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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 July 2023) | Viewed by 18998

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Special Issue Editors

Dr. Sergey Ershkov

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Guest Editor

1. Department of Scientific Researches, Plekhanov Russian University of Economics, 117997 Moscow, Russia
2. Sternberg Astronomical Institute, M.V. Lomonosov’s Moscow State University, 13 Universitetskij Prospect, 119992 Moscow, Russia
Interests: Navier–Stokes equations; Euler equations; analytical methods in fluid mechanics; theoretical hydrodynamics; fluid–body interactions; rigid body dynamics in a fluid; non-Newtonian fluids; glacier dynamics; mathematical modelling in fluid dynamics; tidal phenomena, celestial mechanics; dynamics of rigid body rotation
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Dr. Evgeniy Yur’evich Prosviryakov

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Sector of Nonlinear Vortex Hydrodynamics, Institute of Engineering Science, Ural Branch of the Russian Academy of Sciences, 620049 Ekaterinburg, Russia
Interests: exact solutions; mathematical fluid dynamics; heat and mass transfer; mathematical modelling and simulation in fluid dynamics; geophysical hydrodynamics; counterflows
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Special Issue Information

Dear Colleagues,

This Special Issue will include high-quality peer-reviewed papers on applied mathematics and fluid dynamics with a focus on numerical and analytical studies of fluid flows or on pure theoretical research in the field of theoretical hydrodynamics. In this Special Issue, we invite scientific articles on exact and approximate solutions of the Navier–Stokes equations, Euler equations, vortex hydrodynamics, tidal phenomena, computational fluid dynamics, convection, diffusion, thermal diffusion, MHD phenomena, physicochemical hydrodynamics, and plasma physics. Contributors are given the opportunity to publish research on the solution of new model boundary value problems for geophysical hydrodynamics or applying the ansatz of boundary layer theory, on fluid–body interactions and rigid body dynamics in a fluid, along with solving engineering problems in fluid mechanics, regarding glacier dynamics and the nonlinear hydrodynamics of Newtonian or non-Newtonian fluids, including polymers and other fluids with non-classical properties such as nanofluids and microfluidic phenomena.

Dr. Sergey Ershkov
Dr. Evgeniy Yur’evich Prosviryakov
Guest Editors

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Keywords

exact solution
approximate solutions
analytical methods in fluid mechanics
numerical methods in fluid mechanics
theoretical hydrodynamics
group analysis of the solutions
Navier–Stokes equations
Euler equations
vortex hydrodynamics
tidal phenomena
MHD phenomena
plasma physics
Newtonian and non-Newtonian fluids
heat and mass transfer
mathematical modeling
computational fluid dynamics
convection
diffusion
thermal diffusion
magnetic hydrodynamics
physicochemical hydrodynamics
fluid–body interactions
glacier dynamics
rigid (or quasi-rigid) body dynamics in a fluid
existence and uniqueness theorems
nanofluids
microfluidic phenomena
engineering problems in fluid mechanics

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Published Papers (11 papers)

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Research

10 pages, 3078 KiB

Open AccessArticle

Mathematical Modeling of Single and Phase Autowaves in a Ferrocolloid

by Vladimir Chekanov, Natalya Kandaurova and Anna Kovalenko

Mathematics 2023, 11(16), 3575; https://doi.org/10.3390/math11163575 - 18 Aug 2023

Viewed by 808

Abstract

This paper describes a mathematical model of an autowave process in a cell with a ferrocolloid. The model is a system of differential coupled equations of the second order and differs from the previously presented model in terms of its original boundary conditions. The mathematical modeling of autowaves presented in this work constitutes an innovative approach, since the characteristics of the wave process are not initially included in the model but the model demonstrates a wave motion. A 2D solution of the model, which shows the correctness of the described mechanism of the autowave process, i.e., the recharging of magnetic particles in dense near-electrode layers formed near the electrodes under the influence of an electric field, is obtained. The propagation of single and phase autowaves is demonstrated in a computer experiment. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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15 pages, 449 KiB

Open AccessArticle

Dynamics of Benjamin–Ono Solitons in a Two-Layer Ocean with a Shear Flow

by Pawan Negi, Trilochan Sahoo, Niharika Singh and Yury Stepanyants

Mathematics 2023, 11(15), 3399; https://doi.org/10.3390/math11153399 - 3 Aug 2023

