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In this paper, the structure of a shock wave in a binary gas mixture is studied on the basis of direct solution of the Boltzmann kinetic equation. The conservative projection method is used to evaluate the collision integral in the kinetic equation. The applied evaluation formulas and numerical methods are described in detail. The model of hard spheres is used as an interaction potential of molecules. Numerical simulation is performed using the developed simulation environment software, which makes it possible to study both steady and non-steady flows of gas mixtures in various flow regimes and for an arbitrary geometry of the problem. Modeling is performed on a cluster architecture. Due to the use of code parallelization technologies, a significant acceleration of computations is achieved. With a fixed accuracy controlled by the simulation parameters, the distributions of macroscopic characteristics of the mixture components through the shock wave front were obtained. Computations were conducted for various ratios of molecular masses and Mach numbers. The total accuracy of at least 1% for the local values of molecular density and temperature and 3% for the shock front width was achieved. The obtained results were compared with existing computation data. The results presented in this paper are of theoretical significance, and can serve as a test computation, since they are obtained using the exact Boltzmann equation.

The study of the development of π-periodic perturbations of a converging spherical shock wave leading to cumulation limitation is performed. The study is based on 3D hydrodynamic calculations with the Carnahan – Starling equation of state for hard sphere fluid. The method of solving the Euler equations on moving (compressing) grids allows one to trace the evolution of the converging shock wave front with high accuracy in a wide range of its radius. The compression rate of the computational grid is adapted to the motion of the shock wave front, while the motion of the boundaries of the computational domain satisfy the condition of its supersonic velocity relative to the medium. This leads to the fact that the solution is determined only by the initial data at the grid compression stage. The second order TVD scheme is used to reconstruct the vector of conservative variables at the boundaries of the computational cells in combination with the Rusanov scheme for calculating the numerical vector of flows. The choice is due to a strong tendency for the manifestation of carbuncle-type numerical instability in the calculations, which is known for other classes of flows. In the three-dimensional case of the observed force, the carbuncle effect was obtained for the first time, which is explained by the specific nature of the flow: the concavity of the shock wave front in the direction of motion, the unlimited (in the symmetric case) growth of the Mach number, and the stationarity of the front on the computational grid. The applied numerical method made it possible to study the detailed flow pattern on the scale of cumulation termination, which is impossible within the framework of the Whitham method of geometric shock wave dynamics, which was previously used to calculate converging shock waves. The study showed that the limitation of cumulation is associated with the transition from the Mach interaction of converging shock wave segments to a regular one due to the progressive increase in the ratio of the azimuthal velocity at the shock wave front to the radial velocity with a decrease in its radius. It was found that this ratio is represented as a product of a limited oscillating function of the radius and a power function of the radius with an exponent depending on the initial packing density in the hard sphere model. It is shown that increasing the packing density parameter in the hard sphere model leads to a significant increase in the pressures achieved in a shock wave with broken symmetry. For the first time in the calculation, it is shown that at the scale of cumulation termination, the flow is accompanied by the formation of high-energy vortices, which involve the substance that has undergone the greatest shock-wave compression. Influencing heat and mass transfer in the region of greatest compression, this circumstance is important for current practical applications of converging shock waves for the purpose of initiating reactions (detonation, phase transitions, controlled thermonuclear fusion).

The aim of research is to develop software system for solving gas dynamic problem in multiply connected integration domains of regular shape by high-performance computing system. Comparison of the various technologies of parallel computing has been done. The program complex is implemented using multithreaded parallel systems to organize both multi-core and massively parallel calculation. The comparison of numerical results with known model problems solutions has been done. Research of performance of different computing platforms has been done.

Статья представляет собой пример компьютерного моделирования в области инженерной механики. Численным методом находятся поля скорости в гидроциклоне, которые недоступны прямому измерению. Рассматривается численное моделирование трехмерной гидродинамики на основе k-ε RNG модели турбулентности в гидроциклоне со встроенным инжектором, содержащим 5 тангенциально направленных сопла. Показано, что направление движения инжектируемой жидкости зависит от расхода жидкости через инжектор. Расчеты показывают в соответствии с экспериментами, что зависимость сплит-параметра от расхода инжектируемой жидкости имеет немонотонный характер, связанный с отношением мощности основного потока и инжектируемой жидкости.

Mathematical simulation on unsteady natural convection in a closed porous cylindrical cavity having finite thickness heat-conducting solid walls in conditions of convective heat exchange with an environment has been carried out. A boundary-value problem of mathematical physics formulated in dimensionless variables such as stream function and temperature on the basis of Darcy–Boussinesq model has been solved by finite difference method. Effect of a porous medium permeability 10^–5≤Da<∞, ratio between a solid wall thickness and the inner radius of a cylinder 0.1≤h/L≤0.3, a thermal conductivity ratio 1≤λ_1,2≤20 and a dimensionless time on both local distributions of isolines and isotherms and integral complexes reflecting an intensity of convective flow and heat transfer has been analyzed in detail.

The article contains results of modeling a meteor entering dense atmosphere layers using Galerkin’s method and smoother particle hydrodynamics. Numerical simulations were run using experimental data gathered for the Chelyabinsk meteor while varying the meteor material characteristics and its orientation when entering the atmosphere.

In this paper, we present new parallel algorithms for finite element analysis implemented in the FEStudio software framework. We describe the programming model of finite element method, which supports parallelism on different stages of numerical simulations. Using this model, we develop parallel algorithms of numerical integration for dynamic problems and local stiffness matrices. For constructing and solving the systems of equations, we use the CUDA programming platform.

A method and a complex of computer programs are developed for the numerical simulation of the polaron states excitation process in condensed media. A numerical study of the polaron states formation in water under the action of the ultraviolet range laser irradiation is carried out. Our approach allows to reproduce the experimental data of the hydrated electrons formation. A numerical scheme is presented for the solution of the respective system of nonlinear partial differential equations. Parallel implementation is based on the MPI technique. The numerical results are given in comparison with the experimental data and theoretical estimations.

Excitation waves are a prototype of self-organized dynamic patterns in non-equilibrium systems. They develop their own intrinsic dynamics resulting in travelling waves of various forms and shapes. Prominent examples are rotating spirals and scroll waves. It is an interesting and challenging task to find ways to control their behavior by applying external signals, upon which these propagating waves react. We apply external electric fields to such waves in the excitable Belousov–Zhabotinsky (BZ) reaction. Remarkable effects include the change of wave speed, reversal of propagation direction, annihilation of counter-rotating spiral waves and reorientation of scroll wave filaments. These effects can be explained in numerical simulations, where the negatively charged inhibitor bromide plays an essential role. Electric field effects have also been investigated in biological excitable media such as the social amoebae Dictyostelium discoideum. Quite recently we have started to investigate electric field effect in the BZ reaction dissolved in an Aerosol OT water-in-oil microemulsion. A drift of complex patterns can be observed, and also the viscosity and electric conductivity change. We discuss the assumption that this system can act as a model for long range communication between neurons.

The possibility to study temperature fluctuations using URANS approach is studied. The results of numerical simulation of mixing processes for triple-jet sodium at different temperatures are presented. The processes were simulated using FlowVision software system and LMS model for turbulent heat transfer. The analysis and experiment data are compared. Validated was the possibility to determine the energy-carrying frequencies of temperature fluctuations using URANS approach and LMS model when mixing triple-jet sodium at different temperatures.