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Symmetry
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Applied Mathematics and Fluid Dynamics
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Applied Mathematics and Fluid Dynamics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 6589

Special Issue Editors

Dr. Sergey Ershkov

E-Mail Website
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
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Roman V. Shamin

E-Mail Website
Guest Editor
MIREA—Russian Technological University, 78 Vernadsky Avenue, Moscow 119454, Russia
Interests: giant waves; freak-wave formation in the ocean; hydrodynamics of fluid flows with a free surface; nonlinear wave phenomena in hydrodynamics; tidal phenomena; theoretical hydrodynamics; mathematical modelling and simulation in fluid mechanics; physics of the ocean
Dr. Evgeniy Yur’evich Prosviryakov

E-Mail Website
Guest Editor
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
Special Issues, Collections and Topics in MDPI journals

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, with an emphasis on symmetry concepts stemming from group analysis or topological forms of the solutions. In this Special Issue, you can publish 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. The authors 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.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Dr. Sergey Ershkov
Prof. Dr. Roman V. Shamin
Dr. Evgeniy Yur’evich Prosviryakov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Exact solution
  • Approximate solutions
  • Analytical methods in fluid mechanics
  • Numerical methods in fluid mechanics
  • Symmetry concept
  • 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

Published Papers (4 papers)

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Research

15 pages, 5719 KiB  
Article
On the Semi-Analytical Solutions in Hydrodynamics of Ideal Fluid Flows Governed by Large-Scale Coherent Structures of Spiral-Type
by Sergey V. Ershkov, Alla Rachinskaya, Evgenii Yu. Prosviryakov and Roman V. Shamin
Symmetry 2021, 13(12), 2307; https://doi.org/10.3390/sym13122307 - 3 Dec 2021
Cited by 5 | Viewed by 1809
Abstract
We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be [...] Read more.
We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be recognized as special invariant at symmetry reduction. Examples of such structures are widely presented in nature in “wind-water-coastline” interactions during a long-time period. Our suggested mathematical approach has obvious practical meaning as tracing process of formation of the paths or trajectories for material flows of fallout descending near ocean coastlines which are forming its geometry or bottom surface of the ocean. In our presentation, we explore (as first approximation) the case of non-stationary flows of Euler equations for incompressible fluids, which should conserve the Bernoulli-function as being invariant for the aforementioned system. The current research assumes approximated solution (with numerical findings), which stems from presenting the Euler equations in a special form with a partial type of approximated components of vortex field in a fluid. Conditions and restrictions for the existence of the 2D and 3D non-stationary solutions of the aforementioned type have been formulated as well. Full article
(This article belongs to the Special Issue Applied Mathematics and Fluid Dynamics)
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16 pages, 509 KiB  
Article
Exact Solutions of Boundary Layer Equations in Polymer Solutions
by Oksana A. Burmistrova, Sergey V. Meleshko and Vladislav V. Pukhnachev
Symmetry 2021, 13(11), 2101; https://doi.org/10.3390/sym13112101 - 5 Nov 2021
Cited by 2 | Viewed by 1296
Abstract
The paper presents new exact solutions of equations derived earlier. Three of them describe unsteady motions of a polymer solution near the stagnation point. A class of partially invariant solutions with a wide functional arbitrariness is found. An invariant solution of the stationary [...] Read more.
The paper presents new exact solutions of equations derived earlier. Three of them describe unsteady motions of a polymer solution near the stagnation point. A class of partially invariant solutions with a wide functional arbitrariness is found. An invariant solution of the stationary problem in which the solid boundary is a logarithmic curve is constructed. Full article
(This article belongs to the Special Issue Applied Mathematics and Fluid Dynamics)
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15 pages, 323 KiB  
Article
Solvability Analysis of a Mixed Boundary Value Problem for Stationary Magnetohydrodynamic Equations of a Viscous Incompressible Fluid
by Gennadii Alekseev and Roman V. Brizitskii
Symmetry 2021, 13(11), 2088; https://doi.org/10.3390/sym13112088 - 4 Nov 2021
Cited by 3 | Viewed by 1235
Abstract
We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of electrically conducting viscous fluid in a 3D-bounded domain, which [...] Read more.
We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of electrically conducting viscous fluid in a 3D-bounded domain, which has the boundary comprising several parts with different physical properties. The global solvability of the boundary value problem is proved, a priori estimates of the solutions are obtained, and the sufficient conditions on data, which guarantee a solution’s local uniqueness, are determined. Full article
(This article belongs to the Special Issue Applied Mathematics and Fluid Dynamics)
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18 pages, 410 KiB  
Article
A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
by Noman Sarwar, Muhammad Imran Asjad, Thanin Sitthiwirattham, Nichaphat Patanarapeelert and Taseer Muhammad
Symmetry 2021, 13(11), 2039; https://doi.org/10.3390/sym13112039 - 29 Oct 2021
Cited by 18 | Viewed by 1981
Abstract
In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary [...] Read more.
In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative model generalized to fractional model is based on a generalized Fourier law. The solutions for energy and velocity equations are obtained after making the equations dimensionless. To check the insight of the physical parameters, especially the symmetric behavior of fractional parameters, it is found that for small and large values of time, fluid properties show dual behavior. Since the fractional derivative exhibits the memory of the function at the chosen value of time, therefore the present fractional model is more suitable in exhibiting memory than the classical model. Such results can be useful in the fitting of real data where needed. In the limiting case when fractional parameters are taken β=γ = 0 and α = 1 for both velocity and temperature, we get the solutions obtained with ordinary derivatives from the existing literature. Full article
(This article belongs to the Special Issue Applied Mathematics and Fluid Dynamics)
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