Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.6
Journals
Axioms
Special Issues
Recent Developments in Mathematical Fluid Dynamics
share announcement

Recent Developments in Mathematical Fluid Dynamics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 678

Special Issue Editor

Dr. Andrea Chierici

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA
Interests: computational fluid dynamics; finite element methods; multi-phase flows; optimal control; nonlocal operators; numerical analysis

Special Issue Information

Dear Colleagues,

This Special Issue of Axioms aims to present and promote recent advances in the mathematical foundations and modern analytical, numerical, and computational methods for the study of fluid dynamics. As fluid flows play a central role in many physical, biological, and industrial processes, the rigorous understanding and modeling of their behavior remain a cornerstone of applied mathematics.

The focus of this Special Issue is on the development of axiomatic frameworks, new theoretical insights, and advanced numerical techniques that involve the mathematical modeling of fluids, whether incompressible, compressible, multiphase, non-Newtonian, or turbulent. Topics of interest include, but are not limited to, the following: the analysis of partial differential equations governing fluid motion; existence and uniqueness results; stability and control of flow systems; numerical schemes for multi-physics and multiscale phenomena; and applications to real-world systems.

This Special Issue also encourages contributions that bridge mathematical fluid dynamics with areas such as optimization, uncertainty quantification, machine learning, and high-performance computing. By assembling contributions from leading researchers and emerging scholars, this Special Issue will offer a snapshot of current trends and challenges, while highlighting open questions and directions for future work.

We look forward to your valuable contributions.

Dr. Andrea Chierici
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • mathematical fluid dynamics
  • partial differential equations
  • multiphase flows
  • non-Newtonian fluids
  • numerical methods
  • axiomatic modeling
  • stability and control in fluid dynamics
  • multiscale simulations
  • high-performance computing
  • machine learning in fluid dynamics

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

41 pages, 18402 KB  
Article
Trapped Modes Along Periodic Structures Submerged in a Two-Layer Fluid with Free Surface and a Background Steady Flow
by Gonçalo Dias and Bruno Pereira
Axioms 2025, 14(11), 846; https://doi.org/10.3390/axioms14110846 - 18 Nov 2025
Viewed by 155
Abstract
This study examines the trapping of linear water waves by an endless structure of stationary, three-dimensional periodic obstacles within a two-layer fluid system. The setup features a lower layer of either limited or unlimited depth, overlaid by an upper layer of finite thickness [...] Read more.
This study examines the trapping of linear water waves by an endless structure of stationary, three-dimensional periodic obstacles within a two-layer fluid system. The setup features a lower layer of either limited or unlimited depth, overlaid by an upper layer of finite thickness bounded by a free surface, with each layer exhibiting its own constant background speed relative to the fixed reference frame. For real roots to emerge in the dispersion relation, an additional stability condition on the layer velocities is necessary. By selecting adequate choices for the background flow, a non-linear eigenvalue problem is derived from the variational formulation; its reasonable approximation yields a geometric criterion that guarantees the presence of trapped modes (subject to the aforementioned stability bounds). The selection of the eigenvalue is influenced by velocity owing to the presence of an interface and free surface. Due to inherent symmetries, the overall analysis can be confined to the positive quadrant of the velocity domain. Illustrations are provided for various obstacle setups that produce trapped modes in diverse ways. Full article
(This article belongs to the Special Issue Recent Developments in Mathematical Fluid Dynamics)
►▼ Show Figures

Figure 1

21 pages, 1805 KB  
Article
Assessment of Compliance with Integral Conservation Principles in Chemically Reactive Flows Using rhoCentralRfFoam 
by Marcelo Frias, Luis Gutiérrez Marcantoni and Sergio Elaskar
Axioms 2025, 14(11), 782; https://doi.org/10.3390/axioms14110782 - 25 Oct 2025
Viewed by 359
Abstract
Reliable simulations of any flow require proper preservation of the fundamental principles governing the mechanics of its motion, whether in differential or integral form. When these principles are solved in differential form, discretization schemes introduce errors by transforming the continuous physical domain into [...] Read more.
Reliable simulations of any flow require proper preservation of the fundamental principles governing the mechanics of its motion, whether in differential or integral form. When these principles are solved in differential form, discretization schemes introduce errors by transforming the continuous physical domain into a discrete representation that only approximates it. This paper analyzes the numerical performance of the solver for supersonic chemically active flows, rhoCentralRfFoam, using integral conservation principles of mass, momentum, energy, and chemical species as a validation tool in a classical test case with a highly refined mesh under nonlinear pre-established reference conditions. The analysis is conducted on this specific test case; however, the methodology presented here can be applied to any problem under study. It may serve as an a posteriori verification tool or be integrated into the solver’s workflow, enabling automatic verification of conservation at each time step. The resulting deviations are evaluated, and it is observed that the numerical errors remain below 0.25%, even in cases with a high degree of nonlinearity. These results provide preliminary validation of the solver’s accuracy, as well as its ability to capture physically consistent solutions using only information generated internally by the solver for validation. This represents a significant advantage over validation methods that require external comparison with reference solutions, numerical benchmarks, or exact solutions. Full article
(This article belongs to the Special Issue Recent Developments in Mathematical Fluid Dynamics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop