Issue N^{o} 2, 1994 
STABILITY OF DIFFERENCE SCHEMES FOR PARALLELIZATION IN TERMS OF PHYSICAL PROCESSES
Yu.A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 35.
The results of stability studies are presented for difference schemes, in which different processes are calculated independently at the same time step on different processors. Then computation results are summed up and used for the next step calculation. In a large multiparameter family of onestep difference schemes for parallel calculation of 2 processes one did not find difference schemes with 2nd order of accuracy over time and absolutely stable at the same time. The simplest implicit difference scheme for parallel calculation of 3 and more processes with 1st order of accuracy unlike the analogical splitting scheme turned out to be conditionally stable. The family of absolutely stable schemes is constructed for this case.

SMOOTH REPRODUCTION AND INTEGRATION OF FLAT CURVES G.P. Prokopov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 611.
The algorithms for smooth reproduction and integration of flat curve elements, specified by reference point sequence are developed. The algorithms are based on the usage of special curves simple enough and convinient in practice, allowing to solve the problem in function classes C^{1} and C^{2} and if necessary — in the function classes of higher smoothness.

GENERATION OF GRIDS CONSISTING OF NON DEGENERATE QUADRANGLES USING THE DELAUNAY CRITERION V.M. Uskov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 1216.
The grid is generated by minimizing the functional expressing smoothness measure. Every quadrangular cell is divided by diagonal into two triangles. The discrete functional analog reaching minimum on the Delaunay triangulation is used. The positions of nodes and diagonals are chosen from the minimum condition and the Delaunay criterion, respectively. The simple inequality uniquely corresponding to the Delaunay criterion is proposed. Positive square of triangles and quadrangles and no intersection of opposite quadrangle sides are guaranteed.

HIGHER ORDER APPROXIMATION DIFFERENCE SCHEME FOR TRANSPORT EQUATION E.V. Diyankova, O.S. Shirokovskaya VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 1721.
The method of TVDtype for difference scheme generation is proposed. The obtained scheme is used for numerical solving of trasport equation and is constructed by adding antidiffusional fluxes to initial first order scheme. The scheme has a simple form. It is explicit conservative and third order approximating in the field of smooth solutions (except for extreme vicinities) on the uniform spatial grid. The simple algorithm for difference equation in the case of two spatial variables is proposed. It allows to conserve the scheme approximation order for commutative spatial operators.

ANALYTICAL INTEGRATION OF TRANSPORT EQUATION OVER THE FREE PATH LENGTH FOR TIMEDEPENDENT CASES S.N. Sheludko VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 2226.
Partial analytical integration (over all free path lengths) of the terms from Von Neumann series, describing transport equation solution is executed. Calculations are performed for the problem on homogeneous infinite medium and infinite plane instantaneous source. The results are presented in a form of analytical formulae. The data obtained can be used to construct local estimation for the Monte Carlo method in the problems, related to deep penetration of radiation into material.

CALCULATIONAL METHOD FOR CONTROL OF UNSHOCKED UNLIMITED COMPRESSION OF GAS LAYERS I. A. Bashkirtseva VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 2732.
A detailed generation was performed to prod ice the characteristic series coefficients used to obtain the control laws for unshocked unlimited compression of gas layers. The field of application for expansion obtained is studied. It is found, that only two first terms of a series have no singularities. It is shown, that truncated series, retaining regularity can be used as a solution. The law of a piston movement up to the focusing moment is obtained. The integral curve behaviour is studied for normal difference equation describing the piston movement law. The correctness of approximations obtained is verified by calculations, using characteristic method and illustrated by graphs and tables.

RELATIONS BETWEEN INTEGRAL CHARACTERISTICS, DESCRIBING THE DEVIATION OF FISSILE MATERIAL MEDIA FROM CRITICAL STATE V.P. Gorelov, G.A. Goncharov, G.G. Farafontov, A.A. Chernova VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 3338.
For materials fissioned under the neutron impact, the formulas are obtained to relate the multiplication factor q with the time constant of prompt neutron multiplication λ_{0} and with the effective multiplication factor K_{ef}.

