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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).

This study develops a previously proposed Method of Computer Analogy (MCA) based on formalization of digital computer operations. The paper discusses the position of the proposed approach among other well-known methods. It is emphasized that the primary objective is to derive analytical solutions, although in some cases they have to resort to semianalytical approximations. The paper focuses on constructing solutions for systems which, for certain parameter values, demonstrate the deterministic chaos behavior, namely Lorenz, Marioka – Shimitsu and R¨ossler systems. The paper also considers obtaining solution for Van der Pol equation (reduced to a nonlinear system). The aim of the study is to construct semi-analytical solutions represented as a segment of a power series in a step size of approximating difference scheme. To prevent overflow, authors formalize rank transfer operation. The authors apply a convergent difference scheme, referred to as the “guiding” scheme, to advance to the next step of the independent variable. The resulting approximation by a sum with only a few terms provides an approximation to the solution with any accuracy in accordance with the accuracy of the governing difference scheme. The senior digits in the resulting approximation exhibit probabilistic properties that can be modeled by known distributions, thereby enabling the derivation of analytical and semi-analytical approximations. The paper presents linear approximations that are the base for a complete approximations of solutions and provide important qualitative as well as some quantitative properties of solutions of considered systems. This work describes approximations of various orders, including those that do not guarantee convergence to the exact solution, but simplify the analysis of certain properties of nonlinear equations and systems. In particular, for the Van der Pol equation, authors demonstrate that its corresponding system has a cyclic solution and provide an estimate of its scale. A modification of the MCA that has features of the Monte Carlo method makes it possible to remove recurrent sequences and construct complete solutions in simple situations. The authors mention a promising approach for representing the solution using branched continued fractions.

Main theoretical considerations of dynamical changes of forest vegetation are discussed. It is shown that vegetation dynamics (succession) and soil dynamics are linked, and common dynamics is a result of biological turnover of nutrition elements. Main modelling approaches are examined and unsolved problems are formulated. An example of computer experiment on comparison of forest growth at stationary and global warming scenario is considered.

In this paper a numerical model for blood flow through a venous bifurcation with an obliterating clot is investigated. We studied propagation of perturbations of blood flow velocity and perturbations of pressure inside the vein. The model is built in acoustic (linear) approximation. Computational results reveal conditions for clot resonance oscillation, which can cause its detachment and thromboembolism.

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.

Complex geometric organization of subcellular structures such as photosynthetic or mitochondrial membranes determines mechanism of electron and proton transfer processes. We propose new approach in modeling processes, where geometric shape of membranes is accurately taken into account. Different stages of charge transfer process are simulated using different approaches, which are integrated into a combined model. We implemented this model as software which utilizes parallel computations on high-performance clusters and GPUs for better performance.

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.

This work focuses on the application of a method of construction and conversion of three-dimensional computer models for optimization of geometric parameters of simulated devices. The method is used in design of complex technical devices for control system components of an exhaust gas recirculation vehicle – electric EGR valve with magnetic and electric motor. Three-dimensional geometric computer models were created in KOMPAS-3D environment and converted to Maxwell-2D. In Maxwell-2D environment transient electromagnetic processes for further optimization of parameters of therecirculation system devicewere calculated using a criterion of reducing power loss of the automobile engine.