A NUMERICAL SIMULATION SCHEME FOR 2D DISPERSIVE MEDIUM FLOWS IN CONTINUAL MULTIVELOCITY APPROXIMATION

M. S. Samigulin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 3-8.

      The paper presents a difference scheme for numerically solving equations describing two-dimensional flows of dispersive media in continual multi-velocity approximation.

A. T. Sapozhnikov, P. D. Gershuk, E. L. Malyshkina, E. E. Mironova, L. N. Shakhova
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 9-16.

      The paper offers the equation of state (EOS) for the description of pressures and internal energies in a wide range of densities and temperatures. The thermal components of pressure and energy are represented by tables in a uniform logarithmic net with the bicubic node interpolation. The potential components are represented by the cubic spline on a uniform grid, which density is higher than the normal one. To calculate pressures and energies behind the tabulation domain, simple extrapolation formulas are suggested. The GLOBE equation of state can be used in codes for the continuum dynamics simulation. The equation of state functionality is demonstrated by the example of describing the properties of copper.

Yu. N. Bulkin, B.A. Vyskubenko, Yu. N. Deryugin, Yu.V. Kolobyanin, E. A. Kudryashov, L. N. Shakhova
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 17-22.

      The paper describes the techniques and results of the numerical simulation of turbulent mixing processes for supersonic flows in channels of mixing gas-dynamic lasers. Turbulent flows of a non-equilibrium gas mixture are described by the parabolic Navier-Stokes equations and kinetic vibrational relaxation equations. Both algebraic and differential models of turbulence are used to find the turbulent viscosity value. The equation system is numerically integrated with the McCormack finite-difference method using a Lagrangian grid. For various models of turbulence, the dependence of the calculated results on the difference grid in use and model parameters is analyzed. The calculated results and experimental values of the magnification coefficient and energy sampling are compared.

A. A. Shestakov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 23-26.

      Exact solutions of the “progressing wave” type have been constructed for the system of energy and radiation transport equations in an anisotropically scattering medium. The solutions can be used for the justification and workout of the developed numerical techniques.

B.P. Tikhomirov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 27-31.

      The difference scheme KREST (cross) has been developed for the numerical solution of the nonstationary spectral radiation transport equation and energy balance equation in a 3D geometry. An approach to approximating boundary conditions has been suggested. The scheme stability in energy norm has been analyzed. The Kellogg lemma has been generalized for the estimation of the transition operator norm. The calculated results are presented for a model problem having exact solution.

B. L. Glushak, L. F. Gudarenko, Yu. M. Styazhkin, V. A. Zherebtsov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 32-37.

      In the equation of state given in the paper, pressure and energy are represented by a sum of the potential component and thermal components of nuclei and electrons. The Grueneisen grid factor is described by the density function, its analog for electrons is a constant quantity. The heat capacity of nuclei is a constant quantity, the heat capacity of electrons is a linear function of temperature. The EOS values of parameters are given for molybdenum, iron, lead, copper, aluminum, and tungsten; the calculated and experimental results are compared.

G. A. Goncharov, V. L. Gorelov, V. N. Ivannikova, E. V. Malinovskaya, G. G. Farafontov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 38-43.

      The paper considers the computational algorithms used to calculate group constants for the energy-angular distribution of neutrons scattered in the medium of motionless nuclei.

V. E. Shemarulin, G. G. Farafontov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 44-50.

      The basis of the contact conservation laws of the polynomial type has been found, it describes one-dimensional plane isentropic flows a polytropic gas. It is demonstrated that any “analytical” conservation law is represented in the form of a series of the basis conservation laws, the functions generating the basis conservation laws are obtained by multiply using the recursion operator from unit, while the basis conservation laws themselves are obtained by successively using the recursion operator from the mass conservation law. As a consequence, differential relations have been obtained for special Gegenbauer polynomials. General solutions have been found to the differential equations describing these polynomials.

I. A. Adamskaya, T. A. Seregina, I. F. Sharova
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 51-53.

      The issue of a guaranteed accuracy of solving a system of ordinary differential equations of spherical harmonics for 1D kinetic equation using Godunov’s method is considered. The method accuracy deterioration owing to a finite difference in representing numbers in computer is studied.

P. N. Vabishchevich, N. N. Elkin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 54-57.

      When solving numerically the Cauchy problem, the need in setting boundary conditions occurs due to the transition from an unbounded computational domain to the bounded domain. In the present work effective boundary conditions are set for parabolic equations on the basis of the Cauchy problem solution represented using potentials. The integral formulation of the problem outside the computational domain is combined with the differential formulation inside the computational domain. In practice, the approach is based on solving an auxiliary initial boundary value problem with the preset boundary conditions and, then, the boundary conditions for the major problem are calculated.

