Computational Continuum Mechanics
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description: The journal publishes papers describing recent research and computational results in the field of continuum mechanics. The subject of the journal includes theoretical and numerical methods for solving the problems of mechanics of a deformable solid and fluid mechanics; effective applications of these methods to the study of natural and technogenic phenomena, technological processes, the behavior of machines and structures.
publisher: Institute of Continuous Media Mechanics
language: en
publication name: Computational Continuum Mechanics
issn: 1999-6691
items: Influence of viscosity on nonlinear resonance of forced oscillations of a bubble in a vibrating liquid
items: Natural and forced vibrations of solid bodies with account for damping and prestressed state induced by piezoelectric elements
items: Numerical modeling of diurnal oscillation of insolation in the idealized model of general atmospheric circulation
items: Fluid flow in a thick torus driven by distributed forces
items: The influence of biomechanical parameters of an erythrocyte and viscosity of the surrounding fluid on the hydrodynamic interaction with a solid wall
items: Interaction of mechanical, temperature and diffusion fields in a solid cylinder subjected to transient heating
items: Convection in a closed cavity with a large body of neutral buoyancy
items: Modeling the loss of stability and failure of mine shaft tubing supports
items: Numerical simulation of natural vibration of a partially fluid-filled truncated conical shell in a gravity field
items: Numerical study of the motion of a solid particle in the field of ultrasonic standing wave
items: The onset and evolution of nonlinear convective regimes of binary mixtures in multilayer systems simulating synclinal geological folds
items: Some coupled diffusion problems for ternary systems
items: On one solution to the problem of resonant oscillations of a lifting rope taking into account its slippage when winding on the surface of a drum
items: A magnetic field in the vicinity of a homogeneous magnet filling an axisymmetric, simply connected or multiply connected region
items: Effect of a traveling magnetic field on heat and mass transfer during submerged heater crystal growth
items: Simulation of convective polymerase chain reaction based on multiphase Lagrangian particle tracking model
items: Multi-harmonic balance method in structural element ratcheting problems
items: A three-phase hydrodynamic phase field model with stabilization of the Cahn-Hilliard equation
items: Numerical simulation of flux expulsion in a plain channel MHD flow
items: Modeling the temperature field dynamics during the Czochralski single crystal growth in a non-stationary approximation
items: MHD-stirring of a heavy impurity under a rotating magnetic field generated by a multi-section inductor
items: Numerical simulation of the aerodynamics of a cycloidal rotor in flight
items: Numerical modeling of fatigue fracture in the light alloys produced by additive technology
items: Stability of a liquid layer in a rotating Hele–Shaw reactor under competition of buoyancy effects generated by inertial forces
items: Pressure field in a formation with a hydraulic fracture of finite length
items: Construction and comparison of experimental and calculated interferograms for two-dimensional transparent gas flow
items: A mathematical model of motion of polymer systems with nanoaggregates in the pore space of an oil reservoir
items: Travelling of a reflecting immersed disc in a convective layer heated by incident radiation
items: Computational macromechanics as a generalization of the ideas of S.K. Godunov
items: A hybrid numerical-analytical approach for the simulation of antiplane vibrations of multilayered elastic waveguides with multiple inhomogeneities

Influence of viscosity on nonlinear resonance of forced oscillations of a bubble in a vibrating liquid
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description: The paper presents the results of the study on dynamics of a gas bubble in an oscillating viscous fluid. The focus is on the case when the frequency of external vibrations is close to half the natural frequency of the quadrupole mode of free oscillations, which corresponds to the condition of the nonlinear resonance previously discovered in the inviscid approximation. A viscous potential flow model was used to take into account dissipation. In the framework of this model, the analytical expressions of the main process characteristics were obtained. The solution was expressed as an asymptotic series in a small parameter - the ratio of vibration amplitude to the bubble radius. The first-order theory shows that the bubble oscillates as a whole without deformation. The dependence of the amplitude and the phase shift of these oscillations on viscosity was established. The second-order theory investigates the nonlinear resonance associated with the excitation of the quadrupole deformation mode. It is shown that viscosity does not shift the resonant frequency, which remains half the natural frequency of the quadrupole mode, as in an ideal fluid, but significantly limits the amplitude of resonant oscillations. The results of numerical modeling of 3D axisymmetric bubble oscillations at the resonant frequency show good agreement with the analytical data. These findings are important for understanding and controlling processes in such applications as acoustic flotation, chemical reactors, and medical ultrasound diagnostics.
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creator: Vladimir Vladislavovich Konovalov
creator: Andrey Olegovich Ivantsov
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-02-25
publication date: 2026-02-25
starting page: 385
ending page: 399
doi: 10.7242/1999-6691/2025.18.4.28

Natural and forced vibrations of solid bodies with account for damping and prestressed state induced by piezoelectric elements
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description: The widespread use of thin-walled structures subjected to undesirable dynamic phenomena necessitates the development of effective methods for controlling their vibrational characteristics to prevent resonance. A promising approach to solving this problem is the application of smart materials, particularly, piezoelectric elements, enabling the implementation of passive, active, and hybrid damping systems. This work investigates the natural and forced vibrations of piecewise-homogeneous electro-elastic and electro-viscoelastic bodies using the finite element method. A distinctive feature of the study is the consideration of the prestressed and predeformed state caused by an embedded piezoelectric element as a result of the reverse piezoelectric effect due to DC voltage supply. A mathematical formulation of the problem, interpreting the prestress state in terms of geometric stiffness, and accounting for viscous and Rayleigh damping mechanisms is developed based on the principle of virtual displacements. Using a plate with an embedded piezoelectric element as an example, the influence of the control voltage and the type of damping on the complex natural frequencies and amplitude-frequency responses is studied. It has been established that both viscous and Rayleigh damping have slight effect on the shift of resonant frequencies caused by the prestressed state. The results of solution of the forced vibration problem allow us to quantify a decrease in the vibration amplitude of the plate in the prestressed state caused by the piezoelectric element in the case of external excitation with frequency corresponding to the resonance frequency of the unloaded plate. The results presented demonstrate the influence of the prestressed state on the amplitude-frequency response of a plate with closely spaced natural frequencies at different values of the electric potential on the piezoelectric element.
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creator: Aleksandr Olegovich Kamenskikh
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-11
publication date: 2026-03-11
starting page: 400
ending page: 410
doi: 10.7242/1999-6691/2025.18.4.29

