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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2013  APPLICATION OF THE FUZZY LOGIC METHODS TO SIMULATE THE NUCLEAR WEAPONS NONPROLIFERATION PROCESS
A. N. Vereshchaga, A. K. Chernyshev VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 316.
A model of nuclear choice as a part of the nonproliferation process (the stage of making decision concerning the development of weapons) developed on the base of fuzzy logic methods is presented. A number of internal and external factors characterizing the events concerning the nuclear choice made by the given state are used as input variables. The wellknown international indexes are used to generate the membership functions of fuzzy variables in use. Results of tests estimating the known historical facts are presented for de jure and de facto nuclear states, as well as threshold states, which denied further development of nuclear weapons. Potential application area is given for the developed model. Key words: nuclear weapons, nonproliferation, fuzzy logic, nuclear choice.
 SATURN2005 CODE. MATHEMATICAL MODELS, ALGORITHMS AND PROGRAMS FOR MULTIDIMENSIONAL PARTICLE AND ENERGY TRANSPORT PROBLEMS A. V. Alekseev, I. M. Belyakov, A. I. Bochkov, V. V. Evdokimov, E. A. Irinichev, V. Yu. Morozov, A. N. Moskvin, A. A. Nuzhdin, M. P. Pepelyaev, V. Yu. Rezchikov, V. V. Suchkova, R. M. Shagaliev, E. S. Sharifullin, T. V. Shemyakina, V. A. Shumilin VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 1730.
The paper briefly describes SATURN code for the numerical simulation of 2D and 3D timedependent and timeindependent neutron transport and nonlinear energy transport by gammas, ions, electrons and fastmoving charged particles. The transport equation is solved in kinetic and diffusion approximations. Code SATURN is oriented to simulations on modern distributedmemory multiprocessor supercomputers. The main ideas on which the code is based are described. Physicomathematical models and mathematical methods used to solve the abovementioned classes of multidimensional problems are formulated, as well as paralleling algorithms are described. Key words: twodimensional and threedimensional problems of neutron and Xray transport, kinetic and diffusion multiplegroup approximation, SATURN code, difference schemes, paralleling algorithms.
 A TECHNIQUE FOR NUMERICAL SIMULATION OF 2D FLOWS OF DISPERSE MEDIA USING LAGRANGIANEULERIAN COMPUTATIONAL GRIDS M. S. Samigulin, V. F. Spiridonov, O. A. Voronova, Yu. F. Danilov, V. V. Shkarubskii, A. N. Tarasova, P. A. Avdeev, M. V. Artamonov, S. V. Velichko VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 3143.
The technique offered in the paper is based on the model of disperse medium in which the carrier component dynamics is described in the continual (Eulerian) approximation and the disperse component dynamics is described in the discrete (Lagrangian) approximation. The requirement of equal pressures of components, or incompressibility of the disperse component is used for the condition of joint strain of the both medium components. During the numerical simulation the disperse component is partitioned into quasiparticles, i.e. groups of particles of the same size, mass, velocity, and temperature. The difference equation system is solved by splitting in processes on a LagrangianEulerian computational grid. Results of computations for three test problems having exact solutions are presented. Key words: dynamics of disperse media, numerical simulation, mathematical model, solution method, verification.
 IMPLEMENTATION IN LOGOS SOFTWARE OF A COMPUTATIONAL SCHEME FOR A VISCOUS INCOMPRESSIBLE FLUID USING THE MULTIGRID METHOD BASED ON ALGORITHM SIMPLE A. S. Kozelkov, Yu. N. Deryugin, S. V. Lashkin, D. P. Silaev, P. G. Simonov, E. S. Tyatyushkina VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 3143.
The paper considers the specific features of the multigrid method implementation in program to solve systems of linear algebraic equations using the method of aggregative coarsening. The method has been implemented in LOGOS software for the module oriented to numerically solving equations of hydrodynamics for a viscous incompressible fluid using arbitrarilyshaped unstructured grids. The paper considers variants of solving scalar linear algebraic systems using V, W, and Fcycles of the multigrid method. Special attention is paid to parallelizing the method, the coarse levels problem solution is demonstrated. The algebraic multigrid method performance is compared to the performance of the preconditioned method of conjugate gradients and the multigrid method without the use of global level to solve problems of viscous incompressible fluid flows. Key words: system of equations, multigrid method, algorithm, matrix, aggregative method.
