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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2004  THE ADAPTIVE METHOD FOR SOLVING A MULTIDIMENSIONAL TRANSPORT EQUATION USING REFINED GRIDS IN PHASE SPACE
R. M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 315.
The paper offers the approach to multidimensional transport equation approximation with introduction of adaptive builtin refined grids in phase space. The adaptive method is formulated for the general case of using arbitrary nonorthogonal spatial grids. In 2D problems, the grids in use are either regular nonorthogonal quadrangular, or irregular grids of convex polygons. The mathematical principles of the adaptive method for refined grids have been formulated. Since the problem of approximating the transport equation in phase space using refined grids in angular variables is the most hard to solve, the detailed description of the development of algorithms and difference equations of the adaptive method for such the case is given.
 NUMERICAL SOLVING THE 2D TRANSPORT EQUATION BY USING THE ADAPTIVEBYSPACE METHOD OF FRACTIONAL GRIDS R. M. Shagaliev, A. V. Alekseev, I. M. Belyakov, A. V. Gichuk, V. V. Evdokimov, A. N. Moskvin, A. A. Nuzhdin, N. P. Pleteneva, T. V. Shemyakina VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 1626.
The adaptivebyspacevariables algorithm of grid fractioning, used at numerical solving 2D transport equation, is described in the paper. The results of numerical research of this method, conducted on the example of radiation spread problem computation, are presented. The results obtained by using the adaptive methods, were compared to those, obtained by using standard scheme without adaptivity. For both computations the computation time was determined. The computation time gain, comparing to the standard method, at obtaining approximately the same accuracy of the result, was taken as the adaptive method efficiency criterion.
 METHOD OF HEATCONDUCTIVITY EQUATION SOLVING ON A NONREGULAR GRID A. I. Panov VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 2740.
The method of building parametrized set of heatconductivity equation difference schemes on a nonregular grid is stated. Difference operators preserve symmetry and positive definiteness  the properties typical for the initial differential operator. The issue of precision of the obtained schemes is surveyed.
 THE LEGAK3D COMPUTATION METHOD FOR 3D NONSTATIONARY FLOWS OF MULTICOMPONENT CONTINUUM AND PRINCIPLES OF ITS REALIZATION ON MULTIPROCESSOR COMPUTERS WITH DISTRIBUTED MEMORY S. M. Bakhrakh, S. V. Velichko, V. F. Spiridonov, P. A. Avdeev, M. V. Artamonov, E. A. Bakulina, I. Yu. Bezrukova, V. V. Borlyaev, N. A. Volodina, A. O. Naumov, N. E. Ogneva, T. V. Rezvova, A. A. Rezyapov, S. V. Starodubov, I. Yu. Taraday, A. P. Tikhonova, K. V. Tsiberev, A. A. Shanin, M. O. Shirshova, E. V. Shuvalova VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 4150.
The principles of LEGAK finitedifference LagrangianEulerian method for computing nonstationary flows of multicomponent continuum in the 3D geometry are surveyed. Application of concentrations for computing multicomponent continuum is the peculiarity of the method. The principles of organizing the program complex, that realizes the presented method on multiprocessor computers with distributed memory, are also presented.
 ORDER OF APPROXIMATION, ORDER OF NUMERICAL CONVERGENCE AND OF MULTIDIMENSIONAL GASDYNAMICS COMPUTATION EFFICIENCY IN EULERIAN VARIABLES ON THE EXAMPLE OF "BLAST WAVES" PROBLEM CONVERGENCE COMPUTATION Yu. A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 5161.
Computations for convergence of the well known 1D test problem "Blast Waves" over several gasdynamics difference schemes with different orders of convective item approximation are presented in the paper. It has been established that the order of numerical convergence does not exceed unit, including the Lagrangian case; as for the practically interesting range of grid points the order of Eulerian method convergence is threefold less than the order of approximation. The example of wrong convergence in the nonconservative case is given. Estimations, that connect the computation expenses (number of calculations) with the required error and difference scheme quality parameters, were obtained by means of 1D computation results extrapolation on 2D and 3D cases. The following conclusions were drawn: (1) difference schemes of Eulerian gasdynamics with the first order of convective terms approximation should be abandoned; (2) it is reasonable to pass over to difference schemes with higher orders of approximation depending on the required grade of results accuracy. The crosstype difference scheme with artificial antidispersion with the phase error of the fourth infinitesimal order is briefly described for the 1D Lagrangian gasdynamics.
 METHOD OF COMPUTING 2D NONSTATIONARY ELASTO PLASTIC FLOWS ON NONREGULAR POLYGONAL LAGRANGIAN GRIDS S. S. Sokolov VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 6280.
The Lagrangian method of computing 2D nonstationary elastoplastic problems on nonregular polygonal Lagrangian grids is surveyed. The method is based on the DMK Lagrangian gasdynamics method; a nonregular computational grid, consisting of convex polygons with arbitrary numbers of vertexes remaining convex in the course of the computation, is applied. For equation approximation the explicit finitedifference scheme is used. The method was realized in the DMK program complex for solving problems of continuum mechanics with big deformations in intricategeometry regions.
 NONREGULAR GRID DECOMPOSITION ALGORITHM WITH CONSIDERATION OF THE COMPUTATION LOAD O. I. Butnev, V. A. Pronin VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 8187.
Two algorithms of nonregular grid geometrical decomposition over processors for the 2D case (decomposition into stripes and cells) are proposed in the paper; the technique of computation load balancing during the computation on the problem view writingreading stage is also presented. The algorithms were tested in the frames of the program complex, realizing the MEDUZA freeLagrangian method. They can be successfully applied for other methods, using both structured and nonstructured grids.
 APPLICATION OF THE KORSAR AND RELAP CODES FOR NUMERICAL ANALYSIS OF REACTOR EXPERIMENTS "PETTY LEAKAGE" V. M. Makhin, I. I. Semidotskyi VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 8893.
The results of numerical research of modes of testing the seven and nineteenelement fuel element MIR reactor on the loop facility PVP2 by using the KORSAR/V1.008.000 and RELAP 5/MOD3.2 codes. Fuel elements were tested in the mode, simulating final stages of accidents on WWER with loss of heat carriers and fuel element upper part dehydration (petty leakage). The code conservatism for numerical analysis of examined modes was estimated.
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