NUMERICAL EULER IAN-LAGRANGIAN TECHNIQUE FOR SOLVING 3-D TIME-DEPENDENT PROBLEMS IN GAS DYNAMICS WITH RESPECT TO HEAT CONDUCTION

B. L. Voronin, S. I. Skrypnik, I. D. Sofronov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 3-8.

      We formulate a numerical Eulerian-Lagrangian technique for solving 3-D time-dependent problems in gas dynamics with respect to heat conduction. Its main features are existence of two mutually orthogonal Eulerian and one Lagrangian coordinates with coordinate surfaces including material interfaces: possibility to use Cartesian and curvilinear coordinates in the calculations:splitting by directions and physical processes: possibility of combining different physical regions from 3-D and 1-D calculations. Splitting by directions permits to solve not only 3-D, but also 2-D and 1-D gas dynamics and heat conduction problems. Numerical results are presented for 3-D gas dynamics and heat conduction test problems solved with a program which implements this technique.

G. P. Prokopov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 9-16.

      A qualitative description is obtained for a stationary flow structure satisfying a system of gas dynamics equations with spatial variables in the presence of a space or surface source. In the simplest case where the source power is not too great the flow is defined by a combination of elementary details such as simple waves. Their quantitative characteristics may be evaluated by solving nonlinear algebraic equations. This problem may be used to test and to compare techniques for calculating 2-D flows in gas dynamics, both stationary supersonic and time-dependent ones.

V. M. Bobrov, V. M. Kukhtin, V. М. Chekshin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 17-20.

      Possibilities are considered for implementing the Kalman filter in computational algorithms which use difference schemes. A new approach relies upon assuming stochastic properties of the numerical solution error and a possibility for using a filtering to improve this solution. A problem formulation is given and several filtering algorithm versions are presented. Examples of linear heat conduction and transport equations as well as a nonlinear diffusion equation are considered. The results show that filtering may substantially improve the numerical solution.

E. S. Galpern, V. N. Lyakhovitsky
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 21-26.

      We describe a program modeling the behavior of a proton beam in a linear accelerator section with spatially uniform quadrupole focusing. Some calcula- tional results are given. No symmetries are assumed in electromagnetic field configurations and in a motion of macroparticle groups representing a beam. The beam eigenfield calculation uses Lienar-Wichert potentials combined with a "multilevel" formation of macroparticles representing a beam. Macroparticles at the levels 2 and 3 are formed by averaging level 1 groups of macroparticles simulating the beam behavior which permits to reduce substantially the sorting field of macroparticles from the level 1 and also to decrease the computation time. Calculating a beam moving longitudinally in a section with spatially uniform quadrupole focusing is illustrated by "model examples".

B. P. Tikhomirov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 27-33.

      Assuming a local thermodynamic equilibrium, boundary value problems are examined for a system of energy and time-dependent radiation transport equations in an absorbing, radiating.and isotropically dispersing medium. To solve boundary value problems numerically a weighted running computation scheme is proposed which contains (as a special case) a pure implicit difference approximation considered by others. The maximum principle is proved for radiation transport accounted by a spectral formulation. In a linear case a sufficient convergence condition is obtained for the scheme. An itaration method is developed for solving difference equations and the itarations are shown to converge with a geometric progression rate for cous- tant coefficient in a linear case. Computational results are given for text problems which have exact solutions.

V. A. Bychenkov, V. A. Svidinsky
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 34-37.

      A system of elastic-plastic medium behavior equations incorporated into the Wilkins model is examined. A complete system of equations is proved analytically to be nonhyperbolic for a purely plastic flow in a region of stressed states. The nonhyperbolic nature of the system in a plastic flow makes the total elastic- -plastic model noncorrect for given initial conditions which is exemplified by a problem solved numerically with a difference scheme similar to the Wilkins technique.

V. I. Zuev, V. V. Komosko, V. I. Legonkov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 38-45.

      We outline some principles for constructing and using a data base system which is one of the most important components of the SOYUZ package designed to solve 2-D time-dependent problems in the continuum mechanics. Described are the main components: the combination of 2-D problem data bases and metabases containing base descriptions: data dietionary/directory used for data description and metabase generation; DBMS providing data manipulation and service functions. For problems under consideration, we outline a concept of data base system designed to operate within a nonhomogeneous computer center including several BESM-6, ES EVM and other machines. Implementing this concept relies upon an object-oriented approach ensuring the most natural representation of objects from 2-D problem application domains in terms of structures and operations; making differences between file systems of the nonhomogeneous complex hidden to the user; functionally and structurally distributing DBMS to different computers.

