AbstractIn this paper, we consider the problem of modeling viscous incompressible fluid flow using the quasi-hydrodynamic (QHD) system of equations. The use of this approach makes it possible to avoid instability in the pressure calculation when using the classical formulation of the Navier–Stokes equations, which is manifested when using cellular numerical schemes. For the numerical implementation

AbstractDiabetes Mellitus (DM) during pregnancy is a major global public health burden with various adverse outcomes. In this paper, a mathematical model of the population dynamics of DM during pregnancy is developed and analyzed. Four independent variables have been considered, namely the numbers of nonpregnancy nondiabetic women, diabetic nonpregnant women, diabetic pregnant women and diabetic pregnant

AbstractThis article presents a method of collaborative one-dimensional (1D)–three-dimensional (3D) modeling of computational fluid dynamics. The method is based on the simultaneous calculation of 3D and 1D areas and linking the two parts of the problem by transferring the boundary conditions. The 3D approximation region is modeled based on the solution of Navier-Stokes equations. The 1D regions are

AbstractThe angular motion of a mockup of a satellite’s attitude control system on an air bearing is considered. The general purpose of the work is to verify the one-axis magnetic attitude control algorithm. This control is designed to maintain the satellite’s solar panels attitude towards the Sun. Specific mockup motion patterns are found. These patterns allow comparing the ground-based control performance

AbstractThe paper describes the features and capabilities of the software to simulate the dynamics of near-Earth satellites. The software package allows the passive and controlled angular and orbital motion simulation of both single satellites and formations. The software also allows using the mathematical models of varying precision and complexity while performing the computations. The user-friendly

Abstract—The work is aimed at determining parameters of a deuterium-tritium mixture expanding into a vacuum with an external magnetic field, the output of thermonuclear energy from which compensates or exceeds the initial thermal energy of the plasma. This type of assessment is usually based on the Lawson criterion. In the paper the parameters are determined on the basis of the model of adiabatic expansion

AbstractIn the present work, a numerical modified Verlet scheme (MVS) is obtained. This scheme is intended to solve the equations of motion of charged particles immersed in an external stationary environment and a uniform magnetic field, for example, charged particles of a condensed substance in a buffer plasma (dusty plasma). The influence of the environment on the particle dynamics is described by

AbstractThis article presents the results of generalizing the existing methods for determining the diffuse radiation configuration factors for the radiation transfer calculation in the zone model of the system of bodies with complex-shaped surfaces. Such problems arise in determining construction temperatures, surface illumination, and construction of realistic images in various fields of science and

Abstract—A mathematical model of nonequilibrium crystallization of a binary aluminum alloy (Al-Si) with modifying refractory nanoparticles, which are the centers of nucleation of the crystalline phase, is proposed. The model describes thermodynamic processes, as well as heterogeneous nucleation and crystallization of the α-component and the β-component of a melt. The crystalline phase nucleates on

AbstractA variational problem for a radial gas journal bearing with two sectors is considered. The pressure field in the gas layer can be described by the nonlinear Reynolds equation for arbitrary compressibility numbers. The magnitude of the resultant pressure force vector is used as a functional of the variational problem. The system of necessary conditions of the extremum is qualitatively analyzed

Abstract—A theoretical analysis has been to draw out the flow characteristics of natural convective nanofluid flow along an exponentially accelerating vertical plate in the presence of magnetic field. Three different types of water-based nanofluids containing copper, silver and copper oxide are considered. The governing equations are transformed into dimensionless form and tackled with the usual time-frequency

AbstractThe random variable of passenger journeys between any two stopping points on a route (passenger correspondence) represents a discrete variable. For each value of the discrete random variable, its probability is calculated. As a solution to the problem of determining the number of corresponding passengers between two stopping points on a route, we take the most probable value of the random variable

AbstractA description of two methods for simulation of the flow around complex test configurations is considered. One method implements a well-known approach to solving the Reynolds-averaged Navier-Stokes equations with a closing differential turbulence model. Another method is based on scale-resolving wall-modelled LES approach (WMLES). The classical problem of the flow around the inclined backward-facing

AbstractThe paper presents a dynamical stochastic general equilibrium (DSGE) model for key indicators of the Russian economy. A special feature of the approach is the Keynesian microeconomic foundation, which takes into account market failures such as imperfect competition, as well as inflexible prices and wages. The second specific feature is the hypothesis of rational expectations. The model consists

AbstractAn original algorithm is developed for vortex methods of computational fluid dynamics for determining the intensity of the vortex sheet on the surface of a body in the flow of an incompressible medium. Unlike the common in the vortex methods approach to satisfying the no-slip boundary condition on a streamlined surface, which is based on ensuring that the normal velocity component of the medium

AbstractA mathematical model of the Alfvén wave absorption is proposed, the study of which is based on the equations of two-fluid electromagnetic hydrodynamics (EMHD) having taken the electron inertia and bremsstrahlung into account. Special attention is paid to the research of the additional effects of photorecombinational and synchrotron radiation. The investigation revealed, in particular, the finite

AbstractBased on the application of conservation laws, a compact quasi-gasdynamic system, which was previously obtained using a kinetic model, is derived. The possibility of using algorithms previously used to solve the Navier–Stokes equations to solve this system is discussed.