Numerical modeling of diurnal oscillation of insolation in the idealized model of general atmospheric circulation
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description: The Earth's rotation around its axis causes the sunlit region to constantly shift in the opposite direction. The resulting diurnal oscillations of the surface temperature can influence the structure and dynamics of the general circulation and midlatitude baroclinic waves. This paper presents a numerical study of the influence of diurnal insolation oscillations on the formation and characteristics of large-scale flows using a numerical analogue of the laboratory model of atmospheric general circulation. Two main regimes were considered: with regular and irregular baroclinic waves. Diurnal insolation oscillations were modeled using a localized, moving heat source. It is shown that for both regimes of baroclinic waves, the transition from stationary, zonally uniform heating to non-stationary, zonally inhomogeneous heating does not lead to qualitative changes of the mean flow structure or the distribution of pulsations. This only leads to quantitative changes, the magnitude of which does not exceed 15%. The hypothesis that a moving heat source would lead to an increase in pulsation energy was not confirmed. Moreover, the energy of meridional velocity pulsations, which characterizes the energy of baroclinic waves, decreases in the case of a moving heat source. A relatively weak effect of the transition from a stationary, zonally uniform heating regime to a non-stationary, localized one is explained by the fact that disturbances caused by the movement of the heat source are both spatially and frequency-localized.
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creator: Andrei Anatol′yevich Gavrilov
creator: Andrei Nikolayevich Sukhanovskii
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 5
ending page: 15
doi: 10.7242/1999-6691/2026.19.1.1

Fluid flow in a thick torus driven by distributed forces
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description: In this article, a laminar, steady-state flow of incompressible fluid in a curvilinear channel with a circular cross-section is studied numerically. The influence of the bulk force on the stationary flow is analyzed through the consideration of its three main natural causes: a pressure gradient in the channel, a uniform action of external forces, and an analog of the force generated by the uniform deceleration of a rotating channel (inertia force). The key parameter used to describe flows in a toroidal channel is the Dean number, which takes into account the influence of the channel curvature and flow intensity. Direct numerical simulations at all possible channel curvatures and Reynolds numbers up to 300 showed that to describe all features of flow in thick toroidal channels, it is insufficient to use the Dean number alone. It has been found that the position of the longitudinal velocity maximum depends on the Reynolds number and curvature, and the type of force. At low values of the Reynolds number, that is, less than 40, the maximum may shift towards the outer axis of the torus, whereas at high values, it shifts only away from it. The simulation revealed the splitting of the velocity maximum , as well as the occurrence of a third local maximum ; these effects arise only under a gradient force and at relatively high curvatures. It has been shown that the Dean number is insufficient to fully describe the flow at high curvatures. For the inertial force, the Dean number unambiguously determines the position of the velocity maximum but fails to describe the intensity of the secondary flow at the Reynolds numbers of 50 and higher. At a constant force, the Dean number is applicable only up to certain values of the Reynolds number, while for a pressure gradient, the use of the Dean number is absolutely meaningless. It has been established that the intensity of the secondary flow reaches a maximum at the Reynolds numbers from 50 to 100 (with nondimensionalization performe…
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creator: Anton Viktorovich Chupin
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 411
ending page: 423
doi: 10.7242/1999-6691/2025.18.4.30

The influence of biomechanical parameters of an erythrocyte and viscosity of the surrounding fluid on the hydrodynamic interaction with a solid wall
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description: The nature of blood flow in capillaries, arterioles, and venules largely depends on the mechanical interactions between red blood cells and vessel walls . A theoretical understanding of the principles of hydrodynamic interaction between blood cells and vessel walls is essential for a comprehensive biophysical description of blood flow in the microcirculatory system, as well as for the design of medical microfluidic devices for processing blood samples. In this study, numerical methods are used to investigate the behavior of a single red blood cell (erythocyte) near a solid flat surface under conditions of shear flow of a viscous Newtonian fluid. The aim of the study is to identify the pattern of erythrocyte motion depending on its biomechanical parameters and hydrodynamic conditions. To address these issues, we use a numerical model that combines particle dynamics and the Lattice Boltzmann method with the Bhatnagar-Gross-Krook collision integral. The biomechanical model of the red blood cell takes into account tensile and bending elasticity, as well as the forces that maintain the membrane area and the cell volume. Computer simulation of red blood cell trajectories under various hydrodynamic conditions shows that the velocity of cell repulsion from a solid wall is linearly dependent on the shear rate. It varies non-monotonically as the red blood cell moves away from the wall, and decreases at greater distances. The lift effect in the model is most pronounced when the red blood cell moves in a “tank-treading” mode at high shear stresses. The dependence of the lift velocity on the elasticity and volume of the cell is quantified by varying the biomechanical parameters of the erythrocyte.
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creator: Aleksey Vyacheslavovich Belyaev
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 485
ending page: 499
doi: 10.7242/1999-6691/2025.18.4.35

Interaction of mechanical, temperature and diffusion fields in a solid cylinder subjected to transient heating
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description: The article examines the phenomena caused by the mutual influence of mechanical, temperature and diffusion fields in a continuous orthotropic multicomponent cylinder under the action of unsteady external perturbations set on the cylinder surface. The cylinder does not experience volumetric perturbations. It is assumed that the physico-mechanical processes occurring in the cylinder depend only on the radial coordinate. The mathematical formulation involves a system of coupled nonstationary thermodiffusion equations in a cylindrical coordinate system. The employed heat and mass transfer model accounts for the finite velocity of thermal and diffusion wave propagation. The kinematic relations for thermal and diffusion flows are constructed based on the generalized Lord–Shulman theory. The proposed algorithm for solving a polar-symmetric problem is based on the integral representation of the desired fields in the form of time-dependent convolutions of Green's functions and the functions, describing surface thermomechanodiffusion perturbations. The Green's functions are found by applying the time-domain Laplace transform and the Fourier–Bessel series expansion, which makes it possible to reduce the initial boundary value problem to a system of linear algebraic equations with respect to the coefficients of the Fourier series. The solutions of this system are rational functions, and therefore the inverse Laplace transformation is carried out analytically using the theory of residues and tables of operational calculus. Using a three-component cylinder as an example, a numerical analysis of the interaction between mechanical, temperature and diffusion fields under external unsteady thermal action is performed and the obtained results are compared with the solutions to known problems of thermoelasticity and mechanodiffusion. The effect of the finite velocity of propagation of thermal and diffusion fluxes on the kinetics of heat and mass transfer in continuous media under diffe…
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creator: Andrei Vladimirovich Zemskov
creator: Danila Olegovich Kazimirov
creator: Anatoliy Vladimirovich Malashkin
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-04-04
publication date: 2026-04-04
starting page: 16
ending page: 30
doi: 10.7242/1999-6691/2026.19.1.2

