Abstract The paper proposes a computational algorithm for the numerical simulation of two-dimensional magnetohydrodynamic (MHD) flows, using a symmetry analyzer as an element of the numerical method. The algorithm is based on a finite-volume Godunov-type scheme with an approximate solution of the Riemann problem for calculating flows. A polar mesh is used, but the momentum and magnetic induction equations

Abstract When solving multidimensional problems of gas dynamics, finite-volume schemes using complete (i.e., based on a three-wave configuration) solvers of the Riemann problem suffer from shock-wave instability. It can appear as oscillations that cannot be damped by slope limiters, or it can lead to a qualitatively incorrect solution (carbuncle effect). To combat instability, one can switch to incomplete

Abstract The material of this article is based on the author’s works devoted to the construction of the Pareto set in a two-criterion parameter estimation problem of the linear regression equation with the loss functions corresponding to urban and Chebyshev distances. It is known that the former is not sensitive to outliers, while the latter, in contrast, gravitates to them. In these works, it was

Abstract An algorithm for calculating the plasma composition based on the improved Raizer method is described in detail. The results of calculations by this method and by solving the system of the Saha equations, taking into account the degeneracy of electrons, are compared. A method of solution of scalar equation is proposed, which is just as reliable as the dichotomy method and is faster than the

Abstract The problem of a supersonic flow around a system of bodies freely moving in a gas flow is considered. The mathematical model consists of Euler’s equations for a region filled with gas, supplemented by Newton’s equations for describing the motion of rigid bodies under the influence of pressure. The computational algorithm uses locally adaptive Cartesian grids, in which the adaptation is based

Abstract Ground-based and satellite measurements, as well as numerical modeling of the spatial structure of the equatorial ionospheric bubbles are carried out quite intensively. These data show that the longitudinal and altitudinal gradients of the logarithm of the electron concentration at the vertical boundaries of the bubbles can reach values of 0.001 1/m and 0.0001 1/m, respectively. With such

Abstract An algorithm for solving problems of magnetic gas dynamics, which is adapted to the architecture of computing systems with extramassive parallelism, is discussed. The algorithm is based on a kinetic model that describes the dynamics of an ensemble of neutral and charged particles, as well as a magnetic field. As an illustration, the results of a 3D calculation of the dynamics of a conducting

Abstract The methodology and results of parametric studies of vertical-axis wind turbines (VAWTs) based on three-dimensional aerodynamic calculations are presented. For a model wind turbine with three twisted blades, the dependence of the torque on the wind speed, the speed of rotation of the turbine, and on the variation of geometric parameters that determine the design of the turbine is studied.

Abstract Based on the equations of the classical linear theory of elasticity, a model problem of the stress-strain state of an elastic cylinder simulating a meteoroid falling in the atmosphere with a thin surface layer heated due to thermal loads is formulated and analytically solved. The influence of an inhomogeneous temperature field on this process is isolated and separately investigated within

Abstract Corrections to the harmonic approximation are obtained for the first order of the theory of hyperelasticity in the relaxation approximation for a cubic crystal. The Vlasov equation is constructed for a collisionless gas of phonons in a self-consistent deformation field. Collisions of phonons are considered in the relaxation approximation to the equilibrium distribution. It is shown that the

Abstract A mathematical model of a spacecraft (SC) with an arbitrary number of large flexible structural (appendages) elements (LFSEs) is developed, implemented, and verified. The SC model obtained based on the general equations of dynamics is written in generalized coordinates. It allows three types of articulation between the LFSEs and the SC’s body: cantilever, and with the help of one-step and

Abstract Based on the experiments on the movement of a Pt/Au bimetallic rod in a hydrogen peroxide solution, a model of the hydrodynamic mechanism of such movement is proposed. The proposed model is based on the equations of the hydrodynamics of a viscous fluid and the dynamics of particles and takes into account the hydrodynamic interaction of all charged particles in the fluid between themselves

Abstract Awareness programs by the media play a pivotal role in the control of infectious diseases. In this paper, we formulate and analyse a mathematical model for listeriosis incorporating aware individuals. Mathematical analyses of the model are done and equilibrium points determined. The model has three equilibria; namely; the disease-free, the bacteria-free, and the endemic equilibria. Local asymptotic

Abstract A two-dimensional electrical impedance tomography problem in the case of piecewise-constant electrical conductivity, taking two known values, is considered. It is required to determine the boundary between regions with different conductivity. The initial information for solving the problem consists of several pairs of current and voltage distributions on the outer boundary of the body. A numerical

