Issue N^{o} 3, 1989 
TWODIMENSIONAL ESTIMATE OF EXPLOSION IN WATERFILLED VOLUME OF CUTOFF SPHERE FORM
V. B. Adamsky, A. V. Balabanov, L. V. Nesterenko, I. D. Sofronov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 36.
A number of papers stated that during charge explosion in fluid a vapourgas bubble formed at explosion point may attract to bottom. The paper considers investigation by numerical calculation of the physics of the phenomenon. The numerical test was performed with a program for solving twodimensional gas dynamics problems on an irregular grid based on the "Meduza” technique. Dynamic parameters of matter movement in the volume are obtained for various times. As the computation showed, a vapourgas bubble formed at explosion attracts to bottom and turns into torus extending in the spherical volume surface direction.

SOME RESULTS OF ESTIMATING MULTICOMPONENT MATTER THERMODYNAMIC FUNCTIONS WITH REGARD TO SHELL EFFECTS N. M. Barysheva, A. A. Kosorukova VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 712.
Within the framework of selfconsistent field model some multicomponent matter thermodynamic functions are estimated on the basis of varions conditions of thermodynamic equllibium. The assumed formulations of equilibrium conditions are shown to yield the same results, if the thermodynamic functions of all mixture components are obtained with this model. Influence of shell effects for matters of nearly the same atomic numbers and component concentrations, as well as for matters, in which there is an element of predominant atomic number and concetration, is illustrated by comparison with ThomasFermi model calculations. Comparison with statistic shell model data is made as well.

A SELFADAPTING PROGRAM SYSTEM FOR AUTOMATED CALCULATION OF MATERIAL RESOURCES DISTRIBUTION SCHEDULES G. G. Solovyev, A. V. Suchkov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 1315.
Complex computational arrangement in material resources distribution schedule applications and dependence of personnel number on volume of implemented computations led to the need to automate them. The suggested system consists of programs constructing computer jobs on the basis of data analysis and computing situation. The system allows to obtain statistical information and computational state data in automized mode, to increase amount of computations without enlargement of personnel number, as well as simplifies computing run technique. Job control language is extended with including syntax constructions close to that of PL/1 language. It allows to arrange the distribution schedule application software in a sufficiently simple single approach.

IS0TR0PIZATI0N OF NEUTRON ELASTIC SCATTERING CONSTANTS G. A. Goncharov, V. P. Gorelov, G. G. Farafontov, V. Kh. Khoruzhiy VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 1623.
Results of comparing various isotropizations of group scattering constants are given. A special attention is paid to studying effects of arising negative transport constants. A simple way to overcome negativity is proposed. Computational results are supplied allowing to formulate most desirable way of isotropization for fast neutron transfer applications.

INVARIANT PROPERTIES OF MODEL TRANSFER EQUATION AT COORDINATE SYSTEM TRANSFORMATION V. V. Basharov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 2428.
A simple tranfer equation in an arbitrary coordinate system specified by a differential equation for transfer elocity is considered. Questions of transformation uniqueness and transfer equation evolution in an arbitrary coordinate system are discussed. Two theorems are proved approving the former question and providing sufficient conditions on equation coefficients for transfer velocity maintaining velocity for the latter one.

PARALLEL COMPUTING AT THE N0NSTATI0NARY SPACIAL FLOW ROUTINE O. M. Velichkho VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 2933.
OS SVS has beep implemented on multiprocessor system SVS since 1986, allowing users to parallel problem runs. These OS SVS capabilities were used for parallel computing in the routine of nonstat ionary space fields of flows near blunted bodies with finite difference Godunov method. Sufficienty large volume of virtual memory embodied computing blocks and problem data and thereby allowed to refuse their dynamic loading during step count. The task is represented as a control and several computation processes. The computation processes compute gas dynamics flow parameters simultaneously for several workspaces. The control process performs coordinating functions. Interprocessor information communications are handled by means of semaphores and events. Timings showed that for four processor the total CPU time taken by a task per astronomical time unit amounts to 3,8 units.

TWODIMENSIONAL TRANSFER EQUATION APPROXIMATION ON QUADRANGULAR AND POLYGONAL SPACIAL GRIDS WITH EXTENDED PATTERN DIFFERENCE SCHEME N. P. Pleteneva, R. M. Shagaliyev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 3441.
For a twodimensional transfer equation on quadrangular special grids a conservative finitedifference scheme with additional relations is derived in which grid values of the desired function are evaluated simultaneously, at vertexes (nodes), edges and centers of quadrangular grid cells. The difference transfer operator is of triangular structure. Results of numerical study are supplied showing secondorder accurate convergence of the grid solution to the accurate one both on rectangular and on sufficiently nonorthogonal space grids. The scheme is extended to transfer equation numerical solution on grids of arbitrary convex polygonals.

ON SOLUTION OF P_{2N1}APPROXIMATION OF NEUTRON TRANSFER EQUATION IN A SPHERE WITH CENTRAL POINT ISOTROPIC SOURCE Gorelov V.P., Travin V.V. VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 4248.
A complete solution of P_{2N1}approximation of neutron transfer equation is obtained for the central region of a sphere containing an isotropic source at the origin of coordinates. The involved unknown coefficients are suggested to evaluate with the AdamskayaGodunov method. Divergence of r^{2} even components of the desired vector, divergence of r^{1} odd components are found as compared to known solution, the logarithmic singularity is taken into account.

