Mathematical Modeling for Fluid Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: closed (28 March 2025) | Viewed by 3548

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Guest Editor
Department of Applied Mathematics and Didactics, Universidad a Distancia de Madrid (UDIMA), 28400 Madrid, Spain
Interests: diffusion modeling; p-Laplacian operators; phase change materials; Darcy-Forchheimer fluids; porous media flow modelling; rheological properties; magnetohydrodynamics; geometric perturbation theory; travelling waves; solitons; peakons; flame modeling
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Special Issue Information

Dear Colleagues,

The modeling of fluid flows is an important topic of research due to its connection with chemical and biological processes, physics, engineering, and microfluidics. During the last years, modeling efforts in fluid dynamics (for example, in areas like biofluids, porous media flows, aerodynamics or combustion) have led to new developments in mathematics, in particular in the numerical and analytical advances of PDEs.

We are pleased to invite you to submit works discussing relevant developments and applications of mathematical modeling in fluid dynamics and mechanics. The works can be focused on analytical conceptions, numerical approaches, or a combination of analytical and numerical methods. Experimental works are also welcome, but they should relate to mathematical theories.

This Special Issue aims to present current research in fluid modeling, attracting researchers and serving as a placeholder to concentrate new ideas for the future development of fluid modeling.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

  • Energy formulation of fluids;
  • Variational approaches theory and numerics;
  • Biofluids modeling;
  • Flows in porous media;
  • Combustion theory;
  • Flame propagation modeling;
  • Perturbation approaches;
  • Travelling waves and soliton solutions;
  • Regularity, uniqueness and smoothness of fluid solutions;
  • Higher order parabolic operators in fluid modeling;
  • p-Laplacian, poly-Laplacian and other bizarre operators in fluid modeling;
  • Navier–Stokes equations;
  • Laminar and turbulent flow modeling;
  • Finite element analysis, finite difference method, and finite volume method;
  • Boundary layer theory;
  • Vortex methods;
  • Large eddy simulation;
  • Particle image velocimetry in fluid modeling;
  • Smoothed particle hydrodynamics;
  • Scaling laws and dimensional analysis;
  • Wind tunnel testing and fluid modeling;
  • Wavelet methods for turbulence.

I/We look forward to receiving your contributions.  

Prof. Dr. José Luis Díaz
Guest Editor

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Keywords

  • energy formulation of fluids
  • variational approaches theory and numerics
  • biofluids modeling
  • flows in porous media
  • combustion theory
  • flame propagation modeling
  • perturbation approaches
  • travelling waves and soliton solutions
  • regularity, uniqueness and smoothness of fluid solutions
  • higher order parabolic operators in fluid modeling
  • p-Laplacian, poly-Laplacian and other bizarre operators in fluid modeling
  • Navier–Stokes equations
  • laminar and turbulent flow modeling
  • finite element analysis, finite difference method, and finite volume method
  • boundary layer theory
  • vortex methods
  • large eddy simulation
  • particle image velocimetry in fluid modeling
  • smoothed particle hydrodynamics
  • scaling laws and dimensional analysis
  • wind tunnel testing and fluid modeling
  • wavelet methods for turbulence

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Published Papers (3 papers)

