Abstract The flow in a four-stage axial compressor is investigated by numerical modeling using the Numeca FINE/Turbo software. A few approaches to modeling the rotor-stator interaction are considered: the steady statement with the use of the Mixing Plane boundary condition, the fully unsteady statement (URANS), and the non-linear harmonic (NLH) method. These approaches are compared by considering the

Abstract The methodology of turbulent combustion simulation is presented. The methodology is based on large eddy simulation coupled with a global reaction. The numerical simulation of a flow in a laboratory combustion chamber is performed. The effect of the constants of the model’s rate of chemical reactions on the results of the calculations is analyzed. It is shown that the methodology ensures close

Abstract— The problem of actively shielding a conversation inside a room with an open window from street noise is considered as an example of a more general problem actively shielding a specified domain in real-time from external noise. Active shielding is understood as protection based on additional sound sources installed on the boundary of the domain. These sources are supplemented by measuring

Abstract The Reynolds-averaged Navier–Stokes (RANS)/Implicit Large Eddy Simulation (ILES) method is applied to analyze the effect of variable heat capacity on the flow characteristics and pressure pulsation spectra for various operation modes of a model high-speed air intake. The dependence of the heat capacity on temperature is described by a fourth-degree polynomial. The calculation method and the

Abstract The paper is devoted to the RANS/ILES high-resolution method application for studying the influence of a nonuniformity of the inflow temperature field on the throttle characteristics of a supersonic mixed compression inlet, and the intensity and spectral characteristics of pressure pulsations in the inlet duct. Five cases of inflow parameters are investigated, three of which have a nonuniform

Abstract The paper presents two computational techniques that do not require a change in the topology of the mesh to simulate the flow around oscillating bodies. The first technique uses the immersed boundary method, the second technique uses the method of deformed meshes. The capabilities of these two approaches are demonstrated by solving model problems in a two-dimensional formulation for simulating

Abstract Dual-stream nozzle jet computations conducted using different numerical algorithms developed at Zhukovsky Central Aerohydrodynamic Institute (TsAGI) and Keldysh Institute of Applied Mathematics, Russian Academy of Sciences (KIAM RAS) are presented. The scale-resolving approaches of the DES family based on higher accuracy numerical methods are applied. The flow considered is studied experimentally

Abstract Various methods for the accurate approximation of the gradients entering the diffusion fluxes are considered. Linear combinations of the 2nd order difference schemes for a non-uniform mesh that transform into 4th order schemes in the uniform case are investigated. We also consider 3rd and 4th order schemes for approximating gradients on a non-uniform mesh in the normal and tangential directions

Abstract The features of a flow generated during the injection of a supersonic small body (pellet) from the channel of a spherically blunted cylinder into a supersonic flow are studied. The cylinder’s diameter is 35 times larger than the diameter of the injected body. The numerical simulation is carried out using multilevel Cartesian grids with the local adaptation based on the wavelet analysis. The

Abstract— This paper considers modeling the processes of cleaning air from finely dispersed solid contaminants clustered in the form of nanoparticles. The purification technology chosen for the study involves the use of a system consisting of nanofilters and sorbents. Both cleaning methods used in it are currently in high demand and are often combined in appropriate devices. The first cleaning method

Abstract We describe contrast structures (CSs) arising from the simulation of reaction–diffusion (RD) processes in inhomogeneous media with the power dependence of the source density on the concentration in the vicinity of the roots. The results obtained earlier for homogeneous media are generalized to the case of inhomogeneous media. Sufficient conditions for the existence of a solution of the type

Abstract To compute controlled fusion problems, four nuclear reactions are conventionally used. In the paper, cross sections of many thermonuclear reactions between the lightest elements are compared. We show that, along with the traditional four reactions, a tangible contribution can be made by the reaction \({\text{T}} + {\text{T}} \to 2n + \,{}^{{\text{4}}}{\text{He}}\). At low temperatures, the

Abstract This work studies a stochastic method for the generation of artificial three-dimensional, divergence-free, homogeneous, and isotropic velocity fields. The technique is based on the randomized spectral method. The statistical and spectral properties of turbulent fields constructed by this generator are analyzed. A validation LES-based computation which uses the obtained turbulent fields as

Abstract The results of the direct numerical simulation of a supersonic flow around a cylindrical blunt body with tail expansion are presented. The data obtained are compared with the results of laboratory experiments for the Mach numbers 3 and 4 and the angles of attack of 10 and 20 degrees. The results are obtained by using the quasi-gas-dynamic (QGD) equations.

Abstract The paper is devoted to the development and implementation of a hybrid stochastic fractal-based approach for modeling electron-induced kinetics of polarization switching in ferroelectrics as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes the initial value problem for the fractional order differential equation. Computational schemes for solving

Abstract This study considers discontinuous Galerkin schemes with a Legendre polynomial basis of degree K = 0, …, 5. The schemes built for the convection equation are studied in terms of the amplitude and dispersion error. The relation between wave number and cell size is determined to provide the desired accuracy of the solution in the task with a harmonic wave. The computations for an acoustic wave

Abstract The paper considers bicompact schemes for HOLO algorithms to solve the transport equation. To accelerate the convergence of scattering iterations not only the solution of the transfer equation with respect to the distribution function of a high order (HO) is used but also the quasi-diffusion equation of a low order (LO). For both systems of kinetic equations semidiscrete bicompact schemes

Abstract Active users have appeared who require the solution of inverse problems on a graph with conditions of uncertainty for modeling processes in the economic sphere. Such tasks were not considered by mathematicians earlier. This article provides an analogy with mathematical models which are described by a replicator system (RS) of equations related to the stated theme. The exact and asymptotic

