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Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods
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Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods

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

Deadline for manuscript submissions: closed (20 December 2020) | Viewed by 12184

Special Issue Editor

Prof. Dr. Alexander N. Timokha

E-Mail Website
Guest Editor
1. Centre of Excellence“Centre for Autonomous Marine Operations and Systems” (AMOS), Department of Marine Technology, Norwegian University of Science and Technology (NTNU) , Otto Nielsens vei 10, 7491 Trondheim, Norway
2. Institute of Mathematics, National Academy of Sciences of Ukraine (NASU), Tereschenkivska 3, str., Kiev 01601, Ukraine
Interests: mathematical fluid mechanics; variational formalism in continuum media; fluid–structure interaction; surface wave theory including sloshing

Special Issue Information

Dear Colleagues,

This Special Issue has a three-fold topic. First, the topic covers the mathematical fundamentals (variational formalism, solvability and uniqueness theorems, etc.) of fluid mechanics, with primary emphasis on those appearing in nonlinear fluid dynamics; free-surface problems, including sloshing, porous media, interfacial, and multiphase flows; and Lagrangian-mean mass-transport theories. Secondly, the Special Issue focuses on the contemporary analytical mainstreams in fluid mechanics, which are in particular associated with the applied mathematical modelling of biomechanical swimming and flying, fluid transport at nanoscales, soft matter, and hydrodynamics of bacteria. Thirdly, the Special Issue welcomes authors who are working on developing analytical and semi-analytical methods and approaches in fluid mechanics, as well as authors who consider them as an important alternative/supplement to traditional, nowadays, computational fluid dynamics, simulations. In other words, this Special Issue would appreciate manuscripts written and submitted by researchers who love and enjoy mathematics in the classical and contemporary problems of fluid mechanics, regardless of whether the authors are mathematicians, engineers, or multidisciplinary scientists.

Prof. Dr. Alexander N. Timokha
Guest Editor

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • mathematical fluid mechanics
  • variational formalism
  • free-boundary problems
  • fluid–structure interaction
  • surface wave theory including sloshing
  • applied mathematical modelling in fluid mechanics
  • biomechanics
  • soft matter
  • Lagrangian mean
  • analytical approximate methods in fluid mechanics

Published Papers (5 papers)