 DIRECT NUMERICAL SIMULATION OF A TURBULENT FLOW OF VISCOUS INCOMPRESSIBLE FLUID IN A 2D CHANNEL USING SCHEME CABARET D. G. Asfandiyarov, B. I. Berezin, S. A. Finogenov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 5762.
The direct numerical simulation method is used to study a turbulent flow of viscous incompressible fluid in a 2D channel with Reynolds number 5600 determined using the height of channel and mean flow velocity. Periodical boundary conditions in longitudinal and transverse directions are taken. The longitudinal and transverse sizes of region are 4 and 2, respectively; is a halfheight of channel. A nonuniform grid 257 129 129 concentrated near the boundary is used for simulations, which are performed using scheme CABARET without subgrid models of turbulence. The computational algorithm consists in successively solving the explicit part of the scheme (calculation of velocities at the next time slice) and Poisson equations for pressure. The Poisson equation is solved using the parallel algorithm of fast direct method and parallel running. Supercomputer “Lomonosov” with 128 processors was used for simulations. The total runtime was 9 days (27 648 processor hours). The calculated nearwall turbulence parameters  averaged velocity profile, stress tensor components, contributions from the molecular and turbulent components of viscosity tensor, and the channel resistance factor  are in a good agreement with the data calculated in 1987 by the John Kim team from the Ames Research Center (NASA) by solving a similar problem using similar computational grids. Key words: direct numerical simulation, scheme CABARET, turbulent flow, 2D channel, viscous incompressible fluid.
 HYDROGEOMECHANICS PROBLEMS IN FILTERING POROUS MEDIA WITH POROUS SKELETON OF A VARIABLE MASS U. V. Mikheyeva, M. G. Khramchenkov, E. M. Khramchenkov, A. N. Chekalin VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 6369.
The hydrogeomechanics equations for filtering porous media with porous skeleton of a variable mass are studied. Variations of the porous skeleton mass are caused by heterogeneous chemical reactions. Consequences of the revealed mass transport and strain dependences in such media are analyzed and the specific features of finding rheological ratios are studied. Key words: mass of porous skeleton, hydrogeomechanics, flow, strain, stress, rheology, dissolution, model.
 THREELEVEL PARALLELING IN THE TIM2D CODE A. A. Voropinov, S. S. Sokolov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 7077.
TIM2D is a continuum mechanics simulation code, which uses arbitrarilyshaped unstructured polygonal Lagrangian grids. TIM2D has three paralleling levels. The first level of paralleling in domains and the second level of paralleling in paradomains of the same domain use an MPIbased distributedmemory model. At the third level, computing cycle iterations are paralleled using an OpenMPbased sharedmemory model. Within a single simulation, the paralleling levels can be used both separately and in various combinations. Key words: TIM2D code, unstructured grids, paralleling, mixedmemory model.
 AUTOMATED SETTING OF SMPI LIBRARY PARAMETERS D. V. Dontsov, S. I. Sapronov VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 7882.
MPIBoost toolkit is described, which allows automating the process of selecting optimum values of parameters for SMPI library. MPIBoost has two operation modes: setting the clusterspecific parameters and setting the applicationspecific parameters. The process of setting parameters for SMPI library conventionally has three levels: setting the values of parameters for the most popular cluster architectures and parameters for running applications, these values are used in SMPI library as default values;
 setting parameters of SMPI library with regard to the specifics of a certain cluster, which is performed, if SMPI library package is installed;
 setting parameters of SMPI library with regard to the specifics of a certain application.
Such multilevel process allows getting an optimum ratio between the time spent for setting parameters and the performance of applications achieved on different clusters. Key words: MPI, parallel computations, optimization methods.
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