Cited by 3 | Viewed by 932

Abstract

The results of a theoretical study on Benjamin–Ono (BO) soliton evolution are presented in a simple model of a two-layer ocean with a shear flow and viscosity. The upper layer is assumed to move with a constant speed relative to the lower layer with a tangential discontinuity in the flow profile. It is shown that in the long-wave approximation, such a model can be appropriate. If the flow is supercritical, i.e., its speed (U) exceeds the speed of long linear waves (

c_{1}

), then BO solitons experience “explosive-type” enhancement due to viscosity, such that their amplitudes increase to infinity in a finite time. In the subcritical regime, when

U < c_{1}

, BO solitons experience very slow decay due to viscosity. Soliton amplitude decays with time as

A \sim t^{- 1 / 2}

A \sim t^{- 1 / 3}

, depending on whether both layers are weakly viscous (the former case) or only the lower layer is viscous (the latter case). Estimates of "explosion time" are presented for real oceanic parameters. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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12 pages, 1782 KiB

Open AccessArticle

Euler–Darboux–Poisson Equation in Context of the Traveling Waves in a Strongly Inhomogeneous Media

by Ioann Melnikov and Efim Pelinovsky

Mathematics 2023, 11(15), 3309; https://doi.org/10.3390/math11153309 - 27 Jul 2023

Cited by 4 | Viewed by 1208

Abstract

The existence of traveling waves in an inhomogeneous medium is a vital problem, the solution of which can help in modeling the wave propagation over long distances. Such waves can be storm waves or tsunami waves in the seas and oceans. The presence of solutions in the form of traveling waves indicates that the wave propagates without reflection and, therefore, can transfer energy over long distances. Traveling waves within the framework of the 1D variable-coefficient wave equation exist only for certain configurations of an inhomogeneous medium, some of which can be found by transforming the original equation to the Euler–Darboux–Poisson equation. The solution of the last equation for certain parameter values is expressed in elementary functions, which are the sum of waves running in opposite directions. The mathematical features of such a transformation are discussed in this paper. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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12 pages, 305 KiB

Open AccessArticle

Optimal Dirichlet Boundary Control for the Corotational Oldroyd Model

by Evgenii S. Baranovskii and Mikhail A. Artemov

Mathematics 2023, 11(12), 2719; https://doi.org/10.3390/math11122719 - 15 Jun 2023

Cited by 2 | Viewed by 785

Abstract

In this article, we investigate an optimal control problem for the coupled system of partial differential equations describing the steady-state flow of a corotational-type Oldroyd fluid through a bounded 3D (or 2D) domain. The control function is included in Dirichlet boundary conditions for the velocity field; in other words, we consider a model of inflow–outflow control. The main result is a theorem that states sufficient conditions for the solvability of the corresponding optimization problem in the set of admissible weak solutions. Namely, we establish the existence of a weak solution that minimizes the cost functional under given constraints on controls and states. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

17 pages, 7358 KiB

Open AccessArticle

Mathematical Analysis of Mixed Convective Peristaltic Flow for Chemically Reactive Casson Nanofluid

by Humaira Yasmin and Zahid Nisar

Mathematics 2023, 11(12), 2673; https://doi.org/10.3390/math11122673 - 12 Jun 2023

Cited by 22 | Viewed by 1446

Abstract

Nanofluids are extremely beneficial to scientists because of their excellent heat transfer rates, which have numerous medical and industrial applications. The current study deals with the peristaltic flow of nanofluid (i.e., Casson nanofluid) in a symmetric elastic/compliant channel. Buongiorno’s framework of nanofluids was utilized to create the equations for flow and thermal/mass transfer along with the features of Brownian motion and thermophoresis. Slip conditions were applied to the compliant channel walls. The thermal field incorporated the attributes of viscous dissipation, ohmic heating, and thermal radiation. First-order chemical-reaction impacts were inserted in the mass transport. The influences of the Hall current and mixed convection were also presented within the momentum equations. Lubricant approximations were exploited to make the system of equations more simplified for the proposed framework. The solution of a nonlinear system of ODEs was accomplished via a numerical method. The influence of pertinent variables was examined by constructing graphs of fluid velocity, temperature profile, and rate of heat transfer. The concentration field was scrutinized via table. The velocity of the fluid declined with the increment of the Hartman number. The effects of thermal radiation and thermal Grashof number on temperature showed opposite behavior. Heat transfer rate was improved by raising the Casson fluid parameter and the Brownian motion parameter. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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29 pages, 626 KiB

