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Mathematical Models of Fluid Dynamics
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Mathematical Models of Fluid Dynamics

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydraulics and Hydrodynamics".

Deadline for manuscript submissions: closed (28 August 2025) | Viewed by 5230

Special Issue Editor

Prof. Dr. Muhammad Hameed

E-Mail Website
Guest Editor
Division of Mathematics and Computer Science, University of South Carolina Upstate, Spartanburg, SC 29303, USA
Interests: applied mathematics and modeling; asymptotic analysis; computational fluid dynamics; non-Newtonian and biofluids; moving boundary problems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, titled "Mathematical Models of Fluid Dynamics", aims to concentrate on the comprehensive exploration of fluid mechanics through a rigorous mathematical approach. This collection of articles aims to delve into advanced mathematical models and their practical applications in comprehending and predicting fluid behavior across diverse scenarios in water sciences. Featuring contributions that span a broad spectrum of topics including the Navier–Stokes equations, turbulence modeling, computational fluid dynamics (CFDs), boundary layer theory, multiphase flow, and fluid–structure interactions, this Special Issue aims to showcase innovative mathematical frameworks, numerical methods, and simulation techniques in water sciences. These advancements will hopefully elucidate complex-fluid-phenomena-related water.

Addressing the need for originality, relevance, and mathematical rigor, the articles published in this Special Issue should aim to attract a wide readership. Researchers and scientists from various fields should find this Special Issue invaluable as it will offer a comprehensive overview of the cutting-edge mathematical models employed in fluid dynamics analysis. By bridging theoretical advancements with practical implications, this Special Issue endeavors to stimulate further exploration, encourage interdisciplinary collaborations, and enhance our understanding and manipulation of fluid behavior for technological innovation and scientific progress.

Prof. Dr. Muhammad Hameed
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 250 words) can be sent to the Editorial Office for assessment.

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. Water 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

  • fluid dynamics
  • mathematical models
  • Navier–Stokes equations
  • turbulence modeling
  • computational fluid dynamics (CFDs)
  • boundary layer theory
  • multiphase flow
  • fluid–structure interactions
  • fluid–particle interactions
  • free surface flows
  • interfacial phenomena
  • biofluids
  • astrophysics
  • numerical methods
  • simulation
  • interdisciplinary collaboration
  • water sciences

