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RUSSIAN FEDERAL NUCLEAR CENTER 
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Issue N^{o} 3, 2006  APRIORY ESTIMATION OF FLOW BEHAVIOR IN THE AREA OF CENTERED RAREFACTION WAVE REFLECTED FROM INTERFACE
D. N. Bokov VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 317.
The paper presents calculations of the interaction of a rarefaction wave with a rigid wall and with a contact discontinuity. It considers problems, which have analytical solutions. Relative errors of the calculated solutions are provided. The accuracy of calculation of the rarefaction wave interaction with a contact discontinuity is of great importance because errors in the calculated flow parameters on the contact discontinuity become perturbations in the flow parameters of the transmitted and reflected waves and are transferred both upstream and downstream. The case where EOS parameters on the left and on the right sides of the discontinuity are identical is well studied and described in the literature. It is taken as a test. For the case of different parameters on the left and on the right sides of the discontinuity point we formulate criteria for changing the type of the reflected wave.
 A TECHNIQUE FOR SOLVING PHASE TRANSITION KINETICS EQUATIONS V. A. Bychenkov, N. S. Zhilyaeva, G. V. Kovalenko, I. I. Kuznetsova, A. V. Petrovtsev, A. T. Sapozhnikov, N. D. Strinadkina, L. V. Khardina VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 1827.
Phase transition kinetics simulations are carried out on the assumption that mixture components are in mechanical and temperature equilibrium. A material under strain may undergo several phase transitions at once. Thermodynamic parameters of the mixture components are determined based on the solution of linearized equations for the components’ pressure and temperature increments with the mixture’s known specific volume and energy increments. An efficient algorithm for solving these equations based on the explicit Lagrange difference scheme accounting for the pressure and temperature difference is proposed. The technique has been implemented in the 2D SPRUT code. The paper presents the results of ID and 2D test calculations with the () transition in iron and without such transition.
 INCh TECHNIQUE Rinat M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 2836.
The INChM technique is described. The technique is realized in the software complex, destined for computation of 2D gas dynamic and elastoplastic flows of multicomponent environments with big deformations. The technique difference scheme is explicit, conservative by mass, energy and impulse, it has the secondorder approximation over time and space at symmetrical positioning of particles relative to the Eulerian computational grid nodes. The results of the technique numerical study, performed on the example of a number of computations of solid target punching by penetrating elements, are presented. The computation results are compared with experimental data as well as with the results of some analogous computations performed under the OTI*HULL code.
 USING THE HESSIAN RECONSTRUCTION TECHNIQUE WHEN BUILDING ADAPTIVE GRIDS Yu. V. Vasilevsky, K. N. Lipnikov VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 3753.
Three problem classes occurring when building anisotropic adaptive grids are considered. The tielink of these problems is the reconstructed Hessian of grid function. Using the discrete Hessian allows: a) building grids which optimal in the terms of minimization of some error norm, b) managing the grid adaptation process to build grids with predetermined properties; c) building piecewise quadratic recoveries of triangulated piecewise linear surfaces. The main properties of the proposed methods are illustrated by numerical examples.
 SOLVING EQUATIONS OF RADIOACTIVE DECAY D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 5458.
An algorithm allowing building a stable solution procedure, including analytical solution, for the equations describing the change of matter isotopic composition in time, at minimal computational expenses is described. The algorithm has two steps: at the first step an object called a decay tensor, which depends on only the used isotopes and the decay parameters, is built; at the second step the solution of a certain problem is built using the given tensor.
 APPROXIMATION TO INTEGRALS WITH VARYING LIMITS AND ITS APPLICATION TO CALCULATE THE THIRDORDER DEBYE FUNCTIONS V. G. Eliseyev, G. M. Eliseyev VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 5965.
The paper offers the approximation algorithm for functions, which are a product of the two multiplier factors: an integral with varying limits and another, more simple function. The case with one varying limit (the upper limit) is considered for the sake of simplicity. It is easy to built approximation to the integral factor only. Then, one can calculate the original function derivatives to the same accuracy using the product differentiation formulas. To build the required approximation, we suggest using local Hermitian interpolation, on average, polynomial splines of the fourth order, which are constructed basing on the reference tables of histogram and the first two derivatives of the integral factor. Maple software was used to obtain all the required formulas for the given spline construction. A fiveplace spline approximation to the thirdorder Debye function has been constructed for an example. Fortran program texts for calculation of the Debye function values are presented.
 INITIAL DATA CALCULATIONS FOR 3D PROBLEMS USING THE 3DRND CODE V. L Tarasov, S. V. Rebrov, A. V. Volgin, A. L. Potekhin, P. V. Cherenkov, E. V. Potekhina, V. I. Budnikov, A. V. Marunin, N. S. Averina VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 3. P. 6671.
The paper describes the features of the 3DRND code, which enables interactive calculations of initial data for 3D computational physics problems. Its highly universal user interface reduces the time of data input when the same problem is calculated by different codes. The 3DRND code enables calculating initial data in two modes  scalar and parallel, on multiprocessor computers. The code provides for the use of regular (rectangular, spherical, cylindrical) and irregular tetrahedral grids.
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