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Mathematics
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Advances and Applications in Computational Fluid Dynamics
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Advances and Applications in Computational Fluid Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 November 2025 | Viewed by 4521

Special Issue Editor

Dr. Ramoshweu Solomon Lebelo

E-Mail Website
Guest Editor
Faculty of Applied and Computer Science, Vaal University of Technology, Private Bag X021, Vanderbijlpark 1911, South Africa
Interests: computational fluid dynamics; heat mass transfer
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Modeling in the field of mathematics covers various aspects. Complicated real-life processes are easily clarified and explained through mathematical models using numerical methods to arrive at solutions for real-world situations. Among common processes in life, fluid dynamics dealing with fluid flow in the engineering and scientific fields is one of the various interesting fields under study. Fluids may be categorized into three forms, i.e., liquids, gases, and plasma. Plasma is ionized gas, and much of the universe is thought to consist of plasma. It is often applied to galaxy information applications, as well as modern plasma televisions. The study of fluid dynamics has attracted many researchers because of its widespread applications, including, among others, for biological and medical purposes, flow rate and velocity, Bernoulli’s equation of pressure and speed, Poiseuille’s equation of viscosity, blood flow, surface tension, molecular transport phenomena, pumps, and the heart. In addition to the abovementioned research areas, fluid mechanics covers aerodynamics, which is concerned with the study of air in motion, whose applications, among others, include finding and calculating the forces acting on airplanes and the design of airplane wings.

This Special Issue aims to bring together academics, engineers, researchers, and scientists to share recent ideas, methods, trends, problems, and solutions in the following areas:

  • High-performance computing in CFD;
  • Advanced numerical methods;
  • Surrogate modeling and reduced order models;
  • Data-driven turbulence modeling;
  • Multi-physics and multiscale modeling.

Dr. Ramoshweu Solomon Lebelo
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

  • applied, computational, and mathematical physics
  • combustion and decomposition theories
  • computational thermal engineering
  • heat and mass transfer
  • magnetohydrodynamics (MHD)
  • mechanics of fluids
  • environmental pollution

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Published Papers (5 papers)

