Issue No 2, 2005 |
SOME PARALLEL ITERATION METHODS FOR SOLUTION OF ELLIPTIC AND PARABOLIC EQUATIONS ON LOCALLY REFINING MESHES
O. Yu. Milyukova, V. F. Tishkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 3-14.
An implicit difference scheme has been built for solution of a thermal conductivity equation on locally refining meshes in a rectangular calculation area. Methods of conjugate gradients with prestipulation being the variant of incomplete Cholesky factorization or modified incomplete Cholesky factorization are used to solve a system of equations resulting from approximation of boundary problems for elliptic and parabolic equations. Parallel variants of concerned methods are suggested for task solution on parallel computers with MIMD architecture. Rate of convergence and effectiveness of the offered methods are examined using model problems calculation on moderate number of processors.
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| MEDUSA-3D METHOD FOR CALCULATION OF GAS DYNAMIC THREE-DIMENSIONAL PROBLEMS ON IRREGULAR GRIDS R. A. Barabanov, O. I. Butnev, S. G. Volkov, B. M. Zhogov, V. A. Pronin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 15-26.
With the development of computer engineering power and appearance of computation systems with large-scale parallelism a real chance to calculate gas dynamic three-dimensional problems opens during the last years. Today most of techniques developed in the mathematical department of RFNC-VNIIEF come to a new level of development — 3-D modeling of mathematical physics procedures. One of these techniques is MEDUZA. The principal characteristics of the technique are the use of irregular grid, centering of all the gas-dynamic quantities in the node, availability of a variable differential pattern for numerical integration of differential equations and possibility to change grid topology at the solution time. Contact borders are described using mixed cells calculated with concentration method.
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| CORRECTION OF A LAGRANGIAN COUNTABLE GRID USING IMPOSITION OF A DIFFERENTIABLE RELATIONS GRID ON NODES A. I. Panov, I. G. Novikov, S. S. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 27-34.
Conducting of complex gas-dynamic calculations in Lagrangian coordinates is impossible without use of special procedures respondent for maintenance of a reasonable countable grid without overlap. Countable cells correction is suggested to be carried out using imposition of a relations grid on nodes with relations assigned as inequalities with specified differentiable functions. Functions in inequalities are chosen so that impulse and impulse momentum of corresponding reaction force are equal to zero. It is shown that if imposed relations are not inconsistent such reaction forces may be found that not only provide all corresponding inequalities performance but also do not execute the work. Determination method of such forces is given in the paper.
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| ANALYSIS OF EXPERIMENTS AND CALCULATIONS ON DETERMINATION OF TURBULENT MIXING INTENSITY OF DIFFUSIVE TYPE V. E. Neuvazhaev, L E. Parshukov, L G. Pervinenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 35-46.
Analysis and comparison of the known experimental and calculation (forward computational modeling) results on examination of gravitational turbulent mixing have been conducted from united positions on the basis of semi-empirical model of turbulent mixing. The value of mixing constant α1 defining penetration intensity of a light substance towards a heavy one has been determined during analysis. Unfortunately, scattering of a 1 definition remains great. According to the majority of experimental and calculation results uncertainty of a 1 value comes to α1 = 0.02 ÷ 0.08.
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| ALGORITHM OF EXACT TRANSFER OF GAS-DYNAMIC QUANTITIES GRID DISTRIBUTION Yu. V. Yanilkin, V. Yu. Kolobyanin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 47-54.
A method for exact solution of advection equation is suggested. The method is realized in the framework of Lagrangian-Eulerian gas-dynamic technique EGAK for one-dimensional case. The results of the method testing on one-dimensional linear transport problem having an exact solution are given in the paper. Comparison with the results obtained using donor and piecewise-paraboiic methods is carried out. The suggested method is shown to have a precise solution for grid distribution of quantities in the linear case.
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| GRUNEISEN FUNCTION FOR SOLID EXPLOSIVES Yu. M. Kovalev
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 55-59.
Thermodynamic model of a molecular crystal is suggested which allows finding analytic volume dependence of Gruneisen function.
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| INVESTIGATION OF LAGRANGIAN-EULERIAN DIFFERENCE SCHEMES CONVERGENCE BY THE EXAMPLE OF “BLAST WAVES” TASK S. M. Bakhrakh, I. Yu. Bezrukova, V. F. Spiridonov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 60-64.
The work is devoted to investigation of accuracy and convergence of Lagrangian-Eulerian difference schemes by the example of “Blast Wave” task reflecting plain one-dimensional interaction of two shock waves of different intensity. Computational investigation of three Eulerian difference schemes is given in the paper. Computation has been carried out in three different statements — Eulerian (on the motionless grid), Lagrangian-Eulerian (Lagrangian points correspond to the initial position of shock wave fronts) and using concentration method. Density miscalculation values in the integral norm L1 at the end point of time t = 0.038 as well as orders of convergence are given as a results of the investigation.
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| THERMONUCLEAR BURN OF CYLINDRICAL TARGETS IN A HEAVY-ION DRIVER SYSTEM A. G. Aksenov, M. D. Churazov, D. G. Koshkarev, E. A. Zabrodina
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 65-70.
Thermonuclear burn of cylindrical targets in a powerful relativistic heavy-ion driver system is examined. Energy contribution to the target for DT-fuel comes to ≥ 100 MJ under ion energy ~ 1000 GeV. Burn estimations for perspective sorts of fuel are made.
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| VISUALIZATION OF DATA ON RADIATION-ECOLOGICAL CONTROL OF SANITARY-PROTECTION ZONES AND CONTROL AREA OF RFNC-VNIITF OBJECTS K. V. Dedkova, L. A. Maltseva, L. N. Shabanova, A. M. Shinkarev, L. V. Shinkareva, V. V. Fedorov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2005. No 2. P. 71-77.
An applied geoinformation system presented in the paper is assigned for spatial analysis of radiation pollution of a certain territory. Application GIS REC is created for the officers of radiation safety department. GIS REC serves as an implement for representation of information contained in the database and gives all functions to work with map objects. Moreover GIS REC allows plotting diagrams, mapping special points where investigations are conducted and drawing isolines on a map. Isolines distribution levels may be arbitrarily set by the program, or may be chosen by the research officer.
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