G. V. Dolgoleva
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 58-60.

      The numerical method of solving a 1D system of equations describing the transport of radiation and its interaction with a material is considered. The radiation transport is simulated with spectral quasi-diffusion approximation. The idea of the computational method consists in splitting the difference equation system in the solution process. The mathematical justification of the difference scheme and numerical simulation results are given.

A. A. Sadovoy, V.P. Feodoritov, N.M. Chulkov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 61-65.

      An algorithm is proposed for the EOS parameter recovery using data of experiments, which is based on minimizing the multidimensional nonlinear functional with limitations.
      The equation of state is constructed, which takes into account the thermal oscillation of atoms and thermal excitation of electrons, uses the cubic online-approximation of elastic pressure and Grueneisen factor, and provides continuity of thermodynamic quantities up to and including the second derivatives. The numerical results obtained for iron are compared with data of experiments.

A. I. Golubev, N. A. Ismailova, V. A. Terekhin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 66-70.

      For a non-conducting medium, an exact solution has been obtained to the problem of electromagnetic fields generated by a model source of gammas located in a perfectly conducting plane. On its base, an analytical solution to the problem of electromagnetic fields generated by a model source of gammas located at a distance to the perfectly conducting plane has been constructed using the reflection method. These solutions provide powerful capabilities for analyzing the accuracy of numerical methods for the calculation of nonstationary electromagnetic fields generated by gamma-radiation sources.

O. M. Velichko, T. I. Kravchenko
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 71-75.

      The unsteady process of loading a blunt-nosed cone flying at a supersonic speed by a bow shock wave reflected from a flat screen is studied. The numerical simulation of the problem is performed using the model of an inviscid non-heat-conducting gas. Three-dimensional nonstationary Eulerian equations are integrated with Godunov’s difference scheme. The interaction of the reflected bow shock wave with the cone and screen surfaces is studied. Numerical results are illustrated by figures in the paper.

S. P. Belyaev, N. I. Leonova, I. D. Sofronov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 76-79.

      The current continuum mechanics problems require performing a large amount of computations to solve them. A significant portion of them – from 30% to 70% - is the calculation of EOSes. That’s why of a great importance in practice is the efficient arrangement of EOS calculations. The use of a vector computer complicates the task, because algorithms allowing the efficient use of vector calculations are available for differential equation systems describing the continuum mechanics problems, however, there are no general vector-form algorithms for the calculation of EOSes. The present paper offers a vector algorithm for the EOS calculation and discusses its implementation and performance.

I. P. Ryzhachkin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 80-82.

      An interactive subsystem of OS ES has been developed, which is interfaced with the central components of software for the technological complex for mass computations in a heterogeneous computer system. The subsystem combines the capability of connecting PCs to the processing of data available in the central components and in the standard OS ES environment with its own capabilities of processing texts and programs.

S. V. Kazakov, L. V. Lychagina, Yu. A. Moiseenko, A. B. Olesnitskiy, V. D. Trushchin
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 83-85.

      The paper describes a unified data storage system for a heterogeneous computer system. The unified storage system capabilities, its functional structure and behavior are considered. Some data on the system performance is given and the ways of its further development are pointed out.

N. N. Zalyalov, V. E. Zezyulin, A. L. Lukyanov, S. V. Khlystov, G. V. Akamsina
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 86-89.

      The paper describes the programming system used to perform real time computations on a microcomputer with hardware in the CAMAC standard and write programs for the experimental data processing. It provides tools for the access of application programs to a network-based distribution system. The programming language is close to BASIC.
      The system consists of two independent parts: an off-line programming system and a programming cross-system. The QUASIC/NSS off-line programming system is operated on a microcomputer and consists of the three components: a display used to edit the original program text and control the program flow in computer; a QUASIC compiler; and subprograms used during the program runtime. The programming cross-system consists of two components - a system kernel and a QUASIC cross-compiler, operates on a support computer and develops an executable code.

V. I. Livinskiy
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 90-91.

      The method of deformed coordinates (Lighthill’s method) generalized to the case of discontinuous solutions is applied to find aerodynamic characteristics for solids of revolution under steady supersonic airflows at a slight angle of attack. A high accuracy of results is demonstrated, as well as a possibility to find the method validity limits in a linearized problem.

A. Yu. Kuznetsov
VANT. Ser. Mat. Mod. Fiz. Proc. 1991. No 1. P. 92-94.

      The paper describes algorithms based on the sufficient conditions and used for testing 3D grids of the finite element method. Checking for compliance with the governing conditions for a grid is performed and some combinatorial relations for the boundary components of the grid are also checked.