DESCRIPTION OF A TEST SET FOR 2-D 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. 3-9.

      A problem set is proposed designed for testing 2-D 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.

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. 10-14.

      A problem set is proposed designed for testing 2-D 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.

A. T. Sapozhniкоv, G. V. Kovalenko, P. D. Gershchuk, E. E. Mironоva
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 15-19.

      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 Thomas-Fermi model with quantum and exchange corrections. Thermodynamic water properties are taken for densities and temperatures ranging from 0,001 to 64 g/сm³ and from 300 К to 10⁶ К respectively. An extrapolation beyond the table is provided.
      The GLOBUS may be used in continuum dynamics programs.

N. Yu. Bакaуev, V. V. Vyazankin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 20-24.

      Stability estimated in Banach norms are obtained for difference schemes constructed within the Runge-Kutta method on nonuniform grids (close, in a sense, to uniform ones).

G. A. Gоnchaгоv, V. P. Gorelov, G. G. Farafontov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 25-29.

      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.

S. N. Sheludкo
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 30-33.

      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, thread-like, and plane sources. A time-independent 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.

N. N. Zalуalov, M. M. Leplyavkina, M. S. Dudоrоv, Yu. I. Vinogradov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 34-37.

      Multichannel computer and KAMAK-hardware 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 KAMAK-hardware.
      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 Electronica-60 computers under OS RAFOS or RT-11.

V.A. Zherebtsov, V.P. Kоpуshev
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 38-41.

      General design and operation principles are described for the ZURS-ES Complex intended for investigating various equation-of- state. The Complex comprises a program-set to implement various equation-of-state 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.

B. Sh. Albasarоv, A. A. Вezruкоv
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 42-50.

      Modified high-order IVD-type schemes are used to give a formulation of problems, which adequately simulate a time-dependent process of perfect gas supersonic jet formulation and a time-independent 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.

G. G. Bliznуuk, A. V. Ivanоvsкy, A. A. Sоlоvуоv
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 51-56.

      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 1-D system of equations obtained with a running wave approximation. A system of ionization kinetics equations is solved to find a radiation-induced 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 self-consistent field and a collision integral in the Focker-Plank form. A numerical example is given.

B. L. Glushak, L. P. Gudarenкo, Yu. M. Stуazhкin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 57-62.

      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.

O. V. Diуanкоv
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 63-66.

      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 2-D case.

V. P. Bashurin, A. I. Gоlubev, S. V. Zhikhareva
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 67-72.

      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.

N. V. Ivanоv, V. N. Pisкunоv
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 73-78.

      A turbulent diffusion semi-empirical 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 3-D problem by modelling a 1-D diffusion process with height.
      Analytic solutions for a 1-D 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.

U. N. Derugin, I. P. Кasакоva, M. M. Prоshin, B. P. Tikhomirov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 79-81.

      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 shock-initiated 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.

V. N. Marкelоv
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 82-87.

      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 3-D problem with a shell approximation.

B. P. Tikhomirov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 2. P. 88-91.

      A method is proposed for developing conservative difference schemes with arbitrary hexahedron cells for three-dimensional 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 cell-centered temperatures. Temperatures in the middle point of the edges are determined by linear interpolation in terms of coordinate line curvatures. A cell-centered 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 surface-centered temperature.