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Mathematics
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Mathematical Methods in Computational Fluid Dynamics: Theory and Applications
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Mathematical Methods in Computational Fluid Dynamics: Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 20 February 2027 | Viewed by 945

Special Issue Editor

Dr. John Venetis

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Guest Editor
Laboratory of Strength and Materials, Faculty of Applied Mathematics and Physical Sciences Section of Mechanics, National Technical University of Athens—NTUA, 5, Heroes of Polytechnion Avenue, Zografou Campus, 15773 Athens, Greece
Interests: mechanics; mathematical physics; fluid dynamics; applied mathematics

Special Issue Information

Dear Colleagues,

Computational fluid dynamics constitutes an active and rapidly evolving area that lies on the interface between applied mathematics and physics.

The steady growth of this field is driven by the ever-increasing demands of both natural sciences and engineering practices in order to provide accurate and reliable approaches to mathematical models, which mainly involve boundary value problems, whose exact solutions are either too complicated to be embedded as subroutines in the source code of a software program to be determined or whose existence has not been rigorously proven. The intention of this Special Issue is to contribute to this interesting scientific field by providing a collection of papers that showcase cutting-edge research in Computational fluid dynamics, focusing on the spectral analysis of a three-dimensional homogeneous turbulence, the simulation of fluid flows in free surface channels and/or around mounted and rotated obstacles, etc.

Dr. John Venetis
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. 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

  • Navier–Stokes equations
  • turbulence modeling
  • domain discretization
  • multiphase flow
  • flow–structure interaction

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Published Papers (2 papers)

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Research

28 pages, 16866 KB  
Article
Quantifying Terrain Effects on Turbine Wake Recovery with Field Data and Simulation of a Real Wind Farm
by Andrea Torrejón-Fontana, Luis Silva-Llanca, Sonia Montecinos and Charles Meneveau
Mathematics 2026, 14(9), 1553; https://doi.org/10.3390/math14091553 - 4 May 2026
Viewed by 224
Abstract
Global reliance on wind energy continues to grow, leading to an increasing number of wind farms implemented in complex topographies. However, there remains a significant research gap on how the terrain’s features affect the wake recovery, especially when the irregularities scale with the [...] Read more.
Global reliance on wind energy continues to grow, leading to an increasing number of wind farms implemented in complex topographies. However, there remains a significant research gap on how the terrain’s features affect the wake recovery, especially when the irregularities scale with the wind turbine’s size. This study uses field data and Reynolds-averaged simulations to quantify the influence of topographical features on a wind farm’s wake recovery and power generation. To characterize the terrain surrounding the turbines, this study introduces two parameters—the Downwind Slope and the surface complexity length ζ—which quantify the local average terrain unevenness. The findings demonstrate that turbines in terrains with streamwise positive slopes exhibit faster wake recovery, averaging 6.35D in length (D = turbine diameter), followed by complex-flat terrain (8.7D on average), then descending terrains with the least beneficial wake recovery (9.2D on average). A terrain with a higher surface complexity also improves wake recovery owing to the turbulent entrainment that enhances momentum transport exchange into the wake. Additionally, simulations of the same turbine distribution, but in a completely flat terrain, showed that the complex terrain may lead to lower performance compared to the idealized flat terrain: 11.5% of power generation decrease in our case. The latter highlights the importance of considering topographic effects when planning wind energy projects. Full article
(This article belongs to the Special Issue Mathematical Methods in Computational Fluid Dynamics: Theory and Applications)
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23 pages, 1799 KB  
Article
Slow Translation of a Soft Sphere in an Unbounded Micropolar Fluid with Interfacial Stress Jump
by Shreen El-Sapa
Mathematics 2026, 14(4), 732; https://doi.org/10.3390/math14040732 - 21 Feb 2026
Viewed by 343
Abstract
This study presents a theoretical analysis of the slow translation of a soft sphere through an unbounded micropolar fluid under steady, low Reynolds number conditions, accounting for the influence of interfacial stress jump. The soft sphere is modeled as a rigid solid core [...] Read more.
This study presents a theoretical analysis of the slow translation of a soft sphere through an unbounded micropolar fluid under steady, low Reynolds number conditions, accounting for the influence of interfacial stress jump. The soft sphere is modeled as a rigid solid core surrounded by a permeable porous gel layer, allowing fluid penetration and momentum exchange across the interface. This core–shell configuration captures the essential structural characteristics of coated or gel-like particles encountered in biological and engineering systems. Closed-form expressions for the velocity components, microrotation, stresses, and couple stresses are derived both within the porous micropolar gel layer surrounding the particle and in the exterior micropolar fluid. The flow inside the permeable coating is described using the general Brinkman solution in spherical coordinates, while the governing micropolar fluid equations are applied in the outer region. Appropriate boundary conditions are imposed at the solid core surface and at the permeable soft-sphere interface to ensure continuity of velocity and microrotation, together with the prescribed stress jump. The normalized drag force acting on the particle is obtained as a function of the particle-to-core radius ratio, permeability, stress-jump parameter, and micropolarity parameter. The results indicate that the hydrodynamic drag decreases as the porous layer becomes thicker and remains finite, approaching unity even when the soft sphere behaves as a solid particle or as a porous sphere translating through an infinite micropolar medium, with other parameters held fixed. Overall, the analysis elucidates the coupled roles of micropolar effects, interfacial stress jump, and porous-layer structure in governing the hydrodynamic resistance experienced by soft particles. Full article
(This article belongs to the Special Issue Mathematical Methods in Computational Fluid Dynamics: Theory and Applications)
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