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Since 1978
Published in Sarov (Arzamas-16), Nizhegorodskaya oblast |
RUSSIAN FEDERAL
NUCLEAR CENTER -
ALL-RUSSIAN RESEARCH INSTITUTE
OF EXPERIMENTAL PHYSICS |
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 Русский |  English
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Issue No 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. 3-15.
The paper offers the approach to multidimensional transport equation approximation with introduction of adaptive built-in refined grids in phase space. The adaptive method is formulated for the general case of using arbitrary non-orthogonal spatial grids. In 2D problems, the grids in use are either regular non-orthogonal 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 ADAPTIVE-BY-SPACE 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. 16-26.
The adaptive-by-space-variables 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 HEAT-CONDUCTIVITY EQUATION SOLVING ON A NON-REGULAR GRID A. I. Panov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 27-40.
The method of building parametrized set of heat-conductivity equation difference schemes on a non-regular 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 LEGAK-3D COMPUTATION METHOD FOR 3D NONSTATIONARY FLOWS OF MULTI-COMPONENT CONTINUUM AND PRINCIPLES OF ITS REALIZATION ON MULTI-PROCESSOR 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. 41-50.
The principles of LEGAK finite-difference Lagrangian-Eulerian method for computing non-stationary flows of multi-component continuum in the 3D geometry are surveyed. Application of concentrations for computing multi-component continuum is the peculiarity of the method. The principles of organizing the program complex, that realizes the presented method on multi-processor computers with distributed memory, are also presented.
| | ORDER OF APPROXIMATION, ORDER OF NUMERICAL CONVERGENCE AND OF MULTIDIMENSIONAL GAS-DYNAMICS 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. 51-61.
Computations for convergence of the well known 1D test problem "Blast Waves" over several gas-dynamics 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 three-fold less than the order of approximation. The example of wrong convergence in the non-conservative 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 gas-dynamics 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 cross-type difference scheme with artificial anti-dispersion with the phase error of the fourth infinitesimal order is briefly described for the 1D Lagrangian gas-dynamics.
| | METHOD OF COMPUTING 2D NON-STATIONARY ELASTO PLASTIC FLOWS ON NON-REGULAR POLYGONAL LAGRANGIAN GRIDS S. S. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2004. No 4. P. 62-80.
The Lagrangian method of computing 2D non-stationary elasto-plastic problems on non-regular polygonal Lagrangian grids is surveyed. The method is based on the DMK Lagrangian gas-dynamics method; a non-regular 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 finite-difference scheme is used. The method was realized in the DMK program complex for solving problems of continuum mechanics with big deformations in intricate-geometry regions.
| | NON-REGULAR 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. 81-87.
Two algorithms of non-regular 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 writing-reading stage is also presented. The algorithms were tested in the frames of the program complex, realizing the MEDUZA free-Lagrangian method. They can be successfully applied for other methods, using both structured and non-structured 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. 88-93.
The results of numerical research of modes of testing the seven- and nineteen-element fuel element MIR reactor on the loop facility PVP-2 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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