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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2002  RELAXATION MODEL FOR SHEAR STRENGTH IN LAGRANGIANEULERIAN FORMULATION
S.M. Bakhrakh, I.P. Bakumova, P.N. Nizovtsev, V.A. Raevsky, E.V. Shuvalova VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 38.
The paper presents a model, describing a process of shear strength relaxation both in Lagrangian and Eulerian formulations. When generalizing to flows in Eulerian variables recalculation rules of all values, describing strength are set. It provided a way for computing a large class of problems on relaxation model on Lagrangian and Eulerian grids. The model is implemented in program complex LAGAK for computing 2D timedependent continuum flows in Lagrangian and Eulerian variables. Relaxation model produces good results in pressure range P 1065 GPa, specifically it enables describing experimental results of instability development calculations.
 THE USE OF SURFACE PSEUDOSOURCES AND SURFACE HARMONICS METHODS IS AN EFFECTIVE WAY OF COMPUTING NUCLEAR REACTOR SUITABLE FOR PARALLELIZATION N.I. Laletin, N.V. Sultanov, A.A. Kovalishin VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 922.
The paper states a consistent approach to computing nuclear reactors using methods, which initial approximations meet the requirements of design calculations in a speed of operation, therewith computational results may be comparable with reference in accuracy. The first is the method of surface pseudosource used to calculate cells characteristics. The second is the method of surface harmonics used to calculate both fuel assemblies and the whole reactor on coarse grids. The paper gives a brief description of the methods and gives their applications for calculating VVERtype reactors and PWR benchmark.
 A TECHNIQUE FOR SOLVING TIMEDEPENDENT ELASTICPLASTIC PROBLEMS ON IRREGULAR MULTIFARIOUS LAGRANGIAN GRIDS S.S. Sokolov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 2336.
In solving multidimensional timedependent elasticplastic problems the numerical methods of Whilkins type have received wide acceptance. Finite difference and finite elements methods are the most universal ones. The wide spectrum of solved problems makes it difficult to cover all of them by a unique method particularly in onedimension. Finitedifference methods, based mostly on regular quadrilateral hexagon Lagrangian, EulerianLagrangian and Eulerian grids are progressing most rapidly in solving elasticplastic problems. The paper deals with Lagrangian technique for computing multidimensional timedependent elasticplastic problems on nonregular Lagrangian grids. In two dimensions a technique, based on Lagrangian gas dynamic DMK technique uses a nonregular difference grid consisting of convex polygons with arbitrary vertex number remaining convex during a problem solution. In three dimensions a technique, based on Lagrangian gas dynamic TMK technique uses a nonregular convex multifarious Lagrangian grid of arbitrary configuration. In 3D and 2D techniques explicit finitedifference schemes are used to approximate equations. The described techniques are implemented in TMK and DMK program complexes, allowing the solution of continuum mechanics problems with severe distortions in areas with complicated geometry.
 NUMERICAL SIMULATION OF ISOTROPIC DESTRUCTION OF ELASTICPLASTIC, MEDIA IN MIMOZA TECHNIQUE A.A. Sadovoy, N.V. Sokolova VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 3744.
A large amount of microdeffects of different types are formed during dynamical destruction of elasticplastic materials. A separate description of each microfailure is very laborious and practically impossible. Therefore mechanics of continual (or scattered) destruction has been developed recently, which governing equations introduce some internal variables, characterizing microfailure development. MIMOZA technique implements a kinetic model for viscous plastic NAG destruction, updated to enable the description of destructed materials. Numerical simulation results for some experiments based on it are presented.
 PROGRAM MOTION STABILIZATION METHODS E.V. Voskresensky, T.F. Mamedova VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 4554.
The problems of system controllability and program motion stabilization are the most important ones in a theory of automatic control. It is well known that a great number of various types of controllability in finite time are available. V.I. Zubov, N.N. Krasovsky et al. consider the concept of a controlled system in infinite time. In this case a moving point from certain time on enters neighborhood of a finite point and does not leave it with all t T. It is the requirement not to leave some point neighborhood that occurs in many problems of celestial mechanics. Program motion is a motion equation solution at concrete value of control. The problem on the solution stabilization is of crucial importance here. In this case one should select such a control function that is able to make the solution stable in one sense or another. These problems have been solved in this paper.
 TOPOLOGICAL REDUNDANCY IN MULTIPROCESSOR ENVIRONMENTS S.A. Stepanenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 5560.
The paper proposed the redundancy method which specific features are: first, full identity of backup components and those being reserved and, second, full preservation of the environment topology which means that when replacing a defective component by a backup one only logical numbering of components and links between them changes. No physical changes and degradation, in particular, take place. The method proposed is described for hypercube , where n=2, k=2,3,..., is the hypercube dimension that coincides with Hamming code dimension. This code properties are used in the method presented. The method allows anyone failed component to be replaced. However, if components failed are such that their vectors have obtained by changing one and the same component of the corresponding separated vectors, then 2,3,..., components can be reserved "simultaneously" (by one and the same operation of logical numbering). Probabilities of simultaneously reserving several processor elements have been estimated. It is known that 1D, 2D, 3Dtori and othertype topologies can be constructed in hypercube using Gray codes. The method is usable to provide redundancy of such topologies with no changes required. The method can be used to provide redundancy of any structures (automata, collectives, organisms) having the topologies above.
 HARDWARE ARHITECTURE FOR INTERPROCESSOR COMMUNICATIONS SYSTEM OF MULTIPROCESSOR MPX SYSTEM V.S. Popov, S.A. Stepanenko, A.A. Kholostov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 6164.
The paper studies some principles of construction and structure of multiprocessor communications system hardware for multiprocessor MPX system. The main processes of messaging are shown, the comparison of the system with similar items according to basic parameters is given.
 OpenMP FORTRAN EXTENSION FOR DISTRIBUTED SYSTEMS V.A. Bakhtin, N.A. Konovalov, V.A. Kryukov VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 6570.
Lack of controls for data localization restricts OpenMP use to multiprocessor systems with shared memory or with distributed shared memory. This paper studies proposals on OpenMP extension for Fortran by adding data distribution and distant data access commands which enables using OpenMP on distributed systems.
 THE IMPLEMENTATION OF MPI COMPUTATION PARALLELIZATION V.L. Bogdankevich VANT. Ser.: Mat. Mod. Fiz. Proc. 2002. No 4. P. 7173.
The approach allowing standardized method to transform algorithm of previously developed mathematical models with consecutive modeling of separate subsystems in a new form with simultaneous parallel performance of several branches of calculation is described. The libraries of programs MPI implementing are a tool allowing such a transformation without fundamental labour inputs. Two transformation methods INLINE and CALL are studied program modules developed specially for standardization of these two methods are described.
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