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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 1986  MODULARSTRUCTURAL APPROACH ТО DEVELOPMENT OF LARGE PROGRAMS
V. I. Legonkov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 313.
A new, modularstructural, approach to development of large application programs is proposed which consists in uncontradictory integration of structural and modular approaches and includes their merits. In the frame of this approach the development of a new program follows the "fromtoptobottom" method, and the modules resulting from function decomposition are generated separately so that to be used at developments of future programs with the "fromtoptobottom" method. Principles of integrating modular and structural approaches, discipline of the integrated approach, and means of its ensuring, schemes of practical application of the approach at development of mathematical physics codes are described.
 APPLICATION OF VARIATIONAL PRINCIPLES OF MECHANIES TO DEVELOPING TIMEDISCRETE DIFFERENCE GAS DYNAMICS MODELS. 2. HOLONOMIC BONDS, BOUNDARY CONDITIONS, AND STABILITY OF REST STATE IN "KREST"TYPE DIFFERENCE SCHEMES Yu. A. Bondarenko, A. M. Stenin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 1426.
Development of the variational method generating difference schemes for a set of gas dynamics equations in Lagrangian variables is described which is based on timediscrete approximation of action functional and using Hami1tonOstrogradski principle. On an example of "KREST"type difference schemes ways of accounting holonomic bonds are described which are used for approximation of boundary conditions, when the gas curvilinear boundary is given. It is shown how the virtual work principle should be used, when pressure at boundary is given. The scheme is constructed with allowance made for surface forces. Sufficient stability conditions are obtained on arbitrary Lagrangian meshes of general tyre. The coordinated introduction of holonomic bonds into the scheme is shown not to deteriorate stability conditions.
 PISTON PROBLEM SOLUTION FOR MIXTURE OF ISOTHERMIC GASES AND INCOMPRESSIBLE PARTICLES WITH REGARD TO VELOCITY NONEQUILIBRIUM OF COMPONENTS O. V. Buryakov, V. F. Kuropatenko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 2732.
Assuming that forces of interactions of components due to their velocities differences are absent an acurate solution of the problem of piston movement in mixture of isothermic gas with incompressible particles is derived. For a shock wave the solution is of the form of two sharp discontinuities moving with different velocities. Patial density and velocity of gas experience a jump only at the first sharp discotinuity. Behing the first sharp discontinuity the mixture is enriched with gas and behind the second one, at the piston, with particle matter. For a rarefaction wave three flow modes are possible: with full component separation in the rarefac tion wave of gas; with full component separation in region of constant gas flow at the piston; and with partial component separation and region of constant mixture flow at the piston, where mixture is enriched with gas.
 ON FORMULATION AND APPROXIMATE SOLUTION OF THE FIRST INTERIOR BOUNDARYVALUE PROBLEM FOR A SET OF DIFFUSIONTYPE DIFFERENTIAL EQUATIONS WITH NONLINEARITIES A. Ya. Voronov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 3341.
For a set of differential equations describing properties of partially ionized multicomponent plasma a boundaryvalue problem is formulated in which, in addition to functions, describing distribution of charged particles of plasma and its selfconsistent field in Ω region, Ω averaged ionization factor is also considered unknown. In initial equations nonlinear effect which result from Coulomb interaction between charged plasma components, as well as nonlinear elementary process of volume electronion recombination are taken into account. Solution of the problem formulated for all unknowns is obtained in form of power series expansion of small parameter. In the specific case, when Ωregion is a circle, solutions of the problem are brought up to numerical results.
 COMPUTATION OF ANISOTROPIC GROUP CONSTANTS OF RDK AND RAK CODES G. V. Lukin, V. M. Shmakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 4244.
A new twostage approach to computation of group neutron constants is presented. RAKcode data may be used in routines for solving neutron transfer equations by spherical harmonics method, SNmethod with various transport corrections and some other methods.