Open AccessFeature PaperArticle

Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field

by Gennadii Alekseev

Mathematics 2023, 11(12), 2610; https://doi.org/10.3390/math11122610 - 7 Jun 2023

Cited by 2 | Viewed by 3999

Abstract

The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions for a magnetic field and the Dirichlet condition for velocity are considered. The role of controls in the control problems under study is played by normal and tangential components of the magnetic field given on different parts of the boundary and by the exterior current density. Quadratic tracking-type functionals for velocity, magnetic field or pressure are taken as cost functionals. The global solvability of the control problems under consideration is proved, an optimality system is derived and, based on its analysis, a mathematical apparatus for studying the local uniqueness and stability of the optimal solutions is developed. On the basis of the developed apparatus, the local uniqueness of solutions of control problems for specific cost functionals is proved, and stability estimates of optimal solutions are established. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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25 pages, 5034 KiB

Open AccessArticle

Reconstruction of Unsteady Wind Field Based on CFD and Reduced-Order Model

by Guangchao Zhang and Shi Liu

Mathematics 2023, 11(10), 2223; https://doi.org/10.3390/math11102223 - 9 May 2023

Cited by 1 | Viewed by 1345

Abstract

Short-term wind power forecasting is crucial for updating the wind power trading strategy, equipment protection and control regulation. To solve the difficulty surrounding the instability of the statistical model and the time-consuming nature of the physical model in short-term wind power forecasting, two innovative wind field reconstruction methods combining CFD and a reduced-order model were developed. In this study, POD and Tucker decomposition were employed to obtain the spatial–temporal information correlation of 2D and 3D wind fields, and their inverse processes were combined with sparse sensing to reconstruct multi-dimensional unsteady wind fields. Simulation and detailed discussion were performed to verify the practicability of the proposed algorithms. The simulation results indicate that the wind speed distributions could be reconstructed with reasonably high accuracy (where the absolute velocity relative error was less than 0.8%) using 20 sensors (which only accounted for 0.04% of the total data in the 3D wind field) based on the proposed algorithms. The factors influencing the results of reconstruction were systematically analyzed, including all-time steps, the number of basis vectors and 4-mode dimensions, the diversity of CFD databases, and the reconstruction time. The results indicated that the reconstruction time could be shortened to the time interval of data acquisition to synchronize data acquisition with wind field reconstruction, which is of great significance in the reconstruction of unsteady wind fields. Although there are still many studies to be carried out to achieve short-term predictions, both unsteady reconstruction methods proposed in this paper enable a new direction for short-term wind field prediction. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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10 pages, 1221 KiB

Open AccessArticle

Revisiting Long-Time Dynamics of Earth’s Angular Rotation Depending on Quasiperiodic Solar Activity

by Sergey Ershkov, Dmytro Leshchenko and Evgeniy Prosviryakov

Mathematics 2023, 11(9), 2117; https://doi.org/10.3390/math11092117 - 29 Apr 2023

Cited by 3 | Viewed by 3008

Abstract

Having taken into account the nonsymmetric form of Earth’s surface (which is an oblate spheroid as the first approximation, with oblateness of approx. 1/300), we outline in the current research that additional large-scale torques stem from unbalanced (reactive) reradiating heat flows back into outer space. They arise during long-time dynamics of Earth’s angular rotation depending on quasiperiodic solar activity. The key idea of our research supports the mainstream idea of most of the researchers in the scientific community regarding this matter. It stipulates that the activity of earthquakes strongly correlates with changes in the regime of Earth’s spin dynamics during all periods of observation. We have demonstrated here that the long-time dynamics of Earth’s angular rotation depends on the quasiperiodic solar activity by arising additional large-scale torques stemming from unbalanced (reactive) reradiating heat fluxes. The latter carry the momentum outside and at an unpredictable angle to the overall Earth’s surface back into outer space (due to the nonsymmetric form of Earth’s surface). Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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7 pages, 444 KiB