ON THE USE OF THE GODUNOV METHOD IN SPHERICAL HARMONICS DIFFERENTIAL EQUATION SOLUTION FOR THE ONEDIMENSIONAL STATIONARY KINETIC EQUATION IN MULTIGROUP APPROXIMATION I. A. Adamskaya VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 4955.
Applicability of the special solution orthogonal sweeping method (the Godunov method) is justified for the solution of spherical harmonics differential equations for the onedimensional stationary kinetic equation in multigroup approximation. Boundary conditions of the probiem are proved to allow to derive a full set of linear independent vectors needed to implement the method considered also in the case of multigroup approximation of the kinetic equation.

ON TWO APPROACHES ÒÎ SPEEDINGUP ITERATION CONVERGENCY AT NUMERICAL SOLUTION OF RADIATION TRANSFER EQUATION WITH THE "ROMB" METHOD A. A. Gadzhiev, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 5665.
Iteration speedingup methods are considered for combined solution of energy and radiation transfer equations in multigroup P_{1}approximation witn the "ROMB" method. Speedingup of iteration convergency is achieved by means of introduction of additional stage at which temperature is computed with a certain simplified model of transfer equation. The speedingup methods are based on either Jacobitype iterations or spectrumaveraging method. Extension of Jacobitype iterations to twopointtype differnce schemes is suggested, and a new algorithm of iteration convergency speedingup is derived for the averaging method. The methods considered may be extended to other transfer equation approximations and to more complex geometries.

THE "ROMB" METHOD FOR SOLUTION OF MULTIGROUP RADIATION TRANSFER EQUATION IN P_{1}APPROXIMATION A. D. Gadzhiev, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 6670.
Solution of radiation transfer equation in multigroup P_{1}approximation combined with the energy equation is considered. The difference technique is based on the twopoint scheme "ROMB", possessing a number of advantages, such as single difference cell approximation, single computation of absorbtion coefficient in cell per iteration, simplicity of formulating boundary conditions, extentionabi1ity to many dimensions. The difference scheme includes parameters, the appropriate choice of which allows to combine secondorder accuracy and monotonicity in optically dense media.Solution of radiation transfer equation in multigroup P;approximation combined with the energy equation is considered. The difference technique is based on the twopoint scheme "ROMB", possessing a number of advantages, such as single difference cell approximation, single computation of absorbtion coefficient in cell per iteration, simplicity of formulating boundary conditions, extentionabi1ity to many dimensions. The difference scheme includes parameters, the appropriate choice of which allows to combine secondorder accuracy and monotonicity in optically dense media.

ON APPROXIMATING VOLUME INTEGRALS IN A DIFFERENCE SCHEME DERIVED IN ARBITRARY CURVILINEAR COORDINATES ON BASE OF THE GODUNOV METHOD FOR SOLVING TWODIMENSIONAL GAS DYNAMICS PROBLEMS N. Ya. Moiseyev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 7174.
It is suggested to use intermediate values found at cell edges from the solution of the Riemann problem in the difference scheme derived in arbitrary curvilinear coordinates on the basis of the Godunov method when approximating volume Integrals. This approach to approximating integrals allows to match times at the choice of intermediate values of gas dynamics quantities in the left and right parts of difference equations. Computations of model problems showed higher accuracy of the results and maintaining movement symmetry at approximating geometry with circumferences or straight lines using difference meshes close to uniform.

SOFTWARE FOR LOCAL UNIFORM MULTICOMPUTING SYSTEMS ON THE BASIS OF THE SM COMPUTER O. B. Gushchin, M. M. Savitsky, Yu. V. Feodoritov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 7577.
A software system has been developed for local uniform startype multicomputing systems on the basis of the PDP11type computers. The host computer is controlled by the NTS operating system. NTS communications are used allowing the speed gain and the lower communication overheads in the system.

FORPOST: A FORTRAN HOST SYSTEM O. I. Butnev, A. L. Komarova, A. M. Mikiychuk, V. A. Novichikhin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 7883.
The FORPOST automatized system run on ES computer and designed for development, employment, and modifications of FORTRANIV and FORTRANDubna programs is described. Problems of organization of the system and its structure are considered. Tool set of the system frame is described.

CONTROLLED HEAVYION FUSION AND DEUTERIUM TARGETS M. M. Basko, V. S. Imshennik, D. G. Koshkaryev, M. D. Churazov, K. B. Sherstnev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 8497.
The current state of work on the Herational heavyion fusion and the principal physical aspects of this field of controlled thermonuclear fusion are described. Optimization problems are considered on the example of sphericallysymmetrie target with tritiumdeuterium fuel. Possibility of deriving deuterium targets of iterational haavyion fusion is investigated. A design of cylindrical deuterium target with magnetic thermal isolation and deuteriumfuel combustion detonation mode is suggested.

ON ORGANIZATION OF COMPARISON OF ALGORITHMS AND CODES OF DERIVING REGULAR TWO DIMENTIONAL DIFFERENCE GRIDS G. P. Prokopov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 98108.
In view of a great number of papers on constructing algorithms for deriving difference grids there is a need of formulating unified criteria for checking grid quality and deriving test problems for approbation and comparison of various techniques. The paper deals with discussion of these questions and contains some concrete proposals as for their practical realization.

THE MULTIGRID DIRECTIONSPLIT METHOD FOR NUMERICAL SOLUTION OF MULTIDIMENSIONAL PROBLEMS B. L. Voronin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 109111.
On the basis of the wellknown statement that the Volterra operator with limited nucleus is a compressing transformation, the compressibility condition is formulated for the generaltype integral operator with asymmetric nucleus.

COMPRESSIBILITY INDICATION OF A LINEAR INTEGRAL OPERATOR A. S. Sukhikh VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 111112.
On the basis of the wellknown statement that the Volterra operator with limited nucleus is a compressing transformation, the compressibility condition is formulated for the generaltype integral operator with asymmetric nucleus.

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