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 270

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Faculty of Applied and Computer Science, Vaal University of Technology, Private Bag X021, Vanderbijlpark 1911, South Africa
Interests: computational fluid dynamics; heat mass transfer
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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

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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 (1 paper)

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Research

20 pages, 918 KiB  
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
Viewed by 156
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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