Convection in a closed cavity with a large body of neutral buoyancy
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description: Rayleigh-Benard convection in a square cell with a sufficiently large, heat-insulating body of neutral buoyancy is studied numerically for two moderate values of the Rayleigh number Ra=105 and Ra=106. The emphasis is placed on changes in the dynamics of bodies and convective flows observed at a significant increase in body size. In the absence of a body, stationary two-roll convection is formed in the cell at Ra=105, and at Ra=106 a periodic oscillatory regime occurs. The appearance of a freely floating circular body in a cell changes the flow behavior, which is qualitatively independent of the body size, but fundamentally different for two considered values of the Rayleigh number. Thus, at Ra=105, in the presence of a body, a stable large-scale circulation is formed, occupying the entire cell. The movement of the body is irregular, stopping at two diagonally located corners of the cell. At Ra=106, the body movement scenario changes: a free-floating body performs quasi-stable oscillatory movements, moving back and forth along a trajectory representing the letter Pi rotated by 90 degrees. The introduction of a floating body leads to a decrease in the intensity of convective flow and convective heat transfer. It is shown that the values of the Reynolds and Nusselt numbers decrease significantly with increasing body size. The interaction between body and temperature boundary layers causes noticeable temporary fluctuations in heat fluxes, resulting in quasi-periodic fluctuations in the average temperature of the fluid. The most pronounced correlation between the temperature and the vertical coordinate of body position is observed in the case of large bodies and a higher value of the Rayleigh number.
subject: Articles
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creator: Sergey Anatol′yevich Filimonov
creator: Andrey Anatol′yevich Gavrilov
creator: Andrey Nikolayevich Sukhanovskii
creator: Andrey Yur′yevich Vasiliev
creator: Petr Gotlobovich Frick
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-11
publication date: 2026-03-11
starting page: 373
ending page: 384
doi: 10.7242/1999-6691/2025.18.4.27

Modeling the loss of stability and failure of mine shaft tubing supports
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description: The structural integrity and deformation reliability of mine shaft units play a crucial role in mining operations. A structural failure can lead to water ingress into the shaft and subsequent flooding. The deformation strength and reliability of a mine shaft depends on the efficiency and accuracy of the tubing support manufacturing process, which consists of several stages. This paper presents the results of numerical modeling of the deformation of a tubing ring under the effect of uneven pressure, which can occur during plugging. The following factors are considered in the modeling: contact interaction between tubing sections, contact interaction between the tubing and concrete, and the influence of the initial stress-strain state of the tubing formed during tightening of bolted connections. The problem is formulated within the framework of elastic-plastic deformation with account of finite strains. Based on the numerical solution, the conditions under which the loss of stability and failure of the tubing ring are possible were determined. A significant dependence was found between the pressure causing tubing failure and the area over which this pressure is distributed. This dependence is not monotonic and reaches a minimum when the applied pressure is distributed over the area of two tubing segments. The pressure in this case is approximately ≈1.4 MPa, i.e., it is in the range of realistic plugging pressures, which can reach 3 MPa. The obtained dependences allow assessing the feasibility of critical deformation states in tubing support, and they can be used to select optimal plugging modes when constructing mine shafts.
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creator: Aleksey Petrovich Shestakov
creator: Igor′ Nikolayevich Shardakov
creator: Irina Olegovna Glot
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 424
ending page: 432
doi: 10.7242/1999-6691/2025.18.4.31

Numerical simulation of natural vibration of a partially fluid-filled truncated conical shell in a gravity field
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description: In this article, the behavior of circular truncated conical shells partially filled with an ideal fluid is studied taking into account the gravitational effects on its free surface. The mathematical formulation of the problem of the elastic body dynamics is developed using the variational principle of virtual displacements and the relations of the classical theory of shells, which are based on the Kirchhoff-Love hypotheses. The behavior of the compressible fluid is described by the equations of a potential theory, which together with the boundary conditions are converted to a weak form using the Bubnov-Galerkin method. The hydrodynamic pressure exerted by the fluid on the inner surface of the shell is calculated using the linearized Bernoulli equation. The problem is solved in the framework of axisymmetric formulation based on a semi-analytical version of the finite element method. The natural frequencies are calculated using the QR transform. The identification of coupled vibration modes in the full frequency spectrum is accomplished through an iterative dynamic condensation procedure based on the Muller method. The reliability of the results obtained within the framework of the developed numerical model is confirmed by comparison with known data using examples of elastic and rigid shells. The influence of the cone angle on the lower frequencies of sloshing and coupled vibration modes is analyzed for shells with different boundary conditions (rigidly clamped, simply supported and cantilevered shells), different linear dimensions and levels of filling of the shell with fluid. It has been demonstrated that the character of the change in lower frequencies is determined by the magnitude of the angle at the apex and is determined by its geometric parameters for coupled modes and is independent of them in the case of sloshing modes.
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creator: Sergey Arkad′yevich Bochkarev
creator: Aleksandr Nikolayevich Senin
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 354
ending page: 367
doi: 10.7242/1999-6691/2025.18.3.26

Numerical study of the motion of a solid particle in the field of ultrasonic standing wave
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description: This numerical study examines the dynamics of a solid particle in a viscous fluid within a closed cavity under the influence of an ultrasonic standing wave. The study comprises two stages. First, the distribution of acoustic pressure in the quiescent fluid is calculated, ignoring disturbances induced by the particle or the flow. Two ultrasonic source configurations are considered: a planar ultrasonic vibrator extending throughout the entire lower boundary and a finite-size ultrasonic source. For a planar vibrator, the distribution of acoustic pressure of a harmonic plane wave is derived analytically from the one-dimensional Helmholtz equation. For finite-size sources, the same equation is numerically solved using the finite element method to account for the complex structure of the acoustic field and edge effects near the ultrasonic source. At the second stage, the computed pressure distribution is used to determine the spatial distribution of the Gor'kov potentials and the resulting acoustic radiation force, acting on the spherical particle of a specified size. The particle trajectory in the field of the ultrasonic standing wave is determined by solving numerically the equation of particle motion, taking into account the contributions from the added mass, acoustic radiation force, and drag force. The drag coefficient for the Reynolds numbers ranging from 0.1 to 0.8×10³ is calculated using the Schiller-Naumann correlation. Numerical simulations are conducted for different initial positions of the particle. The calculated data are consistent with the known concept of the solid particle motion in the field of ultrasonic standing wave, according to which a solid particle under the influence of the acoustic radiation forces tends to get into the region of the Gor'kov potential minimum, involving the standing wave nodes. Numerical simulation of the solid particle motion in the field of ultrasonic standing wave induced by the finite - size ultrasonic radiator allowed us t…
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creator: Ivan Olegovich Sboev
creator: Tat′yana Petrovna Lyubimova
creator: Konstantin Anatol′yevich Rybkin
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 433
ending page: 450
doi: 10.7242/1999-6691/2025.18.4.32

