Issue N^{o} 1, 1992 
CONSTRUCTING A SEQUENCE OF ASYMPTOTICS FOR DETERMINING THE AMOUNT OF CUMULATING ENERGY FOR LAYERED SHELL SYSTEM CONVERGENCE
G.V. Dоlgоliоva, A.V. Zabrodin VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 310.
The motion of layered shell systems (with possible gaps) is considered for instantaneous energy release into outmost layers. A hydro dynamic approximation is used. An asymptotic system is constructed which defines the main motion principles when the system converges to the center. Relations are obtained allowing a specific selection of initial data in order to optimize the cumulation parameters. Analytical results are compared with numerical simulation of model fusion targets.

HIGHER CONSERVATION LAWS FOR A WAVE EQUATION V.E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 1117.
Conservation laws for a wave equation are derived. Explicit general formulas axe found for generating functions and their corresponding conservation laws. All leading minors of a special infinite matrix are proved to be nonzero.

ON DIFFERENCE OPERATOR THEORY IN L SPACE N.Yu. Baкaуev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 1820.
Resolvent norm estimates are presented for a difference elliptic operator on the Banach space scale of L_{p} type with 1 ≤ ρ ≤ ∞. The results obtained may be used for investigating difference scheme stability with spectral methods.

USING VARIATIONAL MECHANIC PRINCIPLES FOR CONSTRUCTION OF TIMEDISCRETE DIFFERENCE MODELS IN GAS DYNAMICS. PT.5. PULSE AND PULSE MOMENTUM CONSERVATION LAWS IN DIFFERENCE SCHEMES WITH HOLONOMIC BOUNDS Yu.A. Вondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 2127.
Finitedifference gasdynamic shemes ("cross" type and implicit "weighted" schemes) on Lagrangian meshes are considered. If the cell volumes and holonomic bounds are Invariant with respect to space translations and rotations, the pulse arid pulse momentum conservation laws are shown to be satisfied for difference schemes implemented with a sequential variational method using a discrete time approximation of the HamiltonOstrogradsky action functional. Several examples show that using time approximation which is not consistent with the principle of least action results in that pulse momentum conservation law becomes no longer valid while the same invariance conditions hold.

USING VARIATIONAL MECHANIC PRINCIPLES FOR CONSTRUCTION OF TIME DISCRETE DIFFERENCE MODELS IN GAS DYNAMICS. PT.6. PULSE AND PULSE MOMENTUM CONSERVATION LAWS IN DIFFERENCE SCHEMES WITH A VARIABLE KINETIC ENERGY OPERATOR Yu.A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 2833.
Differential/difference schemes and several finitedifference gas dynamic scheme types with a kinetic energy operator depending on mesh node coordinates are examined. If cell values, holonomlc bounds and kinetic energy are invariant with respect to space translations and rotations then pulse or pulse momentum conservation laws are satisfied, respectively, for difference schemes developed with a sequential variational method based on time approximation of the HamiltonOstrogradsky action functional.

HIGH ENERGY PROCESS SIMULATION AND WIDERANGE EQUATIONS OF STATE FOR METALS L.V. Altschuler, S.E. Brusnikin VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 3442.
Widerange equations of state are obtained for eleven metals which have regular asymptotics and adequately describe experimental state thermodynamics, plasma, condensed phases and melting and vaporization processes. The equations were obtained by combining free energy of experimental data and that of regional theoretical models In the thermodynamic potential form using interpolations. For temperature less than T≤5 keV, dynamic experiments,ultrasonic and thermophysical measurements, spectroscopic data and critical point parameter estimations were used to derive semiempirical equations of state. High energy ranges interpolationally combine plasma models and quantumstatistical descriptions. For the whole phase diagram, the free energy of an electronic subsystem in an approximate form represents selfsimilar solution of ThomasFermi theory and two correction functions. Widerange equationofstate versions for reduced ranges can be implemented In an analytic form for gasdynamic calculations without tabular representations.