S. V. Kolchugin, V. I. Legonkov, S. V. Pchelintseva, I. Yu. Silantieva
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 46-50.

      The SOYUZ package is described which is designed to solve 2-D time-dependent problems in continuum mechanics. One of the main package components is a language system including different languages used for package operation and associated language processors. The purpose of the language system development is to centralize efforts aimed at the creation of integrated and unique (common for each user group) package languages and uniform language processors whiph provides conceptual integrity and consistency for such languages, will eliminate the duplication in language system development for computational experiments and will make all language system improvements commonly available. We justify the necessity for applying a single approach to create the language system and also for centralizing and coordinating these efforts. We outline the capabilities of a unique task processing language ensuring user interaction with any program and a set of language and its processor requirements. Language system development and application will make user/package interaction faster, provided a higher level of automatization for new language processor development, and reduce operation and maintenance cost.

S. I. Kuzmina, A. A. Starostina
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 51-55.

      We describe the SSD system intended for transforming data structures to be transmitted within a single program or between different programs in computational physics problems solved on a single computer or in distributed computations performed on several computers including different-type ones. Data codes and structures are described using a specially designed D-language with a context-free grammar. A detailed description of the D-language is given. Some examples are included to illustrate the SSD system and D- language possibilities. The SSD runs under OS DIAPAK, UPD DIAPAK and MS DUBNA environments on the BESM-6.

V. Yu. Gusev, M. Yu. Kozmanov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 56-63.

      We propose two ways for correcting time-dependent radiation and heat transport equation solutions obtained with a first-order accurate difference scheme. The correction uses the same program which gave the original approximation. Corrected schemes are proved to converge. Numerical results are given which illustrate the accuracy of corrected solutions.

A. V. Kondrashenko, G. M. Mishchenko, T. G. Sevastianova, V. D. Urlin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 64-70.

      We present a computational model of a chemical pulse laser based on F₂+H₂ reaction accounting a deviation from a rotational equilibrium and also a nonharmonic nature of oscillating relaxation processes. Literature analysis and comparison between theoretical values of generation parameters and experimental data yielded a set of kinetic constants for elementary process velocities which allows to predict space, time and energy characteristics of a HF-laser with a sufficient reliability. For optical, electron beam and electric discharge initiation, a good agreement with experiment is achieved. Our results indicate the importance of accounting the nonharmonic nature of oscillating relaxation processes when computationally analyzing kinetic processes in an active environment of such lasers.

A.V. Kondrashenko
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 71-72.

      A numerical technique is proposed for integrating equations describing laser radiation transport, excited level population kinetics and nonisothermal chemical kinetics of the active environment in HF-lasers. This technique relies upon physical process splitting and does not require significant computational cost.

V. A. Lykov, O. S. Shirokovskaya
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 73-78.

      A spectral model of fast electron transport accounting self-consistent electric fields is described. The model is implemented within the ZARYA package intended for computing target implosion by laser radiation. A numerical method for solving fast electron transport equation is presented. Computational results are given to illustrate the importance of accounting fast electron scattering, self-consistent electric fields, inverse current effects along with the possibility to interpret experiments on gas-filled shells both using a compressed target portion (compression level, neutron yield) and fast ions formation resulting from an acceleration by self- -consistent electric fields.

A. V. Rudkevich
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 79-85.

      A new type of data structure is proposed to represent incomplete and fuzzy data from rietrieval system databases, that is a modal function which is a set of modal system times mapped on a linearly ordered modality set. A set of operations over modal functions is examined. Boolean algebra and a chain of isomorphic function nestings are shown to exist for differently defined modality sets. An algorithm is proposed which makes the modal functions suitable for data search. The approach described for modeling an application domain permits to reflect uncertainty and fuzziness in proposition validity values and to set event timing.

I. N. Orlov, A. I. Prokofiev, L. A. Sevastyanova
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 86-90.

      Procedures and capabilities of the LOKOS program are described which is designed for one-group approximation of breeding time constant, λ, from a transport equation for axi symmetric systems. The program is written in FORTRAN. Computations of λ for a number of problems are given and a comparison with results obtained with other programs is made.