The onset and evolution of nonlinear convective regimes of binary mixtures in multilayer systems simulating synclinal geological folds
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description: This paper studies three-dimensional convective regimes of a binary mixture in a system of three porous bent layers, simulating a synclinal geological fold under the influence of a geothermal temperature gradient. The layers are assumed to have identical porosities and different permeabilities. A mixture of tetralin and dodecane taken in equal proportions is considered as the fluid saturating the porous medium. The components of the mixture represent the groups of hydrocarbons found in oil fields. The numerical study is performed to evaluate the linear stability of the mechanical equilibrium of a binary mixture in the inclined porous layer saturated with liquid in a gravity field under the influence of a strictly vertical temperature gradient. The convection threshold found is compared with the threshold obtained for the system with non-linear stability. In three-dimensional nonlinear calculations for a three-layer mixture, the permeabilities of all three layers are varied. Here it is assumed that the permeabilities of the outer layers are identical and always lower than the permeability of the inner layer. It was found that when the permeability of the inner layer is much higher than the permeabilities of the outer layers, the flow is localized in the inner layer. When the permeabilities of the outer and inner layers are sufficiently close, the flow is localized near the outer boundaries of the fold, even if the inner layer is more permeable than the outer layers. As the supercriticality increases, the formation of longitudinal rolls is observed in the initially plane-parallel flow (within each fold limb), and the flow becomes spiral. A further increase in supercriticality leads to a predominance of the longitudinal roll component in the flow and an increase in the number of longitudinal rolls along the fold limb (increase in the wave number of longitudinal rolls).
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creator: Ivan Shubenkov
creator: Tatyana Lyubimova
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-04-04
publication date: 2026-04-04
starting page: 31
ending page: 42
doi: 10.7242/1999-6691/2026.19.1.3

Some coupled diffusion problems for ternary systems
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description: Diffusion plays an important role in creating of new composite materials because it and accompanying phenomena participate in the formation of so-called transition layers. This paper presents possible boundary conditions for diffusion problems involving non--ideal contact between materials. A discontinuity in concentrations is also possible in the presence of ideal contact, due to differences in the mobilities of elements in different materials. Non-ideal contact leads to singularities in the boundary conditions, which may be due to various physical causes and leads to the concept of diffusion resistance at the boundary. It is shown that, within the framework of thermodynamics, the condition with an exponential dependence of the discontinuity in concentrations on temperature is substantiated. An algorithm for numerically solving the conjugate diffusive problem was developed based on component-wise separation of equations and an implicit second--order difference scheme, which is analogous to separation by physical processes. The boundary conditions were also approximated to second order using a Taylor series representation of the unknown quantities over small spatial steps (different for different regions) in the vicinity of the boundary. Using the problem of concentration redistribution between two materials as an example, the convergence of the algorithm and the consistency of the resulting concentration distributions at different points in time are illustrated. The parameters chosen for illustrations comply with thermodynamic constraints. Diffusion resistance at the interface between materials affects the concentration distribution and the rate at which equilibrium is established. Cross-diffusion coefficients do not alter the qualitative influence of imperfect contact on concentration redistribution. Such problems and the proposed algorithm can be useful in modeling the synthesis of composite materials, as well as in problems involving welding, soldering, and coat…
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creator: Sergey Yevgen′yevich Povernov
creator: Anna Georgiyevna Knyazeva
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 451
ending page: 467
doi: 10.7242/1999-6691/2025.18.4.33

On one solution to the problem of resonant oscillations of a lifting rope taking into account its slippage when winding on the surface of a drum
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description: In this paper, we develop a mathematical model and methods for analyzing a non-classical problem of longitudinal oscillations of a rope, the upper end of which is wound on a drum, and a load is fixed to its second end. Taking into account the slippage of rope elements along the drum rim allows one to adequately describe the real dynamic processes in the system. Representing the problem of rope oscillations with moving boundaries as a differential equation with non-integrable boundary conditions provides a non-classical generalization of the hyperbolic problem. The linearization of boundary conditions by the method of averaged estimates simplifies the initial statement of the problem. The construction of equivalent integro-differential equations with symmetric and time-dependent kernels, as well as with time-varying integration limits, creates the basis for applying the apparatus of integral equations. Consideration of cases both with and without slippage provides a comprehensive analysis of the dynamic characteristics of the system. Reducing the integro-differential equation to a dimensionless form by introducing new variables unifies the mathematical model. The solution of the obtained integro-differential equation without taking into account slippage using a combination of the approximate method for constructing solutions of integro-differential equations and the Kantorovich-Galerkin method demonstrates the acceptable level of accuracy for calculations. The expression for the amplitude of oscillations corresponding to the n-th dynamic mode, obtained by the asymptotic method, is an analytical basis for analyzing the resonance properties. The study of the phenomenon of steady-state resonance and passage through resonance of the system by numerical methods and the developed software package has practical value for the dynamic calculation of lifting devices.
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creator: Vladislav L′vovich Litvinov
creator: Maksim Vladimirovich Shamolin
creator: Kristina Vladislavovna Litvinova
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 332
ending page: 345
doi: 10.7242/1999-6691/2025.18.3.24

A magnetic field in the vicinity of a homogeneous magnet filling an axisymmetric, simply connected or multiply connected region
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description: Designing inertial magnetorheological sensors requires calculating the spatial distribution of the magnetic field strength and its gradient, which characterize the magnetic system of their sensing elements. A sensing element includes a combined source of a constant magnetic field, consisting of a set of axially magnetized cylindrical, disc, or ring magnets with a finite aspect ratio of their main parameters and non-magnetic inserts. The assembly of magnets and non-magnetic elements is covered with a magnetic fluid that acts as a lubricant and is held in place by the field created by the assembly. The aim of the study is to obtain an expression that mathematically represents the magnetic field in the vicinity of an individual permanent magnet or a system of these magnets. The magnetostatic problem was solved in two stages using Ampere's method based on abstract magnetic poles. In the first stage, the north pole of a semi-infinite magnetized cylinder was considered. In the vicinity of this magnet an expression for the scalar magnetic potential was found. In the second stage, by applying the principle of superposition, an expression for the field near disc and ring magnets in a cylindrical coordinate system was obtained. The constructed expressions contain infinite series, which makes them difficult to use in practice. The number of terms in a series sufficient to describe the field with a predetermined accuracy was determined by comparing the data of analytical and numerical calculations. The corresponding two-dimensional axisymmetric magnetostatic problem was solved numerically using the Finite Element Method Magnetics package. For disc and ring magnets, the magnetic field strength magnitude at points in the surrounding space was calculated. It is shown that the first six terms in a series are sufficient for analytical and numerical solutions to coincide within 2%, which is an acceptable deviation equal to the typical instrument error of a modern teslameter. As the n…
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creator: Olga Sergeyevna Krylasova
creator: Mikhail Andreyevich Koskov
creator: Alexey Sergeyevich Ivanov
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 346
ending page: 353
doi: 10.7242/1999-6691/2025.18.3.25