Abstract Fully discrete bicompact schemes of the fourth order of approximation in space are investigated for entropy stability in problems of gas dynamics. Expressions for the rate of entropy production in these schemes are derived. Qualitative estimates are obtained for the behavior of this quantity. On the example of one-dimensional Riemann test problems, a numerical analysis of the entropy production

Abstract The problem of the propagation of waves of small amplitude on the surface of shallow water in a reservoir of variable depth is considered. The Korteweg-de Vries (KdV) equation with a variable coefficient taking into account both the bottom profile and the geometric divergence of waves is obtained from the system of shallow water equations. The inverse problem, which consists of determining

Abstract The technology is described for constructing the set of the initial data using the technique of eliminating the model’s bias for seasonal experiments with a numerical climate model of the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS), which was originally developed for multi-annual experiments. A comparative analysis of the multiyear mean correlation coefficients

Abstract The process of dissemination of information in society among its possible adherents (individuals who perceive this information) in the presence of mistrust, which means a decrease in the level of interest in assimilating the proposed information, is considered. It is assumed that the degree of influence of distrust is determined by the hype, i.e., the rate of change in the number of adherents

Abstract A technique for setting boundary conditions on solid surfaces based on the method of near-wall functions is presented. The technique is based on solving the Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras (SA) closure model in the boundary layer approximation. The obtained solution is used to formulate flow boundary conditions that compensate the insufficient mesh resolution

Abstract This paper presents an analysis of the level of description of the main physical processes in the Earth’s atmosphere in modern models of the general circulation of the Earth’s atmosphere and gives a brief overview of the modern models used by the main forecasting centers. The promising directions of the development of models of the general circulation of the Earth’s atmosphere are discussed

Abstract The paper is devoted to numerical simulation of multicomponent gas flows based on extended Euler equations using a modified explicit Godunov-type scheme. A feature of the used algorithm is to take into account strong shock waves and occurrence of pressure oscillations at contact boundaries. This is expressed by the use of exact solutions of the corresponding Riemann problem and special double-flux

Abstract The paper considers the problem of a flow around a thin plate of infinite span. The frontal surface of the plate absorbs gas. For the calculations we use the mathematical flow model containing a combination of the Navier–Stokes–Fourier model and the model kinetic equation of polyatomic gases. The calculations are performed for a supersonic flow with a Mach number of 2.31 for a Knudsen number

Abstract A conservative version of the entropy stable discontinuous Galerkin method is proposed for the Euler equations in variables: density, momentum density, and pressure. For the equation describing the dynamics of the mean pressure in an FE, a special difference approximation in time and conservative in total energy is constructed. The entropy inequality and the requirements for the monotonicity

Abstract Based on the discrete sources method, a mathematical model of the plasmon nanolaser resonator deposited on the prism surface in an active ambient medium is developed and implemented, which allows taking into account the non-local effect (NLE) in the plasmon material. The resonator’s characteristics are optimized, which makes it possible to obtain a field enhancement on the external surface

Abstract A method is proposed for the numerical modeling of acoustic processes in solids, representing a solid in the form of an array of particles in a cubic body-centered crystal lattice. The particle dynamics is described by Newton’s equations of motion. It is shown that the developed numerical model makes it possible to describe resonance phenomena and the process of wave propagation. The results

Abstract— A numerical method proposed in the authors’ previous work to solve the Schrödinger equation is developed. Ambiguity remains in the method described earlier in identifying the average positions of quantum particles in a molecular system, which were prescribed from external considerations without taking into account the Schrödinger equation itself. In this paper, a list of procedures for the

Abstract This study is devoted to the construction and software implementation of a computational algorithm for modeling the process of anomalous diffusion. The mathematical model is formulated as an initial-boundary value problem for a semilinear partial differential equation of fractional order. An implicit finite-difference scheme is constructed based on the approximation of a higher order of accuracy

Abstract A method is proposed to solve the linearized ellipsoidal-statistical Holway equation in the classical problem of a rarefied gas flow between two parallel planes. To approximate the desired solution, the function is expanded in a series in Chebyshev polynomials of the first kind for each variable. The Holway model kinetic equation is reduced by the collocation method to a linear matrix equation

Abstract The perspective n-point problem (PnP), or a three-point photogrammetric resection in space, consists of the problem of finding the position and the orientation of the model of the camera of the central projection by the assigned spatial coordinates of the given points and by the corresponding coordinates of their projections on the image. Due to the available applications in robotics and machine