AbstractThe article is devoted to a description of a mathematical model of a tethered high-altitude unmanned platform in which the power of propulsion systems and payload is supplied from a ground-based energy source via cable. The magnitudes and directions of the forces acting on the unmanned vehicle by the cable are determined from the derived system of differential equations which allows calculating

Abstract—A method is presented for solving interior boundary-value problems for second-order elliptic equations by transition to ray variables. The domain is divided into cells within which the coefficients and sources have the smoothness and continuity properties necessary for the existence of a regular classical solution in the cell. The finite discontinuities of the coefficients (if any) are located

AbstractThe microlevel dynamics of the age-limited production capacities differentiated by the moments of creation set the macrolevel production function. The microdescription is based on the hypothesis of the capacity loss at a constant rate and constant number of jobs from the moment of the creation of the production unit to its closure, when the age limit is exceeded. An analytical expression for

AbstractThe 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

AbstractThe 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 the

AbstractThe 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

AbstractThe 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

AbstractThe 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

AbstractDual-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

AbstractVarious 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

AbstractThe 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

AbstractWe 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

AbstractTo 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

AbstractThis 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 initial

AbstractThe 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.

AbstractThe 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

AbstractThis 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

AbstractThe 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 with

AbstractActive 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 solutions

AbstractA 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

AbstractThe 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

AbstractUsing 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

AbstractDifferential 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

AbstractThe 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

AbstractDynamic 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

AbstractThe 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.

AbstractWe 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

AbstractThe 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

AbstractBased 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

AbstractThe 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

AbstractThis 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 the

AbstractThis 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

AbstractTwo 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

AbstractWe consider methods to construct mathematical models for the automation of circuit design that implement the calculations of the parameters and the structure of the circuit connections of the components of the developed electronic device displayed by its graphic scheme. We note that the modeling of frequency properties of an electronic circuits in a frequency range is among the main problems

AbstractA difference scheme for the transfer problem, constructed as a linear combination of the Cabaret scheme and the central difference scheme, is proposed. The stability and dispersion properties of the scheme are studied. It is shown that the constructed scheme has the best dispersion properties for high-frequency harmonics at small Courant numbers compared with the known Cabaret scheme for the

AbstractAn important task in reservoir simulation is to take into account the effect of a hydraulic fracture on the well’s performance. The upscaling method allows efficiently computing the inflow into a well with a fracture on a coarse grid. A numerical near-well upscaling procedure for hydraulic fractures on an unstructured Voronoi grid is proposed. The upscaling procedure is shown to be significantly

AbstractThe parasite–host system is considered with two different variants of a pathogen agent with complete cross protection, where one of the variants may transform into another with a certain probability. This system corresponds to the epidemic process initiated by the antibiotic-resistant variant of the pathogen agent. The behavior of solutions is studied. It is proved that the main case has a

AbstractIn this paper, we consider some exact solutions of the hemodynamic equations in a contracting vessel in a quasi-one-dimensional approximation in relation to the problems arising in the description of the lymph flow. Solutions for the linearized problem in the case of forced small contractions of the vessel’s lumen are given. An analytical solution of a nonlinear system is obtained and studied

AbstractAlgorithms of the optimal arrangement of heat sources with volumetric heat release within regions of a complex geometric shape are considered. The distribution found has the minimum total power and provides the temperature in the given temperature corridor. Finite-dimensional approximations of the original problem are constructed in the form of a linear programming problem. A method is given

AbstractThis work is devoted to evaluating the performance of a multicore CPU Elbrus-8C processor in supercomputer computational fluid dynamics (CFD) applications. Parallel simulation codes based on highly accurate methods on unstructured meshes for modeling the turbulent flows are considered. The main features of the Elbrus architecture are described, and the approaches for adaptating and optimizing

AbstractThe papers dedicated to the procedures of solving direct problems in seismic exploration of fractured formations are considered in this review article. The fractured formations are known to be potential hydrocarbon reservoirs, which are being studied actively at the present time. Due to high cost of field prospecting works, the numerical simulation is an important part in such research, leading