Effect of a traveling magnetic field on heat and mass transfer during submerged heater crystal growth
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description: The effect of traveling magnetic field (TMF) on heat and mass transfer during the 4" Ga:Ge semiconductor single crystal growth by the Axial Heat Processing technique has been studied numerically. The heat and mass transfer processes in the composite multiphase system consisting of crystal, melt, crucible, and submerged heater were analyzed in an axisymmetric unsteady formulation, with the instantaneous position and shape of the crystallization front being unknown and determined during the simulation. The influence of the TMF is accounted for through an analytically defined Lorentz force applied for the case of electrically insulating boundaries. The flow patterns and dopant distribution in the melt and crystal were determined for various temperature profiles applied to the submerged heater, axial temperature gradients, and at different directions and induction values of the applied TMF. It was found that the temperature boundary conditions applied to the submerged heater significantly affect mass transfer in the melt and, consequently, dopant segregation in the grown crystal. The downward TMF improves the axial and radial dopant homogeneity in the grown crystal. Within a certain range of intensities, the TMF reduced the intensity of flow driven by the radial temperature gradient at the submerged heater and the curvature of the crystallization front. Moreover, the positive effect of the TMF increased with higher growth rates. In the investigated configuration, a fourfold reduction in radial dopant segregation was achieved under stringent growth conditions by expanding the convective dopant transfer zone toward the symmetry axis through the TMF, thereby eliminating the accumulation of dopant concentration in this region.
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creator: Oleg Anatol′yevich Khlybov
creator: Tatiana Petrovna Lyubimova
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 319
ending page: 331
doi: 10.7242/1999-6691/2025.18.3.23

Simulation of convective polymerase chain reaction based on multiphase Lagrangian particle tracking model
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description: The article considers the issues of modeling the convective polymerase chain reaction (PCR) under the assumption that the solution of DNA molecules is a dispersed medium. The Lagrangian model of multiphase flows serves as a basis for simulations. In the framework of this approach, we consider the liquid phase to be continuous, applying the Navier-Stokes equations to describe its dynamics. To model the dispersed phase, we integrate the equation of motion of individual particles (DNA molecules) along their trajectories. Since the volume fraction of DNA molecules during the PCR reaction is small enough, the interphase interaction is assumed to be one-sided: molecular phases do not affect the motion and heat exchange of the solvent. Therefore, the general problem is split into two subproblems: the hydrodynamic part and the transport-reaction problem for particles. The mathematical model incorporates the Navier-Stokes equations written in the Hele-Shaw approximation, the motion equations for DNA molecules, and the specific condition for the PCR reactions. To model the reaction, we develop an original technique in which the history of particle movement through the reaction zone determines the criterion for transformation of a particle from one type to another. A numerical simulation of the convective PCR in a Hele-Shaw cell was carried out. The distribution fields of DNA molecules and the hydrodynamic and thermal fields were obtained. Zones with ongoing reactions were visualized. The dependence of the number of DNA molecules on the reaction time and the doubling time of the number of molecules were established. The results are consistent with the data of other convective PCR models. The positive aspects of the model used are that it provides complete information about the behavior of individual particles, including their coordinates, velocities, residence times in reaction zones, and traveled distances. Additionally, the developed approach can be used to ensure fine-tunin…
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creator: Ramil′ Rifgatovich Siraev
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 307
ending page: 318
doi: 10.7242/1999-6691/2025.18.3.22

Multi-harmonic balance method in structural element ratcheting problems
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description: The ratcheting theory originated in the 1960s. In mechanics of deformable bodies, it is used to assess the strength of structural elements (gas turbines, high-temperature reactors, etc.) operating under intense cyclic thermal stresses. This study aims to investigate possible modes of elastic-plastic deformation in pressure vessels under cyclically varying temperature conditions, assuming an elastic-ideal plastic material behavior model. Due to material hardening, analytical methods are not sufficient to solve this problem, and numerical methods must be used. The number of calculation cycles significantly affects a process's result: a large number of these cycles can create modeling difficulties due to limited time and computational resources. Therefore, the Direct Cyclic Method (DCM) has become increasingly popular in engineering practice for solving this type of problems. This method is an application of the multi-harmonic balance technique to the problems of quasistatic cyclic loading of viscoelastic-plastic materials. The validity of the DCM method is evaluated by comparing it with the method of direct nonlinear analysis of loading history when assessing the adaptability of vessels under cyclic thermal stresses. The computational efficiency of the DCM was investigated for varying finite element mesh sizes and loading cycles. It is shown that the limitations of the DCM become apparent in cases where a stable periodic solution does not exist.
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creator: Roman Valer′yevich Fedorenko
creator: Alexei Vyacheslavovich Lukin
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 295
ending page: 306
doi: 10.7242/1999-6691/2025.18.3.21

A three-phase hydrodynamic phase field model with stabilization of the Cahn-Hilliard equation
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description: A numerical implementation of a three-phase hydrodynamic phase-field model is presented, which combines the Navier-Stokes equations for incompressible fluid and the Cahn-Hilliard equation. The phase field model is highly capable for modeling multiphase media, but the numerical implementation of the phase field method has a number of computational difficulties associated with the stability of numerical schemes and, as a consequence, the need to choose a small time step, which complicates the calculations. The paper proposes a method for stabilizing the numerical algorithm by adding a fictitious relaxation derivative of the chemical potential, which reduces the spectral radius of the iteration matrix for the Cahn-Hilliard equation and allows a significant increase in the time step without losing stability. The implementation uses semi-implicit discretization and the projection method to calculate the velocity and pressure. Verification calculations are performed in a square domain with solid walls for a model fluid consisting of three phases. In static tests for different values of surface tension coefficients, equilibrium configurations were obtained in accordance with the expected contact angles at the junction of the three phases. In dynamic tests, it was shown that the model correctly reproduces the fall of a drop through the boundary of a two-layer system, as well as the collision of two particles of different phases moving in the third phase.
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creator: Sergei Anatol′yevich Prokopev
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 264
ending page: 275
doi: 10.7242/1999-6691/2025.18.3.19