 LIBRARIES OF THE SET OF SOFTWARE CONSTANTS FOR KOBRA COMPUTATIONS. USADE OF ENDL, ENDF LIBRARIES Ya. Z. Kandiyev, E. S. Kuropatenko, G. V. Lukin, Е. I. Cherepanova, V. M. Shmakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 4547.
The content and field of application of ISKHOD and PROM spectral libraries, pregroup BDK1ibrary, group BGRYAK1ibrary are described. The spectral libraries contain consistent information for computations of simultaneous passage of neutrons, gammaray quanta, e^{}, e^{+}, and heavy charged particles in any combination. The pregroup and group libraries contain information on neutronmatter interaction allowing for gammayield. An algoritm of section information reduction in resonance regions is presented.
 USAGE OF SEMICONDUCTOR MEMORY FOR IMPROVING PERFORMANCE OF MONITORING COMPUTING COMPLEXES ON THE BASIS OF THE MICROCOMPUTER "ELECTRONIKA60" V. A. Timofeyev, V. A. Shalimov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 4851.
Structure of monitoring computing complexes is described on the basis of the microcomputer "Electronika60" in which the blocks of semiconductor memory "Electronika256K" are used as external (of "electronic disk" type) and buffer ones in order to enhance information capacity and rate of information entry in automatized acquisition and processing systems, to improve efficiency at processing and developing of software. Software is considered which is used for external and buffer storage, and it is shown that the use of them allow the 12 order increase of the amount of acquired information and 35 times increase of productivity of software development.
 ANGLE PISTON PROBLEM FOR HETEROGENEOUS MIXTURE OF ISOTHERMIC GASES V. A. Suchkov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 5259.
Analytical solutions are obtained for the problem of flow of heterogeneous mixture of isothermic gases within right angle with its edge movement given. Solutions are derived with regard to multivelocity mode of the flow under the assumption of absence of exchange terms in mixture flow equations. The solutions are of special interest for realizing peculiarities of the mathematical model and can serve as test problems for detail investigation of properties of multidimensional numerical procedures describing heterogeneous mixture flow.
 A COMPUTATIONAL TECHN1CUE FOR SPACIAL DISTRIBUTIONS OF POWER OF DOSE AND FLOW DENSITY OF CHARGED PARTICLES IN MULTILAYER PLANE HETEROGENEOUS BARRIERS ON EXPOSURE TO nγRADIATION A. P. Elokhin, V. A. Artemyev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 6067.
A method of numerical calculation of the distribution of dose power P(x) and charged particle flow density in flat systems is considered, for which the MonteCarlo method is unable to compete with regular numerical methods. The spherical harmonics method in Pξapproximat ion is suggested to be used. Application of the method to the problem considered is proved.
 NUMERICAL PROCESSING OF TWORAY AND SHEAR AXISYMMETRIC PLASMA INTERFEROGRAMS BY MEANS OF CUBIC SPLINES AND LOCAL LEASTSQUARES METHOD F. M. Abzayev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 6874.
Solution of the Abelian equation is considered using representation of the input function as a cubic spline on an irregular mesh. Algorithm of smoothing test function with the local leastsquares method is described. Efficiency of Irregular mesh is shown. The scheme of shear interferogram processing by the method of picewise regeneration of the proper ray phase increment in plasma is described. The program performance is tested on model functions, errors being introduced into input data. It is shown that with error dispersion of 0,2 of the interference band the electron concentration computational error in fully ionized plasma in 10,01 density range of critical concentration does not exceed 10%.
 ON A DERIVATION OF GENERALIZED TRANSPORT APPROXIMATION V. M. Shmakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 1. P. 7577.
An approach is suggested which consists in comparison of components of Legendre polynomial expansion of two angle flows generated after one interaction process, whose anisotropy, in its turn, is described in various approximations. Formulas are obtained for crosssection corrections, secondary neutron numbers, and components of intergroup transition matrix expansion. The formulas suggested preseve reproduction properties of (n,2n)  type reactions and angular distribution moments. Limitations on the quantity of the crosssection correction are revealed.
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