Mathematical Modeling and Numerical Analysis in Fluid Dynamics

Dear Colleagues,

Fluid dynamics plays a pivotal role in understanding and predicting the behaviour of fluids across various scales and applications. The complexity of fluid flow phenomena, governed by nonlinear partial differential equations such as the Navier–Stokes equations, necessitates advanced mathematical modelling and numerical analysis to achieve accurate and efficient solutions.​

This Special Issue aims to present cutting-edge research that advances the theoretical and computational aspects of fluid dynamics. We invite contributions that focus on the development of novel mathematical models, the rigorous analysis of existing models, and the creation or enhancement of numerical methods tailored to fluid flow problems. Submissions that bridge the gap between theory and application, demonstrating the practical impact of mathematical and numerical innovations in real-world fluid dynamics scenarios, are particularly encouraged.

The scope of the Special Issue includes, but is not limited to, the following:

• Mathematical Modelling:
  • Derivation and analysis of models for incompressible and compressible flows.
  • Modelling of multiphase and multicomponent flows.
  • Development of reduced-order models and asymptotic analysis.
  • Incorporation of non-Newtonian fluid behaviour into mathematical frameworks.​
• Numerical Analysis:
  • Design and analysis of numerical schemes (e.g., finite element, finite volume, spectral methods) for fluid flow simulations.
  • Stability, convergence, and error analysis of numerical methods.
  • Adaptive mesh refinement and multiscale methods.
  • High-performance computing strategies for large-scale fluid dynamics problems.​
• Applications:
  • Simulation of environmental flows, including atmospheric and oceanic circulations.
  • Modelling of marine renewable energy systems, such as offshore wind and wave energy devices.
  • Industrial applications, including aerodynamics, hydrodynamics, and process engineering.
  • Analysis of fluid–structure interactions and their computational challenges.​

By assembling a collection of high-quality articles, this Special Issue seeks to highlight the synergy between mathematical rigour and computational innovation in the advancement of our understanding and prediction of fluid behaviour. We encourage submissions that not only present novel methodologies but also demonstrate their effectiveness through applications or comparative studies.

Dr. Chenyu Zhao
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.

• mathematical modelling
• computational fluid dynamics (CFDs)
• navier–stokes equations
• multiphase flows
• non-newtonian fluids
• finite element methods
• spectral methods
• adaptive mesh refinement
• fluid–structure interaction