Issue 1/2009

ABSTRACTS:

UDK 519.6:533.7:536.46
SPECIFIC FEATURES OF SOLUTIONS DURING SIMULATION OF NORMAL DETONATION WITH THE INDUCED ENERGY  RELEASE FRONT MOVING WITH THE GIVEN VELOCITY / Yu. A. Bondarenko // P. 3

The paper considers a popular computational method for normal Chapman-Jouguet detonation using the induced front of instant energy release moving with the given mass velocity σ = D_Jouguetρ_initial . Results of computations for convergence using various difference schemes of the second approximation order are described. If artificial viscosity is used for compression only, the numerical solution on a very fine grid changes over from the Chapman-Jouguet type solution to the abnormal self-similar solution with forward compression shock wave and rarefaction shock at the point of induced energy release. Such changeover to the abnormal self-similar solution is not observed with a rather high artificial viscosity during rarefaction, or with no artificial viscosity (even during compression). These facts can be attributed to the specific features of admissibility conditions of rarefaction shocks occurring on the wave front of induced energy release. The abnormal limit solution occurs with the governing role of the scheme variance during rarefaction.
Key words: normal detonation, moving energy release, self-similar solution, rarefaction shock, admissible shocks, viscosity, variance.

UDK 519.6
SPH METHOD OF SMOOTHED PARTICLES FOR GAS DYNAMICS PROBLEMS WITH SPHERICAL AND CYLINDRICAL SYMMETRIES / A. D. Zubov, A. M. Lebedev // P. 19

The paper describes new SPH-approximation formulas for 1D problems with spherical and cylindrical symmetries. Calculations were carried out to find numerically the order of convergence for the SPH method basing on solutions to the "Blast Waves" problem by Woodward–Colella. It has been shown that the SPH method has the first order of accuracy for non-smooth solutions. The paper presents results of model gas dynamic calculations for Riemann problem with spherical symmetry, the problem of point explosion, the self-similar problem of a converging shock wave (for adiabatic and homothermal gases), and Noch problem.
Key words: Key words: gridless methods, SPH method of smoothed particles, computational gas dynamics.

UDK 532.517.4+519.63
ON THE INITIAL INTENSITY OF TURBULENCE AND GROWTH OF TURBULENT MIXING AREA UNDER RICHTMYER-MESHKOV INSTABILITY / A. N. Razin // P. 29

Three model experiments with VIKHR code were carried out to simulate numerically the process of turbulent mixing on gas-gas interfaces. An analytical model was used to study the instability growth, the model by V. V. Nikiforov was used for turbulent mixing simulations. The numerical experiments were carried out with varying the initial intensity of turbulence and dissipation rate.
Key words: turbulent mixing, simulation experiment, turbulence initialization.

UDK 536.715
A METHOD OF CONSTRUCTING WIDE-RANGE  THERMODYNAMICALLY CONSISTENT EQUATIONS OF STATE BASED ON LOCAL EQUATIONS USING THE MIXTURE MODEL / L. F. Gudarenko, V. G. Kudelkin // P. 44

The paper describes a method of constructing thermodynamically consistent global equations of state (EOSes) based on merging local EOSes with the use of one of the mixture models. The merging area's material is a mixture of two materials, which thermodynamic functions are calculated using EOSes valid for the neighboring areas. Thus, no reconstruction of the merged EOSes is required, the original EOSes are only supplemented with the algorithm and program for thermodynamic functions calculation in the transition area. Values of concentrations are selected basing on the requirement of smooth behavior of thermodynamic functions and their derivatives and with regard to physical conditions. The expression describing the mixture's free energy is chosen for an original expression to obtain analytical expressions. To meet the requirement of thermodynamic consistency, expressions for pressure and energy are calculated with regard to concentration as a function of density and temperature.
Key words: wide-range equation of state, mixture model, thermodynamic functions, aluminum.

UDK 519.6
A MECHANISM OF ADAPTIVELY SELECTING A SOLVER IN PMLP/PARSOL LIBRARY / V. A. Erzunov, A. A. Gorbunov // P. 55

The paper describes a mechanism of adaptively selecting a solver from PMLP/Parsol library and presents results of numerical experiments on parallel computations using MEDUZA technique intended for computational physics problems on irregular grids. The described mechanism allows automatically selecting an optimum solver for any phase of computations.
The adaptive mechanism of selecting solvers allows a significant gain in the program runtime.
Key words: solver library, preconditioner, MEDUZA technique, solution of heat conduction equation.

UDK 552.52, 624.131.54
MODELING OF MASS TRANSPORT FOR WASTE DISPOSED IN UNDERGROUND STORAGE FACILITIES / E. M. Khramchenkov, M. G. Khramchenkov // P. 63

The paper describes mathematical models of mass transport processes during injection of contaminated solution to an aquifer with an underlying low-permeability clayey layer (confining bed), as well as during pumping tests in the aquifer with regard to water loss from the underlying clayey layer. The stated problem novelty is in consideration of the nonlinear impact of contamination on the protective capabilities of swelling clay layer underlying the aquifer. The models offered in the paper allow calculating the impact of some factors, such as the aquifer operation time during its late phase, entry of materials preserved in the clay thickness to the aquifer, and penetration of contaminants through the confining clayey layer.
Key words: swelling clay, aquifer, contaminant, migration, underground storage.

UDK 621.039.5
VARIATIONS OF THE EUROPIUM ISOTOPE CONCENTRATION IN ABSORBER DURING LONG-TERM IRRADIATION OF THE ABSORBER MEMBERS IN NUCLEAR REACTOR / Yu. E. Vaneyev, E. P. Klochkov // P. 79

The paper describes an algorithm for simulation of the isotope kinetics of Eu absorber under long-term irradiation in reactor of the Eu-based absorber members. Regularities of variations in the absorbers isotope concentrations were studied numerically using the precision code MCU-RR. The paper presents the distribution in space of concentrations and reactivity values of Eu isotopes among the absorber members in compensating devices of the SM research reactor in comparison with the available data of experiments.
Key words: algorithm of simulation, isotope kinetics, Eu absorber, irradiation in reactor, numerical study, radial and vertical distributions, simulation results, experimental data.