Numerical simulation of flux expulsion in a plain channel MHD flow
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description: Numerical simulation of forced magnetohydrodynamic (MHD) channel flow is performed under conditions where the magnetic Reynolds number is comparable to or significantly exceeds 1. The dimensionless parameters of the problem, used for verification, correspond to flow regimes characterized by the complex MHD interaction between the flow and the magnetic field. The aim of this work is to verify and analyze the performance and accuracy of numerical simulation software packages COMSOL Multiphysics, ANES, OpenFOAM, and Elmer in application to two different formulations of the considered problem: one written in terms of the induced magnetic field, and the other in terms of the magnetic vector potential. The results of the author's calculations are compared with the results from the approximate analytical solution for a one-dimensional formulation and with those from other authors. A comparative analysis indicates the key role of a nonlinear term in the equation of motion, which correctly models the phenomenon of hydraulic resistance crisis during the transition from Hartmann flow to Poiseuille flow. Neglecting this term leads to significant errors in the representation, especially, of unsteady Poiseuille flow. The computational experiments conducted by the authors, as well as those known from literature sources, show that the models of all software packages tested in this work are capable of reproducing the main flow patterns; however, the highest accuracy is achieved with strict adherence to the Courant criterion. The model implemented in OpenFOAM demonstrates values especially close to the published values in the Poiseuille regime. In terms of computational efficiency, the best performance is shown by the OpenFOAM system (open-source) and the freely distributed ANES, both implemented using the finite volume method. The finite element models of COMSOL and Elmer packages are characterized by longer computation time and lower parallelization efficiency. Based on the obtaine…
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creator: Ivan Aleksandrovich Smolyanov
creator: Yevgeniy Igorevich Shmakov
creator: Yaroslav Igorevich Listratov
creator: Daniil Aleksandrovich Berdyugin
creator: Ivan Aleksandrovich Belyaev
creator: Oleg Yur′yevich Zikanov
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 276
ending page: 294
doi: 10.7242/1999-6691/2025.18.3.20

Modeling the temperature field dynamics during the Czochralski single crystal growth in a non-stationary approximation
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description: The transient process of growing axisymmetric crystals by the liquid-encapsulated Czochralski method is considered. The mathematical model accounts for heat transfer in the crucible-crystal-melt-encapsulant, formation of the melt/encapsulant meniscus, crystallization interface movement, and changes in crystal radius. A new algorithm was developed to determine the lateral surface shape of the crystal during the process. The proposed numerical approach utilizes a geometrically conservative difference scheme that guarantees the fulfillment of conservation laws of energy and mass. The special splitting technique is used to solve the corresponding set of finite difference equations. The proposed approach ensures the consistency of crystal shape evolution with conservation laws. The designed numerical procedure is used to evaluate the impact of external thermal regime on the shape of the growing crystal. When the heater temperature is maintained constant, the crystal radius gradually decreases over time. To study the influence of the external temperature field on the shape of the lateral surface, the mathematical model is supplemented with a proportional-integral temperature controller equation that links the change in heater temperature to the radius of the growing crystal. In a general case, the application of an integral temperature controller leads to fluctuations in the crystal radius around a set value, with both the frequency and amplitude of fluctuations increasing progressively. Based on the results of the numerical experiments, the parameter values for a proportional-integral temperature controller that ensure the growth of crystals with a nearly constant radius are determined. The results of transient numerical simulations are compared with the results obtained using the quasi-steady-state model of crystal growth.
subject: Articles
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creator: Andrey Olegovich Gusev
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-10
publication date: 2025-08-10
starting page: 225
ending page: 242
doi: 10.7242/1999-6691/2025.18.2.17

MHD-stirring of a heavy impurity under a rotating magnetic field generated by a multi-section inductor
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description: We study numerically the efficiency of stirring a two-phase dispersed fluid (liquid metal with impurity particles) in a cylindrical cell using a multiphase two-fluid model. The stirring is driven by an electromagnetic force generated by a sectional rotating magnetic field inductor. The inductor consists of six annular segments evenly distributed along the height of the cell. Each segment generates a rotating magnetic field independently. We consider three electromagnetic force configurations. The first configuration corresponds to a co-directional rotation of the magnetic fields of all six inductors, matching the case of a classical rotating magnetic field. In the second configuration, the three upper rings generate a magnetic field rotating in one direction, while the lower three rotate in the opposite direction. In the third configuration, the rotation directions of the magnetic fields alternate along the cell height. We introduce a parameter characterizing the inhomogeneity of the impurity distribution. It was shown that the most efficient mixing is achieved in the second configuration, which is attributed to the emergence of a large-scale oscillatory flow regime. The uniform rotating magnetic field configuration provides the least efficient mixing due to low poloidal velocity. In the third configuration, oscillations in the impurity distribution inhomogeneity parameter associated with the chaotic nature of the flow are observed. The optimal stirring time at which the degree of impurity distribution inhomogeneity is the least is determined.
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creator: Roman Sergeyevich Okatev
creator: Gennadiy Leonidovich Losev
creator: Il′ya Vladimirovich Kolesnichenko
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-10
publication date: 2025-08-10
starting page: 127
ending page: 139
doi: 10.7242/1999-6691/2025.18.2.10

Numerical simulation of the aerodynamics of a cycloidal rotor in flight
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description: The paper presents numerical simulation of the aerodynamics of a cycloidal rotor in various modes. The cycloidal rotor is a rotor consisting of several blades parallel to its axis and capable of changing their pitch angle as it rotates. The rotor’s aerodynamics is modeled in the formulation of a three-dimensional turbulent incompressible air flow. The numerical model is based on the computational fluid dynamics methods, in particular, the computational domain is discretized by the control volume method, and the motion of blades is modeled using the sliding mesh method. The results of test calculations are in good agreement with the experimental data. It is shown that, during rotation, the blade passes two parts of rotor thrust generation, most of which falls on the lower half of the cycle. To find the rotor characteristics under flight conditions, calculations were performed for the flow around a single rotor by the incident flow with varying velocity and direction. It was found that the vertical component of the force increases with increasing rotor descent speed. Under a horizontal flow, the power and, accordingly, the rotor efficiency change greatly. The calculations performed for two rotors in the incident flow show that their parameters change significantly and in opposite directions with increasing flow velocity. In this case, the torque on the front rotor decreases with increasing flow velocity, and on the rear rotor it increases. At a moderate incident flow velocity, the rotors have almost no effect on each other. As the incident flow velocity increases, rotor control requires deflection of the air jet thrown off by the rotors, as a result of which the jet created by the front rotor falls on the rear rotor, which leads to deterioration of its characteristics.
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creator: Aleksandr Anatol′yevich Dekterev
creator: Artem Aleksandrovich Dekterev
creator: Dmitriy Aleksandrovich Dekterev
creator: Vasiliy Vasil′yevich Kretinin
creator: Andrey Vasil′yevich Sentyabov
creator: Sergey Anatol′yevich Filimonov
creator: Konstantin Andreyevich Finnikov
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-10
publication date: 2025-08-10
starting page: 202
ending page: 213
doi: 10.7242/1999-6691/2025.18.2.15