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

56 pages, 8707 KB  
Article
An Integrated Methodology for Novel Algorithmic Modeling of Non-Spherical Particle Terminal Settling Velocities and Comprehensive Digital Image Analysis
by Kaan Yetilmezsoy, Fatih Ilhan and Emel Kıyan
Water 2025, 17(22), 3268; https://doi.org/10.3390/w17223268 - 15 Nov 2025
Viewed by 612
Abstract
Accurate prediction of settling velocities for irregular particles offers significant advantages in various fields, including more efficient water/wastewater treatment, environmental pollution control, industrial productivity, and sustainable resource utilization. These predictions are essential for advancing sustainable hydraulic engineering and environmental management. In this study, [...] Read more.
Accurate prediction of settling velocities for irregular particles offers significant advantages in various fields, including more efficient water/wastewater treatment, environmental pollution control, industrial productivity, and sustainable resource utilization. These predictions are essential for advancing sustainable hydraulic engineering and environmental management. In this study, a new algorithmic modeling framework was proposed to estimate the terminal settling velocity of irregularly shaped particles/materials. The framework integrates advanced non-linear regression techniques with robust optimization methods. The model successfully incorporated seven key input parameters to construct a comprehensive mathematical representation of the settling process. The proposed explicit model demonstrates superior prediction accuracy compared to existing empirical and drag correlation models. The model’s validity was confirmed using a large and morphologically diverse dataset of 86 irregular materials and rigorously evaluated using an extensive battery of statistical goodness-of-fit parameters. The developed model is a robust and highly accurate tool for predicting the settling behavior of non-spherical particles in the transition flow regime. Beyond its technical merits, the model could offer significant sustainability benefits by enhancing the design and optimization of wastewater treatment systems. More precise predictions of non-spherical particle settling behavior could improve sedimentation or particle removal efficiency, potentially reducing energy consumption and mitigating adverse environmental impacts on industrial waste management and aquatic ecosystem preservation. Full article
(This article belongs to the Special Issue Mathematical Models of Fluid Dynamics)
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25 pages, 12790 KB  
Article
Numerical Simulation Study on Three-Dimensional Flow Characteristics and Probability Density Distribution of Water-Permeable Gabion Backflow Zone in Different Curvature Bends
by Peng Xie, Suiju Lv, Zelin Li, Ying Zhang and Jianping Lv
Water 2024, 16(16), 2247; https://doi.org/10.3390/w16162247 - 9 Aug 2024
Viewed by 1617
Abstract
This study explored the three-dimensional flow characteristics in a recirculation zone near a permeable buttress in curved channels with varying curvatures. Understanding these characteristics is crucial for managing natural river bends, as rivers often meander, with backwater zones formed behind obstructions, such as [...] Read more.
This study explored the three-dimensional flow characteristics in a recirculation zone near a permeable buttress in curved channels with varying curvatures. Understanding these characteristics is crucial for managing natural river bends, as rivers often meander, with backwater zones formed behind obstructions, such as mountains in the riverbed. The direct comparison of the recirculation zones across different bend types revealed the correlation between the flow characteristics and bend curvature. However, previous studies have focused on flow velocities and turbulent kinetic energy without a probability density analysis. This analysis provided a more comprehensive understanding of the flow characteristics. Gaussian kernel density estimation was applied in this study to observe the distribution of the flow velocities, turbulent kinetic energy, and turbulent kinetic energy dissipation rate. The results indicated that the longitudinal time-averaged flow velocity in the recirculation zone typically ranged from −0.2 m/s to −0.8 m/s, with all the skewness coefficients exceeding 0. The horizontal time-averaged flow velocity in the recirculation zone fell between −0.175 m/s and −0.1 m/s. The skewness coefficients were negative at water depths of 16%, 33%, and 50% within the 90° and 180° bends, indicating a non-normal distribution. The probability density distribution of turbulent kinetic energy in the recirculation zone was skewed, ranging from 0 to 0.02 m2·s−2, with the skewness coefficient almost always greater than 0. The plot demonstrated multiple peaks, indicating a broad distribution of turbulent kinetic energy rather than a concentration within a specific interval. This distribution included both the high and low regions of turbulent kinetic energy. Although the overall rate of turbulent kinetic energy dissipation in the recirculation zone was relatively low, there were multiple peaks, suggesting the localized areas with higher dissipation rates alongside the regions with lower rates. These findings were significant for managing the meandering river channels, restoring the subaqueous ecosystems, understanding the pollutant diffusion mechanisms in backwater areas, the sedimentation of nutrient-laden sediments, and optimizing the parameters for spur dike design. Full article
(This article belongs to the Special Issue Mathematical Models of Fluid Dynamics)
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21 pages, 6386 KB  
Article
Computational Simulation of Monopile Scour under Tidal Flow Considering Suspended Energy Dissipation
by Jiawei Liu, Junliang Lu and Zejun Liang
Water 2024, 16(14), 1940; https://doi.org/10.3390/w16141940 - 9 Jul 2024
Cited by 5 | Viewed by 1965
Abstract
Local scour around bridge foundations significantly impacts the stability and safety of marine structures. The development of scour holes adjacent to the pile foundations of sea-crossing bridges, influenced by tidal currents, involves multidimensional physical fields, multiscale coupling, and complex variations in marine loads. [...] Read more.
Local scour around bridge foundations significantly impacts the stability and safety of marine structures. The development of scour holes adjacent to the pile foundations of sea-crossing bridges, influenced by tidal currents, involves multidimensional physical fields, multiscale coupling, and complex variations in marine loads. However, experimental models alone are inadequate for investigating the underlying mechanisms. Numerical simulation, a critical tool for studying local scour processes, faces the challenge of accurately modeling sediment transport, particularly under tidal flow conditions near pile foundations. To solve this challenge, this research considers the effect of reciprocating flow on sediment shear as well as its characteristic dissipation based on the immersed boundary method, introduces a reciprocating flow dissipation mechanism, and adds a momentum exchange term between the fluid and the sediment to derive a new controlling equation; a new tidal flow localized scour solver is ultimately constructed, termed TidalflowFOAM. The solver effectively simulates complex flow conditions under tidal currents, extending the modeling capabilities to more realistic three-dimensional bridge scour scenarios under combined wave and current conditions. Validation through cases reported in the literature and a series of controlled experiments, encompassing varying depths, flow velocities, and pile diameters, demonstrates the solver’s proficiency in capturing post-vortex data and accurately reflecting the influence of key factors on scour depth. However, the fidelity of the simulated scour hole morphology under tidal flow conditions behind the piles requires enhancement. The proposed numerical model for tidal flow conditions has high solution accuracy and can guide practical engineering applications. Full article
(This article belongs to the Special Issue Mathematical Models of Fluid Dynamics)
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