Mathematical Dynamic Flow Models

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

Deadline for manuscript submissions: 31 July 2024 | Viewed by 8725

Special Issue Editors

Departamento de Matemática e CIMA, Universidade de Évora, Évora, Portugal
Interests: mathematical analysis and numerical methods for ODE and PDE, with applications related with fluid mechanics
Institute of Earth Sciences, University of Evora, 7000-645 Évora, Portugal
Interests: earthquake source seismology and seismic risk; 3D structure velocity models; strong ground motion modelling; seismotectonics and geodynamic; instrumental seismology and seismic networks; applied geophysics; geodynamic and geophysical models
Special Issues, Collections and Topics in MDPI journals
Faculty of Mechanical Engineering (FS), Czech Technical University, 166 36 Prague, Czech Republic
Interests: mathematical modeling; numerical methods; geophysical flows; stably stratified flows; atmospheric flows; turbulent flows; biomedical fluids flows; non-Newtonian fluids; blood flows; blood coagulation

Special Issue Information

Dear Colleagues,

This Special Issue of Mathematics MDPI aims to attract both theoretical and applied research papers focusing on a wide range of topics in the areas of theoretical and applied mathematical fluid mechanics. This Special Issue is devoted to original research and review papers of high scientific value in all areas of mathematical fluid mechanics and its applications, paying special attention to mathematical models and numerical simulations relevant in various physical, geophysical, chemical, biological, and engineering applications. This issue aims to collect a number of relevant articles in this branch of science, where novelties often appear not only in the theoretical field, but also in the field of applications.

Prof. Dr. Fernando Carapau
Prof. Dr. Mourad Bezzeghoud
Prof. Dr. Tomáš Bodnár
Guest Editors

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Keywords

  • mathematical models
  • newtonian fluids and non-newtonian fluids
  • unsteady and steady flows
  • dynamic flow applications
  • geodynamic models
  • numerical simulations

Published Papers (7 papers)