Open AccessArticle

Inelastic Collision Influencing the Rotational Dynamics of a Non-Rigid Asteroid (of Rubble Pile Type)

by Sergey Ershkov and Dmytro Leshchenko

Mathematics 2023, 11(6), 1491; https://doi.org/10.3390/math11061491 - 18 Mar 2023

Cited by 2 | Viewed by 1470

Abstract

We have considered here a novel particular model for dynamics of a non-rigid asteroid rotation, assuming the added mass model instead of the concept of Viscoelastic Oblate Rotators to describe the physically reasonable response of a ‘rubble pile’ volumetric material of asteroid with respect to the action of a projectile impacting its surface. In such a model, the response is approximated as an inelastic collision in which the projectile pushes the ‘rubble pile’ parts of the asteroid together to form a mostly solidified plug in the crater during the sudden impact on the asteroid’s surface. Afterwards, the aforementioned ‘solidified plug’ (having no sufficient adhesion inside the after-impact crater) will be pushed outside the asteroid’s surface by centrifugal forces, forming a secondary rotating companion around the asteroid. Thus, according to the fundamental law of angular momentum conservation, the regime of the asteroid’s rotation should be changed properly. Namely, changes in rotational dynamics stem from decreasing the asteroid’s mass (due to the fundamental law of angular momentum conservation). As the main finding, we have presented a new solving procedure for a semi-analytical estimation of the total mass of the aforementioned ‘solidified plug’, considering the final spin state of rotation for the asteroid with minimal kinetic energy reduced during a long time period by the inelastic (mainly, tidal) dissipation. The asteroid is assumed to be rotating mainly along the maximal inertia axis with a proper spin state corresponding to minimal energy with a fixed angular momentum. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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17 pages, 1324 KiB

Open AccessArticle

Optimization Method for Solving Cloaking and Shielding Problems for a 3D Model of Electrostatics

by Gennadii Alekseev and Alexey Lobanov

Mathematics 2023, 11(6), 1395; https://doi.org/10.3390/math11061395 - 13 Mar 2023

Viewed by 1436

Abstract

Inverse problems for a 3D model of electrostatics, which arise when developing technologies for designing electric cloaking and shielding devices, are studied. It is assumed that the devices being designed to consist of a finite number of concentric spherical layers filled with homogeneous anisotropic or isotropic media. A mathematical technique for solving these problems has been developed. It is based on the formulation of cloaking or shielding problems in the form of inverse problems for the electrostatic model under consideration, reducing the latter problems to finite-dimensional extremum problems, and finding their solutions using one of the global minimization methods. Using the developed technology, the inverse problems are replaced by control problems, in which the role of controls is played by the permittivities of separate layers composing the device being designed. To solve them, a numerical algorithm based on the particle swarm optimization method is proposed. Important properties of optimal solutions are established, one of which is the bang-bang property. It is shown on the base of the computational experiments that cloaking and shielding devices designed using the developed algorithm have the simplicity of technical implementation and the highest performance in the class of devices under consideration. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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11 pages, 427 KiB

Open AccessArticle

Multi-Shell Models of Celestial Bodies with an Intermediate Layer of Fluid: Dynamics in the Case of the Large Values of the Ekman Number

by Vladislav Sidorenko and Sergey Ramodanov

Mathematics 2023, 11(2), 296; https://doi.org/10.3390/math11020296 - 6 Jan 2023

Cited by 1 | Viewed by 1176

Abstract

We consider a mechanical system that is comprised of three parts: a rigid outer shell with a spherical cavity, a spherical core inside this cavity, and an intermediate layer of liquid between the core and the shell. Such a model provides an adequate description of the behavior of a wide variety of celestial bodies. The centers of the inner and outer liquid’s spherical boundaries are assumed to coincide. Assuming that the viscosity of the liquid is high, we obtained an approximate solution to the Navier–Stokes equations that describes a so called creeping flow of the liquid, which sets on after all transient processes die out. We note that the effect of the liquid on the rotational motion of the system can be modeled as a special torque acting upon the system with “solidified” fluid. Full article

(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)

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