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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 3, 2010 |
APPLICATION OF THE TVD-APPROACH TO SOLVE THE THERMAL RADIATION TRANSPORT EQUATION WITH QUASIDIFFUSION METHOD
A. D. Gadzhiev, S. A. Grabovenskaya, V. V. Zavyalov, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 3-14.
A nonlinear TVD-type scheme of the second order of approximation used to solve the thermal radiation transport equation with the quasi-diffusion method is described. The numerical simulation results for some test problems are also given.
Key words: TVD-scheme, quasi-diffusion method.
| | DIAGONAL ELEMENT SINGLING-OUT SCHEMES USED TO SPEED UP ITERATIONS DURING THE THERMAL RADIATION TRANSPORT EQUATION SOLUTION IN DIFFUSION APPROXIMATIONS A. D. Gadzhiev, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 15-27.
The paper describes the numerical schemes of singling out a diagonal element used to speed up iterations during the thermal radiation transport equation solution in diffusion approximations. The principal idea of such methods can be implemented in three stages: For each computational grid cell, the energy equation is solved first and then the diagonal element singling-out schemes are used to find the temperature value via the density of radiation. The temperature value is used to calculate the Planck function value. The new values of density and radiation flux are found with the sweep method using the known right-hand part of equation.
Key words: acceleration of iterations, thermal radiation transport.
| | DSn-SCHEME OF CHARACTERISTIC TUBES FOR THE TRANSPORT EQUATION IN CYLINDRICAL COORDINATES A. I. Bochkov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 28-37.
A characteristic scheme has been developed to solve the transport equation written in cylindrical coordinates. The scheme includes two stages. In the first stage an ordinary differential particle balance equation is built in a computational grid cell and used to find the total flux of particles on the non-exposed surface of the cell. In the second stage of the DSn-type scheme the outgoing particle flux is distributed over the non-exposed cell`s faces.
Key words: transport equation, difference scheme, DSn-method, DSn-scheme of characteristic tubes.
| | SPECIFIC FEATURES OF THE DETONATION COMPUTATIONS WITH THE DICTATED WAVE FRONT VELOCITY USING EULERIAN GRIDS Yu. A. Bondarenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 38-45.
The paper analyzes results of 1D hydrodynamic computations of the normal detonation using Eulerian grids. A significant effect of a slightly violated (sim1%) conservation of the total energy on the detonation computation accuracy is shown. A self-similar solution with regard to the negative total energy disbalance with the given velocity of the energy release front has been built. There is a good agreement between the results of computations with non-conservative schemes and the self-similar solution features. It has been shown that with the higher accuracy methods used to recalculate the hydrodynamic quantity values from a Lagrangian grid to the Eulerian one a significantly reduced amount of calculations with the accuracy preserved is possible.
Key words: gas dynamics in Eulerian variables, detonation, numerical methods, self-similar solutions, test problems, conservativeness, computation accuracy, nonconservation of total energy.
| | 2D SCALAR ARTIFICIAL VISCOSITY OF EGAK TECHNIQUE IN SPHERICAL SYSTEMS Yu. V. Yanilkin, O. O. Toporova
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 46-54.
The paper considers the problem of a spherically converging shell with a light gas inside it. It is shown that the artificial viscosity type is of a great importance for the numerical solution of this problem. The classic von Neumann-Richtmyer viscosity may give a large error on spherical grids, because it does not take into account the uniform material compression under the spherical convergence conditions. Application of the viscosity earlier proposed by the authors allowed a significant reduction of the error.
Key words: gas dynamics, artificial viscosity, 2D flows, difference scheme.
| | KINETICS OF THE EXPLOSIVE TRANSFORMATION INITIATION OWING TO FRICTION UNDER LOW-VELOCITY IMPACTS WITHIN D TECHNIQUE | M. E. Martynova | , | | , | Yu. D. Chernyshev |
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 55-64.
One of the possible explosive transformation initiation mechanisms under low-velocity impacts is considered. It is based on the surface explosive heating caused by rubbing against the surrounding materials.
The implementation of kinetics equations within D technique is presented. The algorithm of accounting for the forces of friction occurring on the interfaces during the interaction of an explosive with the surrounding materials is described. The paper gives results of the numerical simulation with the described kinetics for experiments of the Stiven Test type.
Key words: D technique, low-velocity impacts, Stiven Test, friction coefficient, initiation of explosive transformations.
| | VERIFICATION OF THE COMPUTATIONAL MODEL OF THE IMPURITY TRANSPORT WITH CONVECTION BY THE EXAMPLE OF CRYSTALLIZATION OF TWO-MATERIAL Pb-Sn MELTS S. M. Ganina, V. P. Ginkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 65-72.
A computational algorithm has been developed for the impurity segregation during crystallization of two-material melts characterized by large-size two-phase areas. The calculation of convection in a porous medium takes into account an additional resistance to flow similar to Darcy law. The liquidus point linearly depends on the concentration of impurity in a liquid phase.
The proposed model has been implemented in GIGAN-2D program complex. Two benchmarks have been run to verify the model: one of them simulated the crystallization of Sn with 10% Pb concentration and another simulated the melting process of Pb with 18% Sn concentration.
Key words: promising materials, intermetallides, directed crystallization, melting, two-phase transient area, benchmark, segregation, mathematical modeling, impurity transport with convection, moving interfaces, computational algorithm.
| | AN UPDATED MANY-PARTICLE POTENTIAL ALGORITHM FOR THE MD SIMULATION USING GRAPHIC ARITHMETIC ACCELERATOR S. V. Kopkin, I. A. Kryuchkov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 3. P. 73-82.
The paper describes main stages of adapting the algorithm of calculating the values of MEAM potential in MD complex to a hybrid computer system. The information about the speedup gained with a varying number of computing devices is presented. Test computations have been carried out and confirm the validity of results.
Key words: arithmetic accelerator, molecular dynamics, potential, MEAM, speedup, hybrid computer system.
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