Abstract A new class of models of hysteretic converters, generalizing the classical backlash definition to the case where the curves defining it are non-deterministic and have a random distribution, is proposed. In this case, the output of the stochastic converter is defined as a random process. The correctness of the definition of the corresponding converter in terms of a special limit construction

Abstract The software for the topological optimization of parts with different constraints of the objective function, as well as for the generation and use of different types of lattice structures for filling the parts, is developed within the project Development of the Atlas of Standard Forms for Topological Optimization of Structures Formed by Selective Laser Melting and Their Production Verification

Abstract Using the support operator technique for two-dimensional problems of the elasticity theory we constructed integrally consistent approximations of the components of the strain tensor and the elastic energy of the medium for the equations of the elasticity theory in terms of displacements. Approximations are constructed for the case of irregular difference grids in the R–Z plane of a cylindrical

Abstract Differential relations include both differential operators and solvers for boundary value problems. The formulas of compact finite difference approximations for first- and second-order differential relations of the form \({{P}_{1}}[u] = {{P}_{2}}[f]\) are obtained. An approximation on three-point stencils is used. Its implementation, as in the case of classical difference schemes, requires

Abstract The paper is devoted to a description of the DiMP-Hydro software package being developed at the Keldysh Institute of Applied Mathematics (Russian Academy of Sciences). It is intended to simulate microflows of single- and two-phase viscous compressible fluids with different rheology in spatial voxel domains. Such geometric models are relevant due to the development and widespread use of computer

Abstract Dynamic theoretic game models for the coordination of private and social interests of agents in the concept of the sustainable development (SD) of the dynamic system controlled by them are investigated. Within this concept, the hierarchical control mechanisms—methods of administrative control and inducement—are formalized as solutions of hierarchical differential games with the phase constraints

Abstract The paper considers the method of the numerical solution of the Schrodinger equation, which can partly be attributed to the class of Monte Carlo methods. The method is presented and simultaneously illustrated by the examples of solving the one-dimensional and multidimensional Schrodinger equation in the problems of a linear one-dimensional oscillator, hydrogen atom, and benzene atom.

Abstract We propose an approach to construct monotonic finite difference schemes for solving the simplest elliptic and parabolic equations with the first derivatives and a small parameter at the highest derivative. For this, the notion of adaptive artificial viscosity is introduced. The adaptive artificial viscosity is used to construct monotonic difference schemes with the flow approximation of order

Abstract The paper proposes a symmetry analyzer as an element of the computational algorithm for the numerical integration of two-dimensional equations of ideal gas dynamics. A symmetry analyzer is an algorithm that allows using grid data to give a preference to a component (in the present work, Cartesian or polar) of a vector field for its reconstruction on the cell interfaces of a computational grid

Abstract Based on a stochastic microscopic collisional model of the motion of charged particles in a strong external magnetic field, a hierarchy of equations of magnetic hydrodynamics is constructed. The transition to increasingly rough approximations occurs in accordance with a decrease in the dimensioning parameter, similar to the Knudsen number in gas dynamics. The result is stochastic and nonrandom

Abstract The article develops and analyzes the model of position selection by individuals in conditions of informational confrontation on two issues. We consider a society, in which two parties holding opposing positions on these issues are competing. The confrontation is manifested as follows: messages regarding these issues are distributed by each of the parties as information flows through affiliated

Abstract This article is devoted to the development and application of the filling cells method for the solution of hydrodynamics problems with a complicated geometry of the computational domain, in particular, a liquid domain, to increase the smoothness and accuracy of the finite-difference solution. The spatial-two-dimensional flow problem of a viscous fluid between two coaxial semicylinders and

Abstract This work is devoted to the molecular dynamic calculations of the properties of technical gases, whose study is a traditional problem of physics of matter. At present, there is increased interest in this problem due to the development of nanotechnologies and their introduction in various industries. The gases’ properties required for simulation are expressed as a set of macroparameters, including

Abstract Two models of machine learning are proposed for the automatic prediction of political views held by Russian users of the Vkontakte social network based on a microapproach to data analysis. The results are tested on various scientific and applied fields. One of them is monitoring of public opinion: based on testing a sample of 22 million digital fingerprints of adult user accounts, two estimates

Abstract Flux Correction method is a family of edge-based schemes for solving hyperbolic systems on unstructured meshes. The cruical operation there is a nodal gradient calculation of physical variables with at least second order of accuracy. There are two well-known procedures meeting this condition. One is based on Least Squares method and the other one is based on spectral elements. In this paper

Abstract In high-speed flows, blunt body elements having an irregular shape due to which gas dynamic parameters undergo significant changes are, as a rule, the most thermally loaded parts. In this respect, a quick evaluation of the thermal load on blunt bodies is important. Laminar boundary-layer equations given in special coordinates in a constant axisymmetric flow of a compressible perfect gas are

Abstract A model for describing wave motions of a flotatimg, viscous, non-compressible fluid partially filling the cavity of a rapidly rotating circular cylinder is proposed. The floating fluid is a fluid with an inertial surface formed by small mass particles floating on a free surface without interaction. The gyroscopic waves in a centrifuged flotating fluid layer on a solid wall of the rotor cavity

Abstract The properties of the solutions of the Klein−Gordon equations for various metrics of the general theory of relativity are considered. It is shown that the presence of singular points of the metric leads to qualitative rearrangement solutions of this equation, and the desingularization of solutions by the choice of a new metric requires a priori assumptions that can lead to formally mathematically

Abstract A finite-difference scheme is presented for the solution of the problem on the interaction of a femtosecond laser pulse with glass in the approximation of nonlinear Maxwell equations supplemented by equations of the hydrodynamic type for conduction electrons. The model takes into account all the basic physical processes involved in this interaction. An axially symmetric problem is considered