Issue N^{o} 3, 1988 
NUMERICAL EULER IANLAGRANGIAN TECHNIQUE FOR SOLVING 3D TIMEDEPENDENT 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. 38.
We formulate a numerical EulerianLagrangian technique for solving 3D timedependent 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 3D and 1D calculations. Splitting by directions permits to solve not only 3D, but also 2D and 1D gas dynamics and heat conduction problems. Numerical results are presented for 3D gas dynamics and heat conduction test problems solved with a program which implements this technique.

ON A PROBLEM FOR TESTING 2D TECHNIQUES IN GAS DYNAMICS G. P. Prokopov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 916.
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 2D flows in gas dynamics, both stationary supersonic and timedependent ones.

SOME POSSIBILITIES FOR IMPLEMENTING THE KALMAN FILTER IN COMPUTATIONAL ALGORITHMS V. M. Bobrov, V. M. Kukhtin, V. М. Chekshin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 1720.
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.

CALCULATING AN ION BEAM EVOLUTION IN A LINEAR ACCELERATOR SECTION WITH SPATIALLY UNIFORM QUADRUPOLE FOCUSING BASED ON A "MULTILEVEL" REPRESENTATION OF BEAM PARTICLES E. S. Galpern, V. N. Lyakhovitsky VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 2126.
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 LienarWichert 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".

A CONSERVATIVE DIFFERENCE SCHEME FOR TIMEDEPENDENT RADIATIVE HEAT TRANSFER PROBLEMS B. P. Tikhomirov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 2733.
Assuming a local thermodynamic equilibrium, boundary value problems are examined for a system of energy and timedependent 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.

NONCORRECTNESS OF AN ELASTICPLASTIC FLOW MODEL IN THE WILKINS METHOD V. A. Bychenkov, V. A. Svidinsky VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 3437.
A system of elasticplastic 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.

A DATA BASE SYSTEM FOR THE SOYUZ PACKAGE V. I. Zuev, V. V. Komosko, V. I. Legonkov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 3845.
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 2D timedependent problems in the continuum mechanics. Described are the main components: the combination of 2D 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 BESM6, ES EVM and other machines. Implementing this concept relies upon an objectoriented approach ensuring the most natural representation of objects from 2D 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.

A LANGUAGE SYSTEM FOR THE SOYUZ PACKAGE 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. 4650.
The SOYUZ package is described which is designed to solve 2D timedependent 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.

DATA STRUCTURE TRANSFORMATIONS IN COMPUTATIONAL PHYSICS PROBLEMS S. I. Kuzmina, A. A. Starostina VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 5155.
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 differenttype ones. Data codes and structures are described using a specially designed Dlanguage with a contextfree grammar. A detailed description of the Dlanguage 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 BESM6.

FIRST ORDER ACCURATE SCHEME WITH A POSTERIORI CORRECTION FOR SOLVING A SYSTEM OF TIMEDEPENDENT RADIATION AND HEAT TRANSPORT EQUATIONS V. Yu. Gusev, M. Yu. Kozmanov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 5663.
We propose two ways for correcting timedependent radiation and heat transport equation solutions obtained with a firstorder 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 COMPUTATIONAL MODEL OF A CHEMICAL PULSE ЯЯLASER WITH RESPECT TO ROTATIONAL EQUILIBRIUM AND NONHARMONIC NATURE OF OSCILLATING RELAXATION PROCESSES 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. 6470.
We present a computational model of a chemical pulse laser based on F_{2}+H_{2} 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 HFlaser 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.

NUMERICAL TECHNIQUES FOR INVESTIGATING ENERGY CHARACTERISTICS OF HFLASERS A.V. Kondrashenko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 7172.
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 HFlasers. This technique relies upon physical process splitting and does not require significant computational cost.

LASER FUSION TARGET CALCULATIONS WITH THE ZARYA PROGRAM ACCOUNTING FAST ELECTRON SPECTRAL TRANSPORT AND SELFCONSISTENT ELECTRIC FIELDS V. A. Lykov, O. S. Shirokovskaya VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 7378.
A spectral model of fast electron transport accounting selfconsistent 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, selfconsistent electric fields, inverse current effects along with the possibility to interpret experiments on gasfilled shells both using a compressed target portion (compression level, neutron yield) and fast ions formation resulting from an acceleration by self consistent electric fields.

MODAL FUNCTIONS. FEATURES AND APPLICATION DOMAIN SIMULATION A. V. Rudkevich VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 7985.
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.

THE LOKOS PROGRAM FOR EVALUATING CRITICAL PARAMETERS OF AXI SYMMETRIC SYSTEMS I. N. Orlov, A. I. Prokofiev, L. A. Sevastyanova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 3. P. 8690.
Procedures and capabilities of the LOKOS program are described which is designed for onegroup 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.

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