Numerical modeling of fatigue fracture in the light alloys produced by additive technology
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description: A new approach to optimization of process parameters of selective laser melting is proposed in this paper. The required fatigue life of the final SLM product is used as an optimization parameter. A two-stage algorithm is proposed to implement this approach. At the first stage, a three-dimensional non-stationary nonlinear problem of heat conduction for a multiphase system is solved. As a result of modeling, geometric parameters of single-layer and multilayer systems of overlapping tracks are determined. The influence of laser melting process parameters (power, speed, laser beam pitch) on the topological features of the formed microstructure is studied. Characteristic types and geometric parameters of quasi-regular defects of the material produced by selective laser melting in the form of "unmelted" and multiple "overmelted" areas are obtained. At the second stage, the influence of single and multiple defects on the fatigue strength of printed samples under high-frequency loading is studied using the previously proposed multi-mode fatigue failure model. It is shown that internal heterogeneity of the microstructure of materials printed by selective laser melting can lead to earlier subsurface initiation of fatigue cracks and significantly reduce the fatigue strength and durability of the product. This effect is more pronounced for systems of multiple defects. The proposed models and calculation algorithms allow calculating the fatigue strength and durability of samples or products obtained by selective laser melting, depending on the selected process parameters. Mathematical modeling and comparison of the fatigue life of corset samples obtained by selective laser melting with experimental data are carried out. Qualitative and quantitative correspondence between the modeling and experimental results is noted.
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creator: Il′ya Stepanovich Nikitin
creator: Vasiliy Ivanovich Golubev
creator: Aleksandr Dmitriyevich Nikitin
creator: Boris Andreyevich Stratula
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-10
publication date: 2025-08-10
starting page: 173
ending page: 189
doi: 10.7242/1999-6691/2025.18.2.13

Stability of a liquid layer in a rotating Hele–Shaw reactor under competition of buoyancy effects generated by inertial forces
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description: Technologies that involve studying heat and mass transfer processes in a rotating Hele-Shaw cell can be effectively used in particular in designing microfluidic devices and small-scale flow-type chemical reactors. A quasi-two-dimensional model allows recording density fields by optical methods, and rotation makes it possible to control them through spatially distributed inertial forces. As is known, in the limit of an infinitely thin layer, the Coriolis force disappears in a standard mathematical model. However, the experimental observations of a fluid flow in a rotating Hele-Shaw cell indicate that the Coriolis effect fully manifests itself. The correct derivation of the equation of motion in the Hele-Shaw and Boussinesq approximation leads to the appearance of a term responsible for the buoyancy of the medium element caused by the Coriolis force. In this paper, to study the new effect, we consider the problem of convective stability of a fluid with internal generation of a transport component, which can be either the concentration of a dissolved substance or the temperature of the medium. The study of the system includes finding its basic state and linear analysis of its stability, analysis of weakly nonlinear solutions near the first bifurcation point, direct numerical modeling of nonlinear convection regimes, and evaluation of the general properties of a disturbance spectrum and the branching of solutions near the equilibrium bifurcation. The character of the branching of solutions is determined by applying the method of multiple time scales. The weakly nonlinear analysis indicates that, when the Rayleigh number reaches a critical value, the steady-state equilibrium of the fluid is replaced by oscillatory convection. The finite difference method is used to obtain a complete picture of the nature of nonlinear dynamics. It is shown that the Coriolis force has a stabilizing effect on the basic state of the system. In the strongly nonlinear regimes of convection, th…
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creator: Vladimir Yur′yevich Utochkin
creator: Dmitriy Anatol′yevich Bratsun
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-04-17
publication date: 2025-04-17
starting page: 15
ending page: 31
doi: 10.7242/1999-6691/2025.18.1.2

Pressure field in a formation with a hydraulic fracture of finite length
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description: The pressure field in a layered, perfectly perforated, heterogeneous formation with a plane fluid flow toward a vertical hydraulic fracture is investigated using an analytical and numerical approach. Information about the pressure field is of great importance for oil and gas production, hydrogeology, and for improving the technology of extracting hydrocarbon raw materials from oil and gas hydrate deposits by pumping chemically active or radioactive solutions. An asymptotic method is used to construct an analytical solution in the leading approximation. A solution is given for the case when a critical pressure is maintained in the area of influence of injection wells on the state of the rock in the vicinity of the fracture tip, which under certain conditions corresponds to its spontaneous growth. A program is created based on the Laplace–Carson numerical image inversion algorithm, and spatiotemporal pressure distributions in the fracture and in the surrounding reservoir rock are calculated. It is shown that the pressure drop in the fracture becomes relatively quickly close to the injection pressure, and the pressure gradient tends to zero. In this case, the main pressure changes in the direction of fracture propagation are concentrated in a zone whose dimensions are significantly smaller than the dimensions of the disturbance zone in the direction transverse to the orientation of fracture. It has been established that in the collector, the pressure gradients along the path of the fracture propagation are much greater than the gradients in the areas of the reservoir that are lateral to the fracture. As a result, favorable conditions are created for crack growth. The results obtained allow us to determine the time it takes to get a critical pressure at the fracture tip, at which the process of autohydraulic fracturing begins.
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creator: Aleksandr Ivanovich Filippov
creator: Al′fred Yadgarovich Davletbaev
creator: Rafael′ Radikovich Gareev
creator: Marat Radikovich Gubaydullin
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-04-17
publication date: 2025-04-17
starting page: 5
ending page: 14
doi: 10.7242/1999-6691/2025.18.1.1

Construction and comparison of experimental and calculated interferograms for two-dimensional transparent gas flow
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description: The numerical simulation made in this research serves as a methodological and proof basis for the previously performed experiments on steady-state thermoconcentration convection in gas mixtures of dry air and undecane or water vapor. Experimental data were obtained by two methods: a thermocouple method for quantitative description of the heat flux and holographic interferometry for qualitative visualization of the transparent gas motion (as an alternative to the particle image velocimetry). Convection due to the simultaneous action of vapor concentration and temperature gradients is described by the ratio of the concentration Rayleigh number for the gas mixture and the thermal Rayleigh number for dry air at the same temperature. The quantitative data from thermocouple measurements are interpreted under the assumption of a single-vortex quasi-two-dimensional flow in a rectangular convective cell of dimensions 15х15х320 mm. The aim of the work is to verify and validate the flow of this type by comparing the experimental and calculated interferograms (light refractive index surface) obtained from numerical simulations of thermal convection of dry air. The boundary conditions and geometry of the problem correspond to the experimental conditions. The equations of thermal convection in the Boussinesq approximation are written in the formulation of the two-field approach. The system of differential equations is solved numerically using a grid method by means of a program written in the Python programming language. The experimental interferograms were processed manually in a graphic editor. A direct comparison of about fifty pairs of coinciding experimental and calculated interferograms relating to the same values of temperatures of the heater and cooler of the cell was performed. The comparison of the calculated data and measurements confirmed the correctness of prediction of a single-vortex two-dimensional convective gas flow.
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creator: Sergey Andreyevich Somov
creator: Aleksey Sergeyevich Ivanov
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-10
publication date: 2025-08-10
starting page: 214
ending page: 224
doi: 10.7242/1999-6691/2025.18.2.16