Abstract We consider random changes in the standard genetic code, in which its structure is preserved, and small variations in the genetic code, in which the structure is preserved or changed. The assumption is substantiated that the standard genetic code provides the best possible overlap of genes. The structure and content of the standard genetic code is determined by the condition of the maximum

Abstract Based on the equations of thermodynamic balances, a model of a stationary non-equilibrium distillation process is proposed. It is shown that the heat consumption for any given efficiency of a distillation column depends monotonically on the parameters of the reversible distillation. Using this result, the authors propose an algorithm for choosing the optimal separation sequence for a system

Abstract We develop/propose the method reducing the dimension of a data matrix, based on its direct and inverse projection, and the calculation of projectors that minimize the cross-entropy functional, remove. We introduce the concept of information capacity of a matrix, which is used as a constraint in the optimal reduction problem, is introduced. The proposed method is compared with known methods

Abstract A family of difference schemes on an explicit five-point stencil for the numerical solution of the linear transfer equation is considered. To construct and study the properties of difference schemes, a generalized approximation condition is used. Difference schemes in the space of undefined coefficients are analyzed. In this case, the problem of constructing the optimal difference scheme is

Abstract— This study carries out the numerical simulation of the propane pyrolysis process in a flow-through chemical reactor where chemical conversions are induced by the external heating of the reaction zone. Navier–Stokes equations in the approximation of small Mach numbers are used for the mathematical description of the studied processes, since the velocity of the gas mixture is much lower than

Abstract— A numerical algorithm is presented for solving the multicomponent gas dynamics equations by the discontinuous Galerkin method on locally adaptive grids. The numerical algorithm uses a data structure and a dynamic local grid adaptation algorithm from the p4est library. We use Lax–Friedrichs–Rusanov and HLLC numerical flows. To get rid of unphysical oscillations, the Barth–Jespersen limiter

Abstract— This paper considers an approach to approximating the sensor data of an autonomous navigation system installed on the Russian segment of the International Space Station (ISS) based on the application of a mathematical model simulating the orbital motion of a spacecraft (SC) in which the midship area is computed with allowance for the aerodynamic drag forces using a geometric model of the

Abstract The problem of optimizing air passenger transport schedules is investigated. It is required to minimize renting and operating costs taking into account heterogeneous fleet, the possibility of multiple visits to the same location, inaccessibility of specified air corridors, etc. Two formalizations of this problem are presented in the form of multi-index problems of binary linear programming

Abstract— The paper considers a three-dimensional gas-dynamic model of a protoplanetary disk that revolves around a gravitating center. The dynamics of small perturbations in a rotational shear flow are modeled. The development of the initial azimuthal perturbations of the rotation speed leads to the formation of spiral density arms, while self-gravity increases its local maxima and creates gravitational

Abstract We consider the problem of modeling hydroelastic oscillations of liquid fuel in the tanks of launch vehicles with the use of mechanical analogs. Here, it is important to ensure the applicability of the computational model with mechanical analogs to the real object in terms of the mass-inertial and dynamic characteristics. In addition, it is necessary to ensure the correct modeling of the external

Abstract The paper presents a modification of the asymptotic averaging method for solving the homogenization problem of elastic properties for composite materials. The elasticity of the phase interface is taken into account. The conditions of a soft imperfect interface are considered, which account for a displacement jump on the phase boundary. A review of the interface-modeling methods in composite

Abstract— The issues of the mathematical modeling of a thermoporoelastic medium taking its damage into account are considered. The employed model generalizes the classical Biot model simulating the behavior of a poroelastic medium taking the thermoelastic effects into account. In order to describe the damage of the medium, the approach of continual damage mechanics is used, in which the state of the

Abstract The possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference. Particular attention is paid to the equality of the spatial coordinates. We investigate

Abstract— The paper is devoted to the simulation of oil displacement by water and the formation of the Saffman–Taylor instability. The problem is solved in two-dimensional formulation. A circular domain with one injection well and eight production wells located along the contour around the injection well is considered as geometry. To study the patterns of oil displacement by water, hydrostatic pressure

Abstract In this paper, a mathematical model of a neural network defuzzificator is presented. It is a two-layer perceptron and serves to convert a fuzzy solution to a numerical form in fuzzy-logic output procedures. The model allows optimizing the computational load that occurs when using the standard center-of-gravity method, through the use of a neural network. Training and testing are conducted