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Research

10 pages, 837 KiB  
Article
Numerical Solution of Transition to Turbulence over Compressible Ramp at Hypersonic Velocity
by Jiří Holman
Mathematics 2023, 11(17), 3684; https://0-doi-org.brum.beds.ac.uk/10.3390/math11173684 - 26 Aug 2023
Viewed by 537
Abstract
This work deals with the numerical solution of hypersonic flow of viscous fluid over a compressible ramp. The solved case involves very important and complicated phenomena such as the interaction of the shock wave with the boundary layer or the transition from a [...] Read more.
This work deals with the numerical solution of hypersonic flow of viscous fluid over a compressible ramp. The solved case involves very important and complicated phenomena such as the interaction of the shock wave with the boundary layer or the transition from a laminar to a turbulent state. This type of problem is very important as it is often found on re-entry vehicles, engine intakes, system and sub-system junctions, etc. Turbulent flow is modeled by the system of averaged Navier–Stokes equations, which is completed by the explicit algebraic model of Reynolds stresses (EARSM model) and further enhanced by the algebraic model of bypass transition. The numerical solution is obtained by the finite volume method based on the rotated-hybrid Riemann solver and explicit multistage Runge–Kutta method. The numerical solution is then compared with the results of a direct numerical simulation. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
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16 pages, 325 KiB  
Article
Remarks on the “Onsager Singularity Theorem” for Leray–Hopf Weak Solutions: The Hölder Continuous Case
by Luigi C. Berselli
Mathematics 2023, 11(4), 1062; https://0-doi-org.brum.beds.ac.uk/10.3390/math11041062 - 20 Feb 2023
Cited by 2 | Viewed by 826
Abstract
In this paper, we first present an overview of the results related to energy conservation in spaces of Hölder-continuous functions for weak solutions to the Euler and Navier–Stokes equations. We then consider families of weak solutions to the Navier–Stokes equations with Hölder-continuous velocities [...] Read more.
In this paper, we first present an overview of the results related to energy conservation in spaces of Hölder-continuous functions for weak solutions to the Euler and Navier–Stokes equations. We then consider families of weak solutions to the Navier–Stokes equations with Hölder-continuous velocities with norms uniformly bound in terms of viscosity. We finally provide the proofs of our original results that extend the range of allowed exponents for inviscid limits producing solutions to the Euler equations satisfying the energy equality, and improve the so-called “Onsager singularity” theorem. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
22 pages, 15078 KiB  
Article
Analysis of Drag Coefficients around Objects Created Using Log-Aesthetic Curves
by Mei Seen Wo, R.U. Gobithaasan, Kenjiro T. Miura, Kak Choon Loy and Fatimah Noor Harun
Mathematics 2023, 11(1), 103; https://0-doi-org.brum.beds.ac.uk/10.3390/math11010103 - 26 Dec 2022
Cited by 1 | Viewed by 1456
Abstract
A fair curve with exceptional properties, called the log-aesthetic curves (LAC) has been extensively studied for aesthetic design implementations. However, its implementation in terms of functional design, particularly hydrodynamic design, remains mostly unexplored. This study examines the effect of the shape parameter α [...] Read more.
A fair curve with exceptional properties, called the log-aesthetic curves (LAC) has been extensively studied for aesthetic design implementations. However, its implementation in terms of functional design, particularly hydrodynamic design, remains mostly unexplored. This study examines the effect of the shape parameter α of LAC on the drag generated in an incompressible fluid flow, simulated using a semi-implicit backward difference formula coupled with P2P1 Taylor–Hood finite elements. An algorithm was developed to create LAC hydrofoils that were used in this study. We analyzed the drag coefficients of 47 LAC hydrofoils of three sizes with various shapes in fluid flows with Reynolds numbers of 30, 40, and 100, respectively. We found that streamlined LAC shapes with negative α values, of which curvature with respect to turning angle are almost linear, produce the lowest drag in the incompressible flow simulations. It also found that the thickness of LAC objects can be varied to obtain similar drag coefficients for different Reynolds numbers. Via cluster analysis, it is found that the distribution of drag coefficients does not rely solely on the Reynolds number, but also on the thickness of the hydrofoil. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
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14 pages, 565 KiB  
Article
Numerical Study of a Confined Vesicle in Shear Flow at Finite Temperature
by Antonio Lamura
Mathematics 2022, 10(19), 3570; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193570 - 30 Sep 2022
Cited by 2 | Viewed by 975
Abstract
The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based [...] Read more.
The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based on a combination of molecular dynamics and mesoscopic hydrodynamics, is used to perform a detailed analysis in a wide range of the Peclet numbers (the ratio of the shear rate to the rotational diffusion coefficient). The suspension viscosity is found to be a monotonous increasing function of the viscosity contrast (the ratio of the viscosity of the encapsulated fluid to that of the surrounding fluid) both in the tank-treading and the tumbling regime due to the interplay of different temperature-depending mechanisms. Thermal effects induce shape and inclination fluctuations of the vesicle which also experiences Brownian diffusion across the channel increasing the viscosity. These effects reduce when increasing the Peclet number. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
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19 pages, 7799 KiB  
Article
Finite Gradient Models with Enriched RBF-Based Interpolation
by Pedro Areias, Rui Melicio, Fernando Carapau and José Carrilho Lopes
Mathematics 2022, 10(16), 2876; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162876 - 11 Aug 2022
Cited by 4 | Viewed by 1110
Abstract
A finite strain gradient model for the 3D analysis of materials containing spherical voids is presented. A two-scale approach is proposed: a least-squares methodology for RVE analysis with quadratic displacements and a full high-order continuum with both fourth-order and sixth-order elasticity tensors. A [...] Read more.
A finite strain gradient model for the 3D analysis of materials containing spherical voids is presented. A two-scale approach is proposed: a least-squares methodology for RVE analysis with quadratic displacements and a full high-order continuum with both fourth-order and sixth-order elasticity tensors. A meshless method is adopted using radial basis function interpolation with polynomial enrichment. Both the first and second derivatives of the resulting shape functions are described in detail. Complete expressions for the deformation gradient F and its gradient F are derived and a consistent linearization is performed to ensure the Newton solution. A total of seven constitutive properties is required. The classical Lamé parameters corresponding to the pristine material are considered constant. From RVE homogenization, seven properties are obtained, two homogenized Lamé parameters plus five gradient-related properties. Two validation 3D numerical examples are presented. The first example exhibits the size effect (i.e., the stiffening of smaller specimens) and the second example shows the absence of stress singularity and hence the convergence of the discretization method. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
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17 pages, 284 KiB  
Article
Liouville-Type Results for a Two-Dimensional Stretching Eyring–Powell Fluid Flowing along the z-Axis
by José L. Díaz, Saeed ur Rahman and Muhammad Nouman
Mathematics 2022, 10(4), 631; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040631 - 18 Feb 2022
Cited by 1 | Viewed by 1025
Abstract
The purpose of this study is to establish Liouville-type results for a three-dimensional incompressible, unsteady flow described by the Eyring–Powell fluid equations. The fluid is studied in a plane Ωp while it moves along the z-axis. Therefore the main functions to [...] Read more.
The purpose of this study is to establish Liouville-type results for a three-dimensional incompressible, unsteady flow described by the Eyring–Powell fluid equations. The fluid is studied in a plane Ωp while it moves along the z-axis. Therefore the main functions to analyze are given by u(x,y,z,t) and v(x,y,z,t), belonging to Ωp. The results are obtained for globally bounded initial data as well as their corresponding derivatives, and the variations in velocity along the z-axis belong to the space L2 and BMO. Under such conditions, Liouville-type results are obtained and extended to Lp, p>2. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
20 pages, 3050 KiB  
Article
Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow
by Marília Pires and Tomáš Bodnár
Mathematics 2022, 10(3), 404; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030404 - 27 Jan 2022
Cited by 2 | Viewed by 1721
Abstract
This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with [...] Read more.
This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with a newly proposed approach using a discrete time derivative of the Laplacian of the extra stress tensor. Both methods are implemented in a finite element code and demonstrated in the solution of a viscoelastic fluid flow in a two-dimensional corrugated channel for a range of Weissenberg numbers. The numerical simulations have shown that this new temporal stress diffusion not only efficiently stabilizes numerical simulations, but also vanishes when the solution reaches a steady state. It is demonstrated that in contrast to the standard tensorial diffusion, the temporal artificial stress diffusion does not affect the final solution. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models)
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