A mathematical model of motion of polymer systems with nanoaggregates in the pore space of an oil reservoir
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description: A percolation-hydrodynamic model of the process of oil displacement by polymer solutions with nanoaggregates of various structures has been formulated and numerically implemented. The model allows taking into account the features of the pore space structure and the nature of the interaction of nanoaggregates with its surface during the filtration of the polymer solution. The possibility of achieving a higher oil recovery factor in the case of using polymers with hyperbranched nanomaterials compared to the classical polymer effect is shown. A cycle of laboratory studies was implemented to verify the results of theoretical calculations obtained using the model and compare them with the experimental data. The oil displacement process was modeled in terms of the composite model of a reservoir element assembled from 10 standard core samples taken from one oil-bearing reservoir. Theoretical estimates are in qualitative agreement with the results of the laboratory experiments also conducted with a composite reservoir model, and their quantitative difference is due to the use of the rheological law for Newtonian fluids in the mathematical model. The experimental results showed that the studied polymers are characterized by a pseudoplastic flow regime, therefore the effective viscosity of the polymer solution is higher than that assumed in the calculations. Based on the theoretical and experimental studies, it can be concluded that the application of polymer systems containing hyperbranched nanoaggregates leads to a significant increase in the residual resistance factor, where the formation of a stable polymer structure significantly decreases a porous medium’s permeability in flooded channels. The percolation-hydrodynamic model presented in this paper allows for a more adequate consideration of the physicochemical processes that occur during polymer flooding of oil-saturated reservoirs.
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creator: Valeriy Vladimirovich Kadet
creator: Ivan Valer′yevich Vasilev
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-14
publication date: 2025-12-14
starting page: 249
ending page: 263
doi: 10.7242/1999-6691/2025.18.3.18

Travelling of a reflecting immersed disc in a convective layer heated by incident radiation
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description: The two-dimensional motions of a disc submerged at a fixed depth but floating freely in an extended layer of liquid heated by a radiation flux falling from above are studied. The motion of a body in a convective layer depends on a number of factors such as the size of the body, the geometry of the cavity and the physical properties of the fluid and the body. The main focus of this work is to reveal the role of the degree of homogeneity of the distribution of heating of the underlying surface by incident radiation. Numerical simulations allowed us not only to describe the motion of the disc, but also to show the full three-dimensional structure of the convective flow for different regimes. Verification laboratory experiments confirmed the adequacy of the numerical simulations and clarified the role of the optical properties of the floating body. The simulation results showed the sensitivity of the system to the homogeneity of the radiation flux. A change in the radiation distribution leads to a change in the structure of the large-scale circulation. In the case of homogeneous distribution, a toroidal vortex is formed with the liquid sinking in the central part, and in the case of inhomogeneous distribution with maximum heating in the centre, on the contrary, a vortex appeared with the liquid rising in the centre. Since the motion of a floating body is determined by large-scale flows, their rearrangement leads to qualitative changes in the spatial and temporal characteristics of the disc motion. The experiments with discs of different radiation transparency demonstrated that, when the transparency coefficient reaches 0.4, the wandering of the disc stops.
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creator: Sergey Anatol′yevich Filimonov
creator: Andrey Anatol′yevich Gavrilov
creator: Kirill Yur′yevich Litvintsev
creator: Andrey Yur′yevich Vasiliev
creator: Andrey Nikolayevich Sukhanovskii
creator: Petr Gotlobovich Frick
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-04-17
publication date: 2025-04-17
starting page: 112
ending page: 121
doi: 10.7242/1999-6691/2025.18.1.9

Computational macromechanics as a generalization of the ideas of S.K. Godunov
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description: This article presents a critical analysis of two approaches to mathematical modeling of physical-and-chemical processes in the continuum approximation. The first (continuous) approach is based on finding solutions of initial-boundary value problems, while the second (discrete) approach generalizes S.K. Godunov's ideas: dividing a domain into finite volumes such that the medium in each volume can be considered continuous, and all volumes are in a thermodynamic equilibrium state. All macroparameters, as well as other functions, are assumed constant within each volume and discontinuous at its faces. The description of physical-and-chemical processes in each finite volume is based on the fundamental conservation laws, combined with phenomenological laws, equations of state, and additional hypotheses. The discontinuous approximation (computational macromechanics) allows one to construct difference schemes without approximating differential equations, using yet physical constraints on the minimum spatial and temporal scales of the modeled physical-and-chemical processes (the hypothesis of continuity and local thermodynamic equilibrium). The article formulates the fundamental principles of computational macromechanics, presents the results of computational experiments and performs comparative analysis of the errors of numerical solutions. The study demonstrates the advantages of this approach for computer modeling, particularly in black-box software and for problems with discontinuous solutions or boundary conditions. The results obtained are of interest to specialists in the field of computational continuum mechanics and software developers.
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creator: Sergei Ivanovich Martynenko
rights: Copyright (c) 2026 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2026-03-13
publication date: 2026-03-13
starting page: 468
ending page: 484
doi: 10.7242/1999-6691/2025.18.4.34

A hybrid numerical-analytical approach for the simulation of antiplane vibrations of multilayered elastic waveguides with multiple inhomogeneities
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description: Computer simulation of the excitation, propagation and scattering of elastic waves holds promise in designing structural health monitoring systems, in developing new ultrasonic non-destructive testing methods, in seismic sounding and sensorics and in other applications. This paper presents a further development of the hybrid numerical-analytical approach that allow analysis of the wave structure of the solution of dynamic boundary value problems in multilayer elastic waveguides with multiple local inhomogeneities, vibration sources and sensors. The approach is based on a grid solution of the corresponding dynamic problem in local domains with obstacles, which subsequently couples with the expansion in the form of traveling waves in homogeneous parts of the waveguide. In this form, the hybrid approach allows to construct solutions for complex geometries and defects, and it uses analytical representations to obtain a physically clear insight into the wave process for homogeneous parts of the waveguide. The proposed computational scheme is described for the problem of SH-wave propagation in a 2-D multilayer waveguide with single or multiple obstacles, and it can be generalized to the case of oscillations of isotropic and orthotropic materials. The hybrid approach is numerically verified based on comparison with the solutions of the considered problems obtained by other methods. The possibility of optimizing the developed computational scheme in the case of waveguides with multiple regions with inhomogeneities in order to reduce computational costs is indicated. The problem of diffraction of the SH-waves on a stringer, which were excited by a surface source of vibrations and measured by a piezoelectric sensor, is considered as an example of the use of a hybrid approach for parametric analysis of wave processes.
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creator: Aleksandr Aleksandrovich Evdokimov
creator: Polina Alekseyevna Nets
creator: Bogdan Mikhaylovich Lesin
creator: Artem Aleksandrovich Eremin
rights: Copyright (c) 2025 Computational Continuum Mechanics http://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-10
publication date: 2025-08-10
starting page: 140
ending page: 154
doi: 10.7242/1999-6691/2025.18.2.11