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Research

13 pages, 1202 KiB  
Article
Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall
by Constantin Fetecau, Rahmat Ellahi and Sadiq M. Sait
Mathematics 2021, 9(1), 90; https://doi.org/10.3390/math9010090 - 04 Jan 2021
Cited by 24 | Viewed by 2921
Abstract
Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the [...] Read more.
Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state. Full article
(This article belongs to the Special Issue Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods)
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12 pages, 1755 KiB  
Article
Application of Implicit Pressure-Explicit Saturation Method to Predict Filtrated Mud Saturation Impact on the Hydrocarbon Reservoirs Formation Damage
by Mingxuan Zhu, Li Yu, Xiong Zhang and Afshin Davarpanah
Mathematics 2020, 8(7), 1057; https://doi.org/10.3390/math8071057 - 01 Jul 2020
Cited by 41 | Viewed by 2379
Abstract
Hydrocarbon reservoirs’ formation damage is one of the essential issues in petroleum industries that is caused by drilling and production operations and completion procedures. Ineffective implementation of drilling fluid during the drilling operations led to large volumes of filtrated mud penetrating into the [...] Read more.
Hydrocarbon reservoirs’ formation damage is one of the essential issues in petroleum industries that is caused by drilling and production operations and completion procedures. Ineffective implementation of drilling fluid during the drilling operations led to large volumes of filtrated mud penetrating into the reservoir formation. Therefore, pore throats and spaces would be filled, and hydrocarbon mobilization reduced due to the porosity and permeability reduction. In this paper, a developed model was proposed to predict the filtrated mud saturation impact on the formation damage. First, the physics of the fluids were examined, and the governing equations were defined by the combination of general mass transfer equations. The drilling mud penetration in the core on the one direction and the removal of oil from the core, in the other direction, requires the simultaneous dissolution of water and oil flow. As both fluids enter and exit from the same core, it is necessary to derive the equations of drilling mud and oil flow in a one-dimensional process. Finally, due to the complexity of mass balance and fluid flow equations in porous media, the implicit pressure-explicit saturation method was used to solve the equations simultaneously. Four crucial parameters of oil viscosity, water saturation, permeability, and porosity were sensitivity-analyzed in this model to predict the filtrated mud saturation. According to the results of the sensitivity analysis for the crucial parameters, at a lower porosity (porosity = 0.2), permeability (permeability = 2 mD), and water saturation (saturation = 0.1), the filtrated mud saturation had decreased. This resulted in the lower capillary forces, which were induced to penetrate the drilling fluid to the formation. Therefore, formation damage reduced at lower porosity, permeability and water saturation. Furthermore, at higher oil viscosities, due to the increased mobilization of oil through the porous media, filtrated mud saturation penetration through the core length would be increased slightly. Consequently, at the oil viscosity of 3 cP, the decrease rate of filtrated mud saturation is slower than other oil viscosities which indicated increased invasion of filtrated mud into the formation. Full article
(This article belongs to the Special Issue Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods)
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16 pages, 524 KiB  
Article
Effect of a Boundary Layer on Cavity Flow
by Yuriy N. Savchenko, Georgiy Y. Savchenko and Yuriy A. Semenov
Mathematics 2020, 8(6), 909; https://doi.org/10.3390/math8060909 - 03 Jun 2020
Cited by 1 | Viewed by 2319
Abstract
Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines [...] Read more.
Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines coinciding with the streamlines. The flow between the streamlines is vortex free. The problem is to determine the shape of the streamlines and cavity boundary. The pressure on the cavity boundary is constant and equal to the vapour pressure of the liquid. The pressure is continuous across the streamlines. The theory of complex variables is used to determine the flow in the following subregions coupled via their boundary conditions: a flow in channels with curved walls, a cavity flow in a jet and an infinite flow along a curved wall. The numerical approach is based on the method of successive approximations. The numerical procedure is verified considering a body with a sharp edge, for which the point of cavity detachment is fixed. For smooth bodies, the cavity detachment is determined based on Brillouin’s criterion. It is found that the inflow vorticity delays the cavity detachment and reduces the cavity length. The results obtained are compared with experimental data. Full article
(This article belongs to the Special Issue Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods)
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25 pages, 6491 KiB  
Article
Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories
by Sayed M. Abo-Dahab, Alaa A. El-Bary, Yas Al-Hadeethi and Mohamed Alkashif
Mathematics 2020, 8(5), 735; https://doi.org/10.3390/math8050735 - 07 May 2020
Cited by 4 | Viewed by 1876
Abstract
The main aim of this paper is to study two temperature thermoelasticity in a generalization form to solve the half-space problem of two dimensions under gravity, perturbed magnetic field, and initial stress. The fundamental equations are solved considering a new mathematical technique under [...] Read more.
The main aim of this paper is to study two temperature thermoelasticity in a generalization form to solve the half-space problem of two dimensions under gravity, perturbed magnetic field, and initial stress. The fundamental equations are solved considering a new mathematical technique under Lord-Şhulman (LS), Green-Naghdi (GN type III) and three-phase-lag (3PHL) theories to investigate displacement, stress components, and temperature distribution. The results obtained by the three theories, i.e., (LS), (GN type III), and (3PHL), considering the absence and the presence of gravity, initial stress, and magnetic field have been compared. The results were numerically calculated and graphically displayed to exhibit the physical meaning of the phenomenon and the external parameters’ effect. A comparison has been presented between the results obtained in the absence and the presence of the external considered parameters and with the previously obtained results by other researchers. Full article
(This article belongs to the Special Issue Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods)
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11 pages, 1977 KiB  
Article
Impulsive Motion Inside a Cylindrical Cavity
by Yuriy Savchenko, Georgiy Savchenko and Yuriy A. Semenov
Mathematics 2020, 8(2), 192; https://doi.org/10.3390/math8020192 - 05 Feb 2020
Cited by 2 | Viewed by 1954
Abstract
Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive [...] Read more.
Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive force generated by the impacts is the main concern in this paper. The analysis is performed in the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. The primary interest of the study is to determine the added mass taking into account the shape of the cavity. The theoretical study is based on the integral hodograph method, which makes it possible to obtain analytic expressions for the flow potential and for the complex velocity in an auxiliary parameter plane and obtain a parametric solution to the problem. The problem is reduced to a system of two integro-differential equations in two unknowns: the velocity magnitude on the cavity boundary and the slope of the velocity angle to the body. The equations are solved numerically using the method of successive approximations. The obtained results show that the added mass of an arc impacting a cylindrical cavity depends heavily on the arc angle. As the angle tends to zero or the radius of the cavity tends to infinity, the obtained solution predicts the added mass corresponding to a plate impacting a flat free surface. Full article
(This article belongs to the Special Issue Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods)
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