Analytic solutions for a 1D diffusion equation with constant coefficients served to develope an efficient scheme for numerical simulation of particle paths. Problems having analytical solutions were used to show the possibilities of the procedure. The procedure proposed can be applied to a broad class of problems in air and envir6nment physics.

AN APPROXIMATE DESCRIPTION OF DISCONTINUITY BREAKUP IN FLOW CALCULATIONS WITH THE GODUNOV SCHEME U. N. Derugin, I. P. Кasакоva, M. M. Prоshin, B. P. Tikhomirov VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 7981.
A widely used discontinuity breakup model is considered based on replacing rarefaction waves by rarefaction "jumps" assuming that left and right quantities differ only slightly. Numerical results of shockinitiated nozzle and detonation ware propagation from a closed tube and calculations with the Godunov scheme are analyzed. For this type of problems, an approximate discontinuity breakup model is shown to give errors in the numerical solution and to distort the results. The calculations indicate that more accurate models must be used in the Godunov scheme.

A PROCEDURE FOR COMPUTING DYNAMIC SHELL RESPONSE WITH THE FINITE ELEMENT METHOD V. N. Marкelоv VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 8287.
The OTSEK procedure is proposed for computing a dynamic response of rotational shells under nonaxisymmetric loading. Given elastic plastic material properties and geometry changes due to strong deflection, the finite element method was used to obtain a numerical solution for the Timoshenko shell. The shell was approximated by curvilinear hexahedron elements with a linear field of generalized shifts. The motion equation was solved with the Newmark difference scheme for shift increments and an iteration method for an algebraic system. The procedure accuracy is estimated. The procedure efficiency is shown for solving a 3D problem with a shell approximation.

ON DIFFERENCE APPROXIMATION OF A HEAT FLUX ON NONORTHOGONAL GRIDS IN RADIANT HEAT CONDUCTION PROBLEMS B. P. Tikhomirov VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 8891.
A method is proposed for developing conservative difference schemes with arbitrary hexahedron cells for threedimensional heat conduction equation. For a difference scheme to be constructed, auxiliary temperatures are introduced on edges and surfaces in addition to wasic quantities, that is cellcentered temperatures. Temperatures in the middle point of the edges are determined by linear interpolation in terms of coordinate line curvatures. A cellcentered temperature is derived from flux and temperature continuity conditions. For unidirectional flux calculations, the scalar function gradient is splitted into three linearly independent vectors with vector directions chosen so that coefficients are nonnegative in a difference expression for the flux. This condition provides the equation resolution for defining a surfacecentered temperature.

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