DESIGN1NG GAS DYNAMIC EQUATION MODELS USING KINETIC AND INTERNAL ENERGY MUTUAL CONVERSION IN THE CONTINUUM

V.N. Isaev, I. D. Sofronov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 3-7.

      A method for an equation-of-mot ion space approximations in 1-D and 2-D gas dynamic problems is presented. It is shown that a technique for approximating the equations of motion with a space variable is defined by choosing a representation of an elementary volume kinetic energy.

O. M. Kozyrev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 8-13.

      A method is proposed for estimating the convergence and stability of difference schemes with exchangeable boundary conditions assuring a single region computation at a time. The stability and convergence are studied in terms of special energy norms generated by the difference scheme operators. For a difference scheme which approximates a 1-D linear heat conduction equation, a set of parameters is described that serve as exchangeable boundary conditions which cause the stability to occur in the energy norms considered. Some cases of the initial-value problem and mixed initial-value problem having first, second, and third order external boundary conditions are examined.
      For the mixed initia1-va1ue problem with first order external conditions, the difference-to-exact solution convergence is proved for norms consistent with the L₂-norm in a continuous argument, function space.

V. T. Gukov, R. P. Fedorenko, I. L. Chihladse
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 14-17.

      The RTT package is designed to accomplish 3-D neutron, thermal, and combined neutron-thermophysical calculations, to compute the critical core size, and to evaluate the campaign depending on fuel burn out in solid coolant reactor systems using the BESM-6 computer. To describe a neutron field a two-group diffusion approximation is introduced and two-group constant space-dependence on the fuel temperature and burn out is taken into account. The temperature distribution is described by a heat conduction equation with respect to the solid coolant reactor specific features. Two-group constants such as temperature, initial concentration, and burn out depth functions are provided in a tabular form using a 69-group constant library. The RTT package is a specialized one, that is oriented only to a solid coolant reactor calculation which is due to its geometry and physical features and also to the computer limitations.

V. Ya. Urm
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 18-24.

      Several aspects concerning an asymptotic behavior of partial differential equation solutions are considered. Running waves behavior is studied including their locations and discontinuity "smear” criteria. Appropriate formulae are obtained which are applied to a number of difference schemes being investigated. The method proposed is generalized onto 1-D and 2-D system of difference equations.

A. I. Panov, V. V. Rasskazova
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 25-28.

      An implicit scheme for solving a radiant heat conduction equation on irregular grids is considered. A group relaxation method was used to solve a difference equation.

A. G. Shklovsky, M. L. Miller
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 29-32.

      The spectrum and the work function of an electron emmited from hypothetical metallic hydrogen single crystal is studied in OZK-modification. Equilibrium grid parameters are estimated for the same crystal. The correlation energy is taken into account by the Gell-Mann-Bruckner approximation.

A. G. Shklovsky
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 33-36.

      An algorithm is developed to solve the Hartree-Fock equation in a crystal with any preset accuracy. Self-consistent Hartree-Fock potential matrix elements are calculated for a hypothetic metallic hydrogen crystal in OZK-modificat ion.

S. M. Bakhrah, A.V. Pevnitsky, G. P. Simonov, V. P. Soloviev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 37-40.

      The paper discribes a method for computing the dynamics of thin-wall hardened rotation shells contacting with a fluid under pulse loading conditions. The main equations are given and a finite-difference scheme is constructed. The method performance is exemplified by an axisymmetric camera housing deformation problem.

O. I. Butnev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 41-44.

      Some techniques to find an eigenvalue of a time-dependent kinetic equation using a stabilization method are given. The method features are compared with those developed by other authors. Numerical results are presented.

P. A. Avdeev, V. A. Shumilin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 45-48.

      A technique and a FORTRAN-subroutine are described for a numerical solution of a stationary one-group neutron transport problem assuming an axial symmetry. The subroutine calculates a new approximation and corresponding quasidiffusion coefficients using a predetermined neutron density approximation. The subroutine communicates with the external environment through parameters, so it may be easily included in any FORTRAN-program.

R. Ya. Gatilova, T. G. Ivchenko, N. I. Leonova, L. M. Sidorova, Z. V. Suraeva
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 49-54.

      An application program from the "Odnomerny Complex" package is described which is designed to calculate a 1-D time-dependent flow taking into account the impact of nonlinear heat conduction and external energy sources. Gas dynamics equation integration uses a through finite-difference method with artificial viscosity (a "crest"-type scheme). The energy equation is approximated by an implicit four-point difference scheme which is first order accurate in time. Four self-similar problems were used to compare numerical solutions obtained with self-similar ones.

B. A. Vyskubenko, Yu. N. Deryugin, S. P. Ilyin, G. A. Kirillov, S. B. Kormer, Yu. V. Kolobyanin, B. P. Tikhomirov, E. A. Kudryashov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 55-58.

      The paper presents some results obtained from comparing theoretical and experimental energy characteristics of homogeneous GDL. The model taking into 52 account shock jumps in a real flow is shown to agree well with experimental data.

B. A. Vyskubenko, Yu. N. Deryugin, Yu. V. Kolobyanin, S. B. Kormer, B. P. Tikhomirov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 59-61.

      A cylinder model is proposed for computing flow- -parameters and generation power of a mixing GDL with D nozzle grid. The comparison between predictions and experimental data is carried out. The model proposed is shown to be suitable for a quantitative description of the generation power.

P. A. Avdeev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 1. P. 62-63.

      The paper briefly describes a set of cataloged procedures written in the ES OS command language which were used to develop a sufficiently large program. These allow module text editing, its translation, link editing, and independent execution of modules. To use similar procedures for a new program development, they need to be modified and given different names.