Abstract This paper considers continuous models of informational warfare based on the traditional neurological scheme. Using the method of substituting differential equations by cellular automata we propose a discrete version of the information warfare model. This model is used to simulate a propaganda campaign by two parties and to carry out a number of computational experiments. It is shown that

Abstract This paper provides a vector autoregression model with an additional regularization problem similar to the Hodrick–Prescott filter problem to model a single, i.e., balanced, growth rate of the structural component of the main macroeconomic indicators of the Russian economy. This model includes the real GDP without government expenditure, the real household consumption, real fixed capital investment

Abstract— This article considers interpretation of matrix models of texts and models of text collections based on them. Examples of computationally generated models of text collections are presented to demonstrate the high quality of the modeling results and practical applicability of the proposed approaches. An original method of the experimental verification of the text models’ applicability to problems

Abstract A numerical solution method based on the reduction of systems of ordinary differential equations to the Shannon form is considered. Shannon’s equations differ in that they contain only multiplication and summation operations. The absence of functional transformations makes it possible to simplify and unify the process of numerical integration of differential equations in the form of Shannon

Abstract The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been a subject of considerable interest over the past decades. This is primarily due to the importance of these phenomena in various fields of science and engineering. In addition, it should be noted that studies of the characteristics

Abstract— The aim of this work is to study and compare various approximations for the system of radiative heat transfer equations (TEs) in optically dense and transparent media. For this purpose, in optically dense media, asymptotic analysis is used; and in optically transparent media, an approach that allows reducing the solution of diffusion equations to solve a kinetic equation. The performed studies

Abstract The results of a study of the oscillations of microcantilevers (MCs) made of nanoporous anodic aluminum oxide and constituting the base of biochemical sensors are described. Finite-element modeling of an MC’s vibrations reveal the sources of resonances in the frequency spectrum that do not correspond to the cantilever’s oscillations and complicate the development of sensors. It is shown for

Abstract— Steady-state solutions for the problem of magnetohydrodynamic motion of an incompressible polymer fluid over an infinite rotating disk are considered. The representation of the solution used here is similar to the Von Kármán self-similar solution for a viscous fluid. Examples of the numerical steady-state solutions for various values of the problem parameters are presented.

Abstract The generation of an electromagnetic field in a region with a perfectly conducting boundary by a long duration pulse of ionizing radiation is considered. The problem of calculating the field by numerically solving the complete system of Maxwell equations is posed. The approximations of the large and small radiation conductivity of the medium in the region are formulated. Analytical estimates

Abstract The era of the development of fundamentally new materials began with the discovery of graphene. Their unique properties already allow us to create many useful products in electronics, biomedicine, and other high-tech industries. However, the study of graphene and its derivatives is continuing. The mechanism of the formation of the graphene lattice and the state parameters of its individual

Abstract The problem of the propagation of deformations and stresses in a thin fiber under a dynamic mechanical load, as well as the destruction of the fiber, is considered. High-speed interactions in which the striker’s speed is comparable to the speed of sound in the fiber are considered. The numerical results are compared with an analytical solution for a point impact. Various loading modes are

Abstract— The impact of the choice of the proximity measure for the numerical and reference solutions is discussed in terms of the verification of the calculations and software. If no reference solution is available, the deterministic and stochastic options for estimating computational errors are considered using an ensemble of solutions obtained by different numerical algorithms. The relation between

Abstract The method of Lebesgue moments for simulating the reversal of resonances, resonance self-shielding, and block effect in the neutron spectra of extended heterogeneous objects, such as nuclear reactors, radiation shielding, and installations for studying the properties of matter, is developed. The method uses a more accurate averaging procedure over neutron energy than the group averaging. The

Abstract— The multicriteria problem of optimizing the state regulation of the quality of human capital in an information society is considered. A discrete dynamic model of human capital is described taking into account the age dynamics of the awareness and cognitive abilities possessed by an individual as a carrier of information. On trajectories, The lifelong indices of human capital are considered

Abstract A numerical simulation of the evolution and interaction of flow discontinuities in a channel caused by a pulsed volume discharge is performed. The algorithm is based on a system of quasi-gasdynamic equations in compact form. A comparison is made with the experimental data and calculation results based on the Euler and Navier-Stokes equations.

Abstract— A general equilibrium model, which describes the interaction of heterogeneous agents who choose between the labor market and self-employment and the state, which plays the role of an inspection body (auditor) in a model that controls the fact of tax evasion, is considered. It is shown that in the case of information asymmetry, the tax rate that maximizes the amount of tax revenues increases