GA.SDYHAMIC FLOW CALCULATIONS USING KUROPATEHKO METHOD IN A ONEDIMENSIONAL PACKAGE (ROSA PROGRAM) G.G. Ivanоva, T.A. Mikiychuk VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 4346.
The ROSA program is described intended for numerical simulation of unsteady continuum motion. It represents a "bundle" of modules operating within the applications package "Odnomemy complex". The program implements a heterogeneous computation method selecting strong and weak discontinuities (Kuropatenko method).

ON ACCURACY OF EXTERNAL BOUNDARY CONDITIONS POR CALCULATIONS OP ELECTROMAGNETIC FIELDS PRODUCED BY GAMMA QUANTUM POINT SOURCE A.I. Gо1ubev, N.A. Ismailova, V.A. Teriокhin VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 4749.
A numerical solution of the model problem was used as an example to compare three different techniques of setting boundary conditions for calculations of electromagnetic fields produced by a gamma quantum point source located on a conducting surface. These techniques are baaed on representing electromagnetic fields as multipole decompositions beyond the source region. Their accuracies are compared by considering solutions on an external boundary of the computational region and one obtained for a problem where the external boundary is considerably far from the source.

AH ALGORITHM FOR CONVERTING THE MULTIGROUP P APPROXIMATION INTO A SMALLGBOUP DIFFUSION ONE B.D. Abramоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 5052.
Group reduction iteration algorithms are formulated intended for maintaining an expanded collection of К_{of} like functionals, processor numbers, integral flows and surface currents in regions and groups when the original multigroup P approximation reactor model is converted into a smallgroup diffusion one.

EFFICIENT CAVITY AND GAP DESCRIPTIONS IN DIFFERENTIAL Р_{2N1} OR S_{N} EQUATIONS IN A SPHERE V.P. Gоrelоv, G.G. Farafontоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 5358.
Efficient techniques for describing a cavity or a gap in differential Р_{2N1} OR S_{N} equations in a sphere are proposed. These techniques allow to avoid the integration of the above equations in a cavity or in a gap which must result in reducing the amount of computations for large size of these regions.

A MEAN ION MODEL FOR CALCULATING IONIZATION KINETICS, EXCITED LEVEL POPULATIONS AND SPECTRAL RADIATION TRANSPORT COEFFICIENTS IN THE SNDP PROGRAM S.А. Вelкоv, G.V. Dоlgoliova VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 5961.
The use of a mean ion model for consistent gas dynamics and nonequilibrium laser plasma radiation transport is described. Standard mean ion model equations were generalized to the case of plasma consisting of an atomic combination with various nucleus charges. A numerical method for solving the resulting system is described. The results obtained using the method presented are compared with known data derived by different techniques.

METHOD FOR GENERATION OF BLOCK OPTIMAL GRIDS IN TWODIMENSIONAL MULTIPLYCONNECTED REGIONS O.B. Khairullina VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 6266.
A method for generating block curvilinear optimal grids in simplyconnected and multiplyconnected regions with simple and complex topology is suggested. The generated grids have a smoothness quality at the inner boundaries of adjacent blocks. The possibilities of the MOPS2 program have been described. The examples of computed grids have been presented.

ITERATION CONVERGENCE SPEEDUP METHOD FOR NUMERICAL SOLUTION OF A ONEDIMENSIONAL NONSTATIONARY RADIATION TRANSPORT EQUATION IN A MULTIGROUP KINETIC APPROXIMATION E.T. Grоshev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 6772.
An iteration convergence speedup method is proposed for numerical solution of a 1D nonstationary radiation transport equation in a multigroup kinetic approximation using a ST^{γ=1}scheme. The method relies upon choosing a "correction" operator as a spectral P_{1}approximation for the transport equation in combination with Newton temperature linearization. The correction system is reduced to a threepoint form with respect to the spatial variable and is solved with Jacobi iteration method.

A NONSTATIONARY FREEGROUP ITERATION METHOD A.A. Maleev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 1. P. 7376.
A family of nonstationary iteration procedures is described designed for solving a linear system with nondegenerate complexvalue matrix called FreeGroup Iteration (FGI). This family is shown to include a block Jacobi method and a group relaxation method, the nonstationary GaussZeidel method being the partial case of the latter. FGI convergence is proved (with some natural restrictions) for systems of linear equations with matrices having strong diagonal domination or irreducible dominant diagonal.

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