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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 34, 2007  ROME NUMERICAL METHOD TO SOLVE 3D HEAT CONDUCTION EQUATION IN CURVILINEAR COORDINATE SYSTEM
V. N. Pisarev, S. V. Chernova VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 314.
Described here is the numerical solution algorithm of 3D heat conduction problem in curvilinear coordinate system. The heat conduction equation is approximated on structured grids with sheet structure. The finitedifference scheme is based on the implicit finitevolume method ROMB and it is the generalization of method to solve 2D heat conduction equation in the axisymmetric case. The iterative method with stabilizing correction reducing the 3D difference problem to the set of ID problems solved by the direction sweep is used to solve the system of difference equations. The numerical results are given.
 NUMERICAL TECHNIQUE FOR SPECTRAL TRANSFER CALCULATION OF XRADIATION AND LASER ABSORPTION IN SECTOR APPROXIMATION IN BOXCONVERTER OF XRAY TARGET (SNDLIRA CODE) S. V. Bondarenko, G. V. Dolgoleva, E. A. Novikova VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 1526.
Numerical technique SNDLIRA based on the sector approximation in continuous way in 3D formulation allows calculation of laser radiation propagation and absorption with multiple reflection from the internal face of the box, as well as generation and Xradiation transfer with spectrality and medium nonequilibrium.
 THE TUR COMPLEX FOR CONSTRUCTION AND INVESTIGATION OF EQUATIONS OF STATE A. T. Sapozhnikov, E. E. Mironova VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 2736.
Described here are the structure and functionalities of the TUR program complex meant for construction and investigation of equations of state. The complex includes programs which implement theoretical models of thermodynamic properties, programs for problem solving resulting from construction and investigation of equation of state properties, libraries of equation of state modules and set of constants. Briefed here are the algorithms implemented in the complex programs.
 INTEGRATED INFORMATION AND TECHNOLOGICAL ENVIRONMENT FOR DEVELOPMENT OF EQUATIONS OF STATE O. V. Verbitskaya, O. V. Kuznetsova, E. E. Mironova, A. T. Sapozhikov, V. P. Sokolov VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 3745.
Described here is interface shell of the TUR complex representing the dedicated integrated information and technological environment (ITE) — the working place of equations of state developers. The implemented here are different dedicated databases used for storage organization of calculation results, experimental data and reference information. The archive of EOS forms and constant set are the basis of the system. Two experimental data bases are developed within the limits of ITE and contain the information about shock wave compression and adiabatic expansion of condensed matters. The availability of information and technological environment of the TUR complex allowed considerable acceleration of the process of EOS investigation and development, as well as increase of their accuracy.
 THE EXACT SOLUTION OF CAUCHY PROBLEM FOR SMALL TRANSVERSE OSCILLATIONS IN ELECTRON NONRELATIVISTIC PLASMA A. L Golubev, V. A. Terekliin, E. V. Uvarov VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 4654.
The exact solution of Cauchy problem for small transverse oscillations in electron nonrelativistic plasma with step undisturbed electron distribution velocity function has been obtained. Given here are explicit time dependences of electric and magnetic field amplitudes for stable and unstable oscillations. The description of the smoothing method of step distribution is given, which does not result in significant change of dispersive properties of plasma. The derived solution can be used as a test for the procedures of numerical simulation of collisionless plasma behavior.
 FORMAT FOR DESCRIPTION OF NONREGULAR POLYHEDRAL GRID IN THE TIM TECHNIQUE A. A. Voropinov, S. S. Sokolov, A. I. Panov, I. G. Novikov VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 5563.
The TIM technique solves timedependent 3D continuum mechanics problems using arbitrarily structured nonregular polyhedral Lagrangian grids. The authors faced the problem of the format implementation to describe the grid structure at developing the technique foundation. The storage format should be economical enough, that is it requires the minimum main memory capacity and satisfies the implementation of the counting algorithms of the technique. Three universal formats have been investigated, and “boundbybound” storage structure has been chosen for the TIM technique: bound list is stored for the cell, a pair of cells and node list are stored for the bound, the number of one of the bounds is stored for the node.
 NONREFLECTING BOUNDARY CONDITION FOR SMALL PERTURBATIONS IN GASDYNAMIC SCHEMES ON SPACED GRIDS Yu. A. Bondarenko, E. A. Goncharov, V. Yu. Kolobyanin, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 6474.
Described here is nonreflecting boundary condition for gasdynamic problems using Lagrange and LagrangeEuler counting grids. This condition is realized for twodimensional (2D) gasdynamic EGAK technique. 2D test problem has been stated for which the numerical simulation has been performed using the suggested nonreflecting boundary condition. The calculation results in ID and 2D approximation show high efficiency and accuracy of the suggested technique. The algorithms of nonreflecting boundary condition are quite general and can be used in other techniques using velocity representation in counting grid nodes, and density and energy representation — in grid centers.
 APPLICATION OF OpenMP INTERFACE FOR TIM PARALLELIZATION A. A. Voropinov, L G. Novikov, S. S. Sokolov VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 34. P. 7482.
The computational technique TIM is to solve timedependent multidimensional continuum mechanics problems using arbitrarily structured Lagrangian grids. This technique allows computations for 2D problems (TIM2D) in cylindrical and Cartesian coordinates and 3D problems (TIM3D) in Cartesian coordinates. To reduce runtimes, TIM implements parallelization in the shared memory model using OpenMP interface. The parallelization is performed by OpenMP parallelization directives added to each loop, which iterations may be independent of each other. The computational modules for gas dynamics, elasticityplasticity, magnetic hydrodynamics, twoflow and twotemperature behavior, and maintenance of grid, as well as a number of support procedures have been parallelized. Each loop has been parallelized independently. In some cases we had to revise algorithms used for sequential computations. The parallelization has been implemented for the computational modules requiring 99 % of the total runtime during the sequential computations. The algorithms implemented in the code have been verified for a number of tests, methodical and production runs. The efficiency of computations on 8 processors is 85 % on average.
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