A TECHNIQUE FOR SOLVING 1-D MULTIREGION PROBLEMS IN HIGH-TEMPERATURE GAS DYNAMICS

N. A. Dmitriev, I. D. Sofronov, B. P. Tikhomirov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 3-8.

      The formulation of 1-D boundary-value problems in radiation gas dynamics approximated with radiant heat conduction equations for heterogeneous media is considered. A calculation method based on the gas dynamics approximation with the "Crest" scheme is briefly described. The heat transfer is computed using a purely implicit difference scheme. The package structure and its principal capabilities are given.

E. A. Negin, I. D. Sofronov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 9-17.

      An application package is described for solving boundary-value problems associated with a system of differential equations having a single space and time variable assuming its quasi1 inearity and the correctness of the problem formulation. The package is shown to be suitable for solving a broad class of problems in the continuum mechanics, neutron physics, radiation physics, magnetic field etc. The package structure description introduces a "production run” notion, points out a substantial difference between an operational program and methodical one, shows a way for minimizing application program machine-dependencies when moving the complex on other computers.
      The operation practice analysis revealed the complex efficiency increasing reserve and some ways for its improvement are outlined.

B. A. Vyskubenko, Yu. N. Deryugin, G. A. Kirillov, Yu. V. Kolobyanin, S. B. Kormer, V. D. Nikolaev, B. P. Tikhomirov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 18-22.

      2-D generation power calculation results for mixing plane nozzles are presented. A comparison with an experiment is made. A mixing GDL computer model is shown to be suitable for a quantitative generation power simulation.

Yu. N. Deryugin
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 23-26.

      A program package for GDL computations is described. The package in question permits to calculate both 1-D and 2-D flows over the whole gas dynamic path of a homogeneous or mixing-tiype gas dynamic laser.

I. V. Demin, M. I. Kaplunov, V. A. Saraev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 27-29.

      The paper investigates the efficiency of several well-known data compaction techniques allowing the data to be fully restored. 2-D gas dynamics problem solutions taking into account some other physical processes were at the origine of these studies. An analysis of those statistic solution features provided compaction ratio estimates which was achieved using the techniques considered both separately and in combination. These estimates may be used to choose a compaction technique for similar-type data.

A. M. Buiko, S. F. Garanin, E. V. Gubkov, V . M. Danov, O. Yu. Dementieva, V. V. Zmushko, T. B. Lezhepekova, V. I. Uatyshev, V. N. Mokhov, E. S. Pavlovsky, V. B. Yakubov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 30-32.

      A means is considered for heating a magnetic plasma with a sufficiently great Alfven sound speed by a shock wave when passing it through a nozzle. The results of 2-D MHD calculations show the possibility to obtain a hot plasma in that way for fusion studies.

S. F. Bazhenov, N. A. Dmitriev, L. U. Dibirova, K. S. Isaeva, P. A. Perepelkin
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 33-35.

      A method is developed to solve a 2-D nonstat ionary kinetic radiation transport equation in a nonhomo- geneous region being a rotational body. The method takes into account isotropic radiation scattering and absorption and also material equilibrium radiation. The radiation entering a region through its boundary surface is assumed to be Lambert-distributed. A system of source equations is given. The computational scheme derivation is described and its major features are presented.

O. V. Butneva, Yu. M. Matveev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 36-40.

      A family of S_n method-like difference schemes is considered to solve a 1-D nonstationary spherical symmetry transport equation. Their numerical comparison is presented. A possibility is provided for using these scheme combinations to increase the computation accuracy which proved to be reasonable.

Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 41-43.

      The paper describes a computer model, an implicit difference scheme along with the main complex design concepts and its features. The program complex is developed for modeling physical processes in a high-temperature dense plasma.

V. M. Bobrov, V. M. Kukhtin, V. M. Chekshin
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 44-49.

      A dynamic filtering problem is formulated for linear partial differential equations. For this problem, assuming the presence of additive Gauss noise in initial and boundary conditions was a point of departure. A program implementing a filtering algorithm was used to investigate the dynamic behavior of the Kalman filter covariant portion on difference schemes developed for heat conduction and transport equations. A relationship between the dynamic filtering stability and that of a solution obtained with difference schemes is shown.

V. P. Rudenko, I. F. Travov, A. K. Volkov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 50-54.

      SM-3/SM-4 software operation practice is generalized. Program components in terms of several parameters are analyzed. Some conclusions concerning the components suitability for solving different problems are given. An analysis is carried out revealing the trends observed in modern minicomputer software development.

A. I. Morenko
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 55-58.

      Using the Monte-Carlo method to solve nonlinear problems is examined. A solution represented as a random sequence in a solution space permits to obtain a limiting random process when minimizing the time step size.
      These process paths decribe solutions given by the Monter-Carlo method with a sufficiently small time step size. Some equations for conditional mathematical expectations of functionals being calculated are derived.

Yu. N. Mazurin, G. P. Okhrimenko., S. A. Petunin
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 59-61.

      A description of the OS-100MD operation system for SM-4 minicomputer is given which provides a control function for 100 MB discs in the BESM-6 based multicomputer complex. The OS-100MD functional structure is presented.
      A detailed description of its kernel is provided which implements a base level control within the operation system. The 0S-100MD reliability requirements are examined along with several techniques allowing to avoid, detect, and correct errors caused by hardware malfunctions or nonfatal failures.

K. A. Belyakov, G. V. Orlov, S.A. Petunin
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 62-64.

      A disc operation system (DOS SP) is developed for a connected processor based on the M400 minicomputer. The main concepts used in the OS are described. The OS multitask operation requirements are examined. The connected processor data flow control is studied. Two job classes (C-and T-jobs) are justified which take into account the M400 features when operating as a connected processor. The DOS SP allows a data transfer between the BESM-6 computer system and remote terminal computers (such as SM-4). The connected processor access to the multicomputer shared disc storage permits to achieve a high system throughput by exploiting this communication link in an efficient manner. In addition, the paper describes a simple BESM-6 /connected processor communication protocol.

M. Yu. Kozmanov, E. B. Rachilov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 65-67.

      The paper presents exact solutions for radiation energy and diffusion equations in a 1-D plane case without scattering obtained using different approximation methods: grey matter approximation and full spectral formulation both with and without nonstation- ary terms in diffusion equations. These exact solutions are derived for specifically chosen absorption coefficient, equation of state, initial data, and boundary conditions. The exact solutions obtained can be used to check approximate numerical methods.

V. Ya. Urm
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 68-72.

      Some issues are discussed concerning the numerical solution of a time-dependent kinetic equation written in spherical harmonics for the case of spherical symmetry and that of infinite cylinder symmetry. Finite-differece approximation methods are proposed which are second-order accurate in time, conservative, monotonuos, and characterized by both conditional and unconditional stability properties when free parameters are properly chosen.

V. E. Troshchiev, R. M. Shagaliev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1983. No 3. P. 73-76.

      A class of schemes referred to as interpolation-invariant or J-schemes is proposed for heat conduction equations. Mesh temperatures are set at polygon nodes. The J-scheme feature is that after a double temperature interpolation, that is from nodes to cell centers and vice versa, the solution on the mesh nodes remains unchanged. These schemes are of some interest in terms of solving heat conduction equations together with other equations where mesh functions to be found are introduced at polygon centers.