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Issue No 4, 2013


APPLICATION OF THE FUZZY LOGIC METHODS TO SIMULATE THE NUCLEAR WEAPONS NON-PROLIFERATION PROCESS

A. N. Vereshchaga, A. K. Chernyshev
VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 3-16.

A model of nuclear choice as a part of the non-proliferation 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 well-known 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, non-proliferation, fuzzy logic, nuclear choice.
SATURN-2005 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. 17-30.

The paper briefly describes SATURN code for the numerical simulation of 2D and 3D time-dependent and time-independent neutron transport and nonlinear energy transport by gammas, ions, electrons and fast-moving charged particles. The transport equation is solved in kinetic and diffusion approximations.
Code SATURN is oriented to simulations on modern distributed-memory multiprocessor supercomputers.
The main ideas on which the code is based are described. Physico-mathematical models and mathematical methods used to solve the above-mentioned classes of multidimensional problems are formulated, as well as paralleling algorithms are described.


Key words: two-dimensional and three-dimensional problems of neutron and X-ray transport, kinetic and diffusion multiple-group approximation, SATURN code, difference schemes, paralleling algorithms.
A TECHNIQUE FOR NUMERICAL SIMULATION OF 2D FLOWS OF DISPERSE MEDIA USING LAGRANGIAN-EULERIAN 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. 31-43.

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 quasi-particles, 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 Lagrangian-Eulerian 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. 31-43.

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 arbitrarily-shaped unstructured grids. The paper considers variants of solving scalar linear algebraic systems using V-, W,- and F-cycles 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. 57-62.

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 half-height of channel. A non-uniform grid 257 129 129 concentrated near the boundary is used for simulations, which are performed using scheme CABARET without sub-grid 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 near-wall 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. 63-69.

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.
THREE-LEVEL PARALLELING IN THE TIM-2D CODE

A. A. Voropinov, S. S. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 70-77.

TIM-2D is a continuum mechanics simulation code, which uses arbitrarily-shaped unstructured polygonal Lagrangian grids. TIM-2D has three paralleling levels. The first level of paralleling in domains and the second level of paralleling in para-domains of the same domain use an MPI-based distributed-memory model. At the third level, computing cycle iterations are paralleled using an OpenMP-based shared-memory model. Within a single simulation, the paralleling levels can be used both separately and in various combinations.


Key words: TIM-2D code, unstructured grids, paralleling, mixed-memory model.
AUTOMATED SETTING OF S-MPI LIBRARY PARAMETERS

D. V. Dontsov, S. I. Sapronov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2013. No 4. P. 78-82.

MPIBoost toolkit is described, which allows automating the process of selecting optimum values of parameters for S-MPI library. MPIBoost has two operation modes: setting the cluster-specific parameters and setting the application-specific parameters.
The process of setting parameters for S-MPI library conventionally has three levels:
  1. setting the values of parameters for the most popular cluster architectures and parameters for running applications, these values are used in S-MPI library as default values;
  2. setting parameters of S-MPI library with regard to the specifics of a certain cluster, which is performed, if S-MPI library package is installed;
  3. setting parameters of S-MPI 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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