PROPAGATION OF RAREFACTION AND SHOCK WAVES IN HETEROGENEOUS MIXTURES OF TWO ISOTHERMIC GASES

O. V. Burjakov, V. F. Kuropatenko
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 3-7.

      A 1-D plane analytical solution of piston movement problem is obtained for a heterogeneous mixture of two isothermic gases. The rarefaction wave is shown to have both a zone of poor 1ight-component mixture and a zone of rich mixture. Mass concentration of light component, scattered into vacuum near the piston, equals one, i.e. there is absolute component separation. In the moving-in piston problem the shock wave splits. Mixture is substantially rich of light component in the interval between the light and heavy component gaps and rich of heavy component between heavy component gap and piston.

E. V. Malinovskaya, A. V. Nikiforova, L. P. Fedotova
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 8-16.

      The divergent scheme of the method of characteristics is described for numerical solution of 2-D stationary transport equation for axisymmetric geometry with isotropic presentation of scattering indi- catrix. The peculiarity of the method is introduction of special planes for integrating transport equations along neutron movement path and use of divergent curvilinear mesh fits in (r, z, φ)-phase space. Abilities and structure of 2-D neutron calculation routines are described for the solution of stationary transport problems in axisymmetric geometry. The routine is written in FORTRAN in the "Dubna" monitor system. Several examples of 2-D neutron numerical calculations are supplied and comparison with other results is made.

S. V. Bazhenov, V. V. Gorev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 17-21.

      Various economic differece schemes are given for solving heat equation on the boundary between regions with different meshes, based upon solution prediction on the upper temporary layer on the basis of lower layers results. Stability analysis is considered. Test results for various 2-D difference schemes are provided.

P. N. Vabishchevich, L. M. Degtyarev, V. V. Drozdov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 22-32.

      The numerical solution method of TOKAMAK plasma evolution and MHD-equi1ibrium problems is developed with plasma pressure and stability reserve factor given. The numerical algorithm is based upon inversion of variables with use of orthogonal flow coordinates. Comparison is made between numerical and accurate solutions illustrating the effectiveness of the method. Examples of calculating plasma equilibrium evolution with pressure raising are given, the border being free and fixed.

V. A. Volkov, V. K. Ladagin
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 33-38.

      Stationary 2-D gas flow with energy release is linearly investigated. Some analytical results are obtained for subsonic mode on the basis of analogy with electrostatics. A numerical algorithm is proposed for the problem considered. With subsonic mode the upper relaxation method is used in combination with R.P.Fedorenko method. With supersonic mode with large Mach numbers a suitable form of equations is chosen to enhance integration accuracy.

V. G. Novikov, V. B. Uvarov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 39-41.

      Quasi-pulse-order series expansion is obtained for energy and wave functions of electrons in energy zone in approximation of spherical Wiegner-Seitz cells. Recursion formulas are developed to calculate the coefficients of this expansion.

I. A. Gavrikov, G. M. Trubacheev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 42-47.

      The possibility of presenting photo-mass-spectro- gram peaks by the hyper-Gauss funstion is investigated, the latter being Gauss-function "modulation" (ion peak intensity) by the hyperbolic tangent function (photographic emulsion characteristic curve). Visual comparison of test and calculated peaks, as well as quantitative estimates show this function to well describe real photopeaks, both weak and saturated. It is ascertained that to enhance accuracy of ion peak parameters it is necessary to simultaneously process several photopeaks of the same mass- -spectral line but of various exposure.

Yu. I. Vantrusov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 48-51.

      Drawbacks of current approach to automatized control system projecting are considered and ways to overcome them are proposed. The necessity of system analysis of automatization objects is stated. A way of automatized control system projecting organization, choosing automatization projects, and estimating efficiency of the system developed is proposed with reference to literature and practical experience on the basis of notions of "structural model of controlled system" and "transport tree".

V. N. Gorbunov, I. V. Demin, M. I. Kaplunov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 52-58.

      A general characterization of the integrated complex "SIGMA" is given. Computing control system, including instruction interpreter and macrolibrary; teleprocessing system using teletype or alphanumeric display; archive centralizing resource usage on magnetic tapes; and run disparalI eling system of several computers with common disk unit are described.

N. N. Anuchina, V. N. Ogibina
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1981. No 2. P. 59-65.

      Results of numerical analysis are reported concerning development of sinusoidal disturbances of inviscid non-heat-conduction gas interface affected by constant acceleration (Ray 1eigh-Taflor instability). The computations are based on the difference scheme, a modification of "Particlc-in-CelI" method. The computation results are compared with analytical and test analyses.