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Research

18 pages, 265 KiB  
Article
Strong Solution for a Nonlinear Non-Newtonian Shear Thickening Fluid
by Yukun Song, Lin Jin and Yang Chen
Mathematics 2025, 13(5), 878; https://doi.org/10.3390/math13050878 - 6 Mar 2025
Viewed by 392
Abstract
This paper consider a nonlinear shear thickening fluid in one dimensional bounded interval. The model illustrates that the movement of the compressible fluid is driven by non-Newtonian gravity, and represents a more realistic phenomenon. The well-posedness of strong solution was proved by considering [...] Read more.
This paper consider a nonlinear shear thickening fluid in one dimensional bounded interval. The model illustrates that the movement of the compressible fluid is driven by non-Newtonian gravity, and represents a more realistic phenomenon. The well-posedness of strong solution was proved by considering the influence of damping term. The essential difficulty lies in the equation’s significant nonlinearity and the initial state may allow for vacuum. Full article
(This article belongs to the Special Issue Mathematical Modeling for Fluid Mechanics)
25 pages, 18531 KiB  
Article
The Impact of Heat Transfer and a Magnetic Field on Peristaltic Transport with Slipping through an Asymmetrically Inclined Channel
by Muhammad Magdy, Ahmed G. Nasr, Ramzy M. Abumandour and Mohammed A. El-Shorbagy
Mathematics 2024, 12(12), 1827; https://doi.org/10.3390/math12121827 - 12 Jun 2024
Cited by 1 | Viewed by 1002
Abstract
This theoretical investigation explores the intricate interplay of slip, heat transfer, and magneto-hydrodynamics (MHD) on peristaltic flow within an asymmetrically inclined channel. The channel walls exhibit sinusoidal undulations to simulate flexibility. The governing equations for continuity, momentum, and energy are utilized to mathematically [...] Read more.
This theoretical investigation explores the intricate interplay of slip, heat transfer, and magneto-hydrodynamics (MHD) on peristaltic flow within an asymmetrically inclined channel. The channel walls exhibit sinusoidal undulations to simulate flexibility. The governing equations for continuity, momentum, and energy are utilized to mathematically represent the flow dynamics. Employing the perturbation method, these nonlinear equations are systematically solved, yielding analytical expressions for key parameters such as stream function, temperature distribution, and pressure gradient. This study meticulously examines the influence of various physical parameters on flow characteristics, presenting comprehensive visualizations of flow streamlines, fluid axial velocity profiles, and pressure gradient distributions. Noteworthy findings include the observation that the axial velocity of the fluid increases by 55% when the slip parameter is increased from 0 to 0.1, indicative of enhanced fluid transport. Furthermore, the analysis reveals that the pressure gradient amplifies by 80% with increased magnetic field strength from 0.5 to 4, underscoring the significant role of MHD effects on overall flow behavior. In essence, this investigation elucidates the complex dynamics of peristaltic flow in an asymmetrically inclined channel under the combined influence of slip, heat transfer, and magnetohydrodynamics. It sheds light on fundamental mechanisms that govern fluid dynamics in complex geometries and under diverse physical conditions. Full article
(This article belongs to the Special Issue Mathematical Modeling for Fluid Mechanics)
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29 pages, 1110 KiB  
Article
Analytical and Computational Approaches for Bi-Stable Reaction and p-Laplacian Diffusion Flame Dynamics in Porous Media
by Saeed ur Rahman and José Luis Díaz Palencia
Mathematics 2024, 12(2), 216; https://doi.org/10.3390/math12020216 - 9 Jan 2024
Cited by 1 | Viewed by 1116
Abstract
In this paper, we present a mathematical approach for studying the changes in pressure and temperature variables in flames. This conception extends beyond the traditional second-order Laplacian diffusion model by considering the p-Laplacian operator and a bi-stable reaction term, thereby providing a more [...] Read more.
In this paper, we present a mathematical approach for studying the changes in pressure and temperature variables in flames. This conception extends beyond the traditional second-order Laplacian diffusion model by considering the p-Laplacian operator and a bi-stable reaction term, thereby providing a more generalized framework for flame diffusion analysis. Given the structure of our equations, we provide the boundedness and uniqueness of the solutions in a weak sense from both analytical and numerical approaches. We further reformulate the governing equations in the context of traveling wave solutions, applying singular geometric perturbation theory to derive the analytical expressions of these profiles. This theoretical development is complemented by numerical assessments, which not only validate our theoretical predictions, but also optimize the traveling wave speed to minimize the error between numerical and analytical solutions. Additionally, we explore self-similar structured solutions. The paper then concludes with a perspective on future research, with emphasis being placed on the need for experimental validation in laboratory settings. Such empirical studies could test the robustness of our model and allow for refinement based on actual measurements, thereby broadening the applicability and accuracy of our findings in practical scenarios. Full article
(This article belongs to the Special Issue Mathematical Modeling for Fluid Mechanics)
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