LATENT ACCURACY IN VARIATIONAL DIFFERENCE HIGHORDER APPROXIMATION SCHEMES FOR LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS Yu.A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 3944.
Some threelayer difference schemes, explicit and implicit ones, are constructed for linear equation d^{2}u/dt^{2}+ A(t)u = 0 using the method of discrete approximation for operation functional by GamiltonOstrogradskiy with the 4^{th} order accuracy. The variational difference schemes constructed approximate initial equation with only the 2^{nd} order accuracy, when operator A(t) is a function of time t. It appears that there always exists a substitution of difference solution of the form u(t^{n}) = (1 + τ^{2}B(t^{n}))v(t^{n}) so that for a new unknown function a difference scheme approximates initial equation with the 4^{th} order accuracy, that is the real accuracy has the 4^{th} order accuracy and corresponds to the error of the operation functional approximation, but it is latent. The whole analysis is performed for a constant time step.

NUMERICAL SIMULATION OF THE STATICAL GAS NEUTROLIZER TARGET OF THE NEGATIVE DEUTERIUM ION BEAM A.S. Roshal, L.P. Shevchenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 4550.
An effective method of numerical simulation of the gasdynamic processes having higher accuracy and stability than the convenient particle method is proposed. The optimization problem of the neutralizer gas target of the negative deuterium ion beam is solved on the basis of the proposed method. The results of the modeling of the statical gas target corresponding to the maximum neutral atoms yield are presented.

EGAK CODES. LAGRANGIANEULERIAN METHOD FOR2D GAS DYNAMIC FLOWS IN MULTICOMPONENT MEDIUM N.S. Darova, O.A. Dibirov, G.V. Zharova, A.A. Shanin, Yu.V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 5158.
LagrangianEulerian method for 2D gasdynamic flows in multicomponent media using explicit and implicit finitedifference schemes in LagrangianEulerian variables is described. Some computational results are given.

CALCULATIONAL TECHNIQUE FOR TURBULENT MAKING IN ONEDIMENSIONAL GAS DYNAMIC FLOWS (VIKHRTECHNIQUE) V.A. Andronov, V.I. Kozlov, V.V. Nikiforov, A.N. Rasin, Yu.A. Yudin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 5964.
VIKHRtechnique for gravitational turbulent mixing (TM) calculation with (or without) heat conduction is described. Oneflow TM model is discussed as a partial case of multiflow model with pressure gradient infinitesimal in TMzone. The calculational method is based on splitting in terms of physical processes. In the first stage the gasdymamic equations in Lagrangian form with respect to turbulent pressure are solved with implicit difference scheme. Then equations for turbulent values without diffusion terms are integrated using explicitimplicit scheme. In the third stage the radiant heat conduction equation is calculated with weighted implicit difference scheme. In the final stage the diffusion equations for turbulent values, for material concentrations and ones for turbulent heat flow calculation are solved according to purely implicit schemes. The technique is implemented in a form of program package VIKHR on IBM PC AT in Fortran.

ESTIMATED NEUTRON DATA BANK BEND: THE PRINCIPLES OF BANK AND PROGRAM PACKAGE STRUCTURE FOR OPERATION ON BANK DATA A.N. Grebennikov, G.G. Farafontov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 6571.
General structure and function principles of the estimated neutron data bank BEND on EScomputer are presented. The bank is designed for support of neutron calculation with multigroup and spectral constants, 7radiation field calculation with 7generation constants and energy release calculation with energy constants.

EXACT SOLUTIONS OF ENERGY TRANSFER EQUATIONS IN TWO COMPONENT PLASMA A.A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 7277.
The paper is dedicated to finding analytical solutions for radiant energy transfer problem in twocomponent plasma. Exact solutions of multidimensional timedependent spectrum equation for energy transfer with respect to ion and electron temperature are obtained with specially selected coefficients of heat conduction, absorption and scattering. The solutions are exemplified by kinetic and diffusion equations. The results obtained can be used for the validation of difference methods.

ON QUALITY OF ION BEAM REPRESENTATION BY MACROPARTICLE ENSEMBLES E.S. Galpern, V.N. Lyakhovitskiy VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 7887.
On the base of model beam, corresponding to ITEF‘s project on heavy ion thermonuclear fusion, the procedure of ion clustering into macroparticles is analyzed. The nonidentity is shown for numerical models, corresponding to different methods of initial beam generation. It retains great freedom in beam representation, which may cause a variety of physical results or false physical pattern. The example of such false pattern is beam representation by macroparticle ensembles, which decreases the value of their side separation forces and may cause undesirable consequences, for example, when calculating focusing of such beams on a target. Some recommendations to overcome this situation are given.

TRANSPOSING THE RECTANGULAR MATRICES A.S. Shvedov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 2. P. 8889.
The rectangular matrix transposition algorithm is presented. Only one additional mesh is used which is critical for large size of the matrices transposed and insufficient main memory.

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