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Research

29 pages, 3520 KB  
Article
Thermal Entropy Generation in Magnetized Radiative Flow Through Porous Media over a Stretching Cylinder: An RSM-Based Study
by Shobha Visweswara, Baskar Palani, Fatemah H. H. Al Mukahal, S. Suresh Kumar Raju, Basma Souayeh and Sibyala Vijayakumar Varma
Mathematics 2025, 13(19), 3189; https://doi.org/10.3390/math13193189 - 5 Oct 2025
Viewed by 183
Abstract
Magnetohydrodynamic (MHD) flow and heat transfer in porous media are central to many engineering applications, including heat exchangers, MHD generators, and polymer processing. This study examines the boundary layer flow and thermal behavior of an electrically conducting viscous fluid over a porous stretching [...] Read more.
Magnetohydrodynamic (MHD) flow and heat transfer in porous media are central to many engineering applications, including heat exchangers, MHD generators, and polymer processing. This study examines the boundary layer flow and thermal behavior of an electrically conducting viscous fluid over a porous stretching tube. The model accounts for nonlinear thermal radiation, internal heat generation/absorption, and Darcy–Forchheimer drag to capture porous medium resistance. Similarity transformations reduce the governing equations to a system of coupled nonlinear ordinary differential equations, which are solved numerically using the BVP4C technique with Response Surface Methodology (RSM) and sensitivity analysis. The effects of dimensionless parameters magnetic field strength (M), Reynolds number (Re), Darcy–Forchheimer parameter (Df), Brinkman number (Br), Prandtl number (Pr), nonlinear radiation parameter (Rd), wall-to-ambient temperature ratio (rw), and heat source/sink parameter (Q) are investigated. Results show that increasing M, Df, and Q suppresses velocity and enhances temperature due to Lorentz and porous drag effects. Higher Re raises pressure but reduces near-wall velocity, while rw, Rd, and internal heating intensify thermal layers. The entropy generation analysis highlights the competing roles of viscous, magnetic, and thermal irreversibility, while the Bejan number trends distinctly indicate which mechanism dominates under different parameter conditions. The RSM findings highlight that rw and Rd consistently reduce the Nusselt number (Nu), lowering thermal efficiency. These results provide practical guidance for optimizing energy efficiency and thermal management in MHD and porous media-based systems.: Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
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21 pages, 3981 KB  
Article
Investigating the Performance of Longitudinal Groove on Noise Reduction in a NACA0015 Hydrofoil Using Computational Fluid Dynamics
by S. Suresh Kumar Raju, Nasser Firouzi, Fatemeh H. H. Al Mukahal and Przemysław Podulka
Mathematics 2025, 13(19), 3125; https://doi.org/10.3390/math13193125 - 30 Sep 2025
Viewed by 316
Abstract
Nowadays, hydrodynamic noise reduction in hydrofoils is of great importance due to their wide applications in marine industries, submarines and water systems. One of the modern methods for reducing this noise is the use of longitudinal grooves on the surface of the hydrofoil. [...] Read more.
Nowadays, hydrodynamic noise reduction in hydrofoils is of great importance due to their wide applications in marine industries, submarines and water systems. One of the modern methods for reducing this noise is the use of longitudinal grooves on the surface of the hydrofoil. In this study, the effect of longitudinal grooves on the reduction in noise generated around a NACA0015 hydrofoil was investigated. For this purpose, numerical methods based on computational fluid dynamics (CFD) and acoustic analysis using ANSYS Fluent 2024 R1 software were used. The Fuchs–Williams and Hawkings (FW-H) acoustic model was used for acoustic analysis. The results obtained from the hydrofoil without grooves and the hydrofoil equipped with longitudinal grooves were compared. In total, 11 numerical noise reading stations were installed around the hydrofoil to calculate the noise in two modes with and without grooves. The results show that the use of longitudinal grooves reduces the flow turbulence in the area near the hydrofoil surface and, as a result, prevents the formation of large and unstable vortices. This leads to a significant reduction in hydrodynamic noise, especially at low and medium frequencies. This study shows that the appropriate design of longitudinal grooves on the NACA0015 hydrofoil can be used as an effective solution to reduce hydrodynamic noise. The findings of this research can be the basis for the development of quieter hydrofoils in industrial and military applications. The results show that at low frequencies (up to approximately 10 Hz), the noise intensity of the ungrooved hydrofoil is higher than that of the grooved hydrofoil, but in the frequency range of 10 to 20 Hz, the noise intensity of the grooved hydrofoil increases significantly and exceeds that of the ungrooved hydrofoil. Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
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25 pages, 2142 KB  
Article
Viscoelectric and Steric Effects on Electroosmotic Flow in a Soft Channel
by Edson M. Jimenez, Clara G. Hernández, David A. Torres, Nicolas Ratkovich, Juan P. Escandón, Juan R. Gómez and René O. Vargas
Mathematics 2025, 13(16), 2546; https://doi.org/10.3390/math13162546 - 8 Aug 2025
Viewed by 2649
Abstract
The present work analyzes the combined viscoelectric and steric effects on electroosmotic flow in a soft channel with polyelectrolyte coating. The structured channel surface, which controls the electric potential, creates two different flow regions: the electrolyte flow within the permeable polyelectrolyte layer (PEL) [...] Read more.
The present work analyzes the combined viscoelectric and steric effects on electroosmotic flow in a soft channel with polyelectrolyte coating. The structured channel surface, which controls the electric potential, creates two different flow regions: the electrolyte flow within the permeable polyelectrolyte layer (PEL) and the bulk electrolyte. Thus, this study discusses the interaction of various electrostatic effects to predict the electroosmotic flow field. The nonlinear governing equations describing the fluid flow are the modified Poisson–Boltzmann equation for the electric potential distribution, the mass conservation equation, and the modified Navier–Stokes equations for the flow field, which are solved numerically using a one-dimensional (1D) scheme. The results indicate that the flow enhances when increasing the electric potential magnitude across the channel cross-section via the rise in different dimensionless parameters, such as the PEL thickness, the steric factor, and the ratio of the electrokinetic parameter of the PEL to that of the electrolyte layer. This research demonstrates that the PEL significantly enhances control over electroosmotic flow. However, it is crucial to consider that viscoelectric effects at high electric fields and the friction generated by the grafted polymer brushes of the PEL can reduce these benefits. Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
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15 pages, 1957 KB  
Article
General Solutions for Magnetohydrodynamic Unidirectional Motions of a Class of Fluids with Power-Law Dependence of Viscosity on Pressure Through a Planar Channel
by Constantin Fetecau and Dumitru Vieru
Mathematics 2025, 13(11), 1800; https://doi.org/10.3390/math13111800 - 28 May 2025
Viewed by 315
Abstract
An analytical study is conducted on unsteady, one-directional magnetohydrodynamic (MHD) flows of electrically conducting, incompressible, and viscous fluids, where the viscosity varies with pressure following a power-law relationship. The flow takes place within a planar channel and is driven by the lower plate, [...] Read more.
An analytical study is conducted on unsteady, one-directional magnetohydrodynamic (MHD) flows of electrically conducting, incompressible, and viscous fluids, where the viscosity varies with pressure following a power-law relationship. The flow takes place within a planar channel and is driven by the lower plate, which moves along its own plane with an arbitrary, time-dependent speed. The effects of gravitational acceleration are also considered. General exact formulas are derived for both the dimensionless velocity of the fluid and the resulting non-zero shear stress. Moreover, these are the only general solutions for the MHD motions of the fluids considered, and they can produce precise solutions for any motion of this type for respective fluids. The proposed analytical method leads to simple forms of analytical solutions and can be useful in the study of other cases of fluids with viscosity depending on pressure. As an example, solutions related to the modified Stokes’ second problem are presented and confirmed through graphical validation. These solutions also help highlight the impact of the magnetic field on fluid dynamics and determine the time needed for the system to achieve a steady state. Graphical representations indicate that a steady state is reached more quickly and the fluid moves more slowly when a magnetic field is applied. Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
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20 pages, 918 KB  
Article
The Linear Stability of a Power-Law Liquid Film Flowing Down an Inclined Deformable Plane
by Karim Ladjelate, Nadia Mehidi Bouam, Amar Djema, Abdelkader Belhenniche and Roman Chertovskih
Mathematics 2025, 13(9), 1533; https://doi.org/10.3390/math13091533 - 7 May 2025
Cited by 1 | Viewed by 721
Abstract
A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal [...] Read more.
A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal stress difference in the base state at the fluid–solid interface. To solve the linearized eigenvalue problem, the Riccati transformation method, which offers advantages over traditional techniques by avoiding the parasitic growth seen in the shooting method and eliminating the need for large-scale matrix eigenvalue computations, was used. This method enhances both analytical clarity and computational efficiency. Results show that increasing solid deformability destabilizes the flow at low Reynolds numbers by promoting short-wave modes, while its effect becomes negligible at high Reynolds numbers where inertia dominates. The fluid’s rheology also plays a key role: at low Reynolds numbers, shear-thinning fluids (n<1) are more prone to instability, whereas at high Reynolds numbers, shear-thickening fluids (n>1) exhibit a broader unstable regime. Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
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