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Mathematics
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Advanced Computational Fluid Dynamics and Applications
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Advanced Computational Fluid Dynamics and Applications

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 2330

Editor

Dr. Roman Chertovskikh

E-Mail Website
Guest Editor
SYSTEC-ARISE, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
Interests: fluid dynamics; dynamo theory; convection; optimal control; numerical methods

Special Issue Information

Dear Colleagues,

Computational fluid dynamics (CFD) has become an indispensable tool in science and engineering, translating the fundamental principles of fluid mechanics into powerful predictive capabilities for real-world problems. This Special Issue, situated within the domain of applied mathematics, focuses on the cutting edge of CFD, emphasizing the development and application of complex computational or combined analytical–computational techniques. The accurate simulation of fluid phenomena is vital across diverse fields, impacting everything from aerospace vehicle design, the control of complex technological processes and meteorological forecasting, to biomedical engineering and environmental management.

Addressing the inherent complexities of fluid dynamics—including turbulence, multiphase flows, intricate convection patterns, magnetohydrodynamics (MHD), and flow control systems—demands robust and efficient numerical methods. Furthermore, the scale of these problems necessitates the use of high-performance computing (HPC). Therefore, one of the topics of this Special Issue is the creation and analysis of scalable algorithms (e.g., advanced finite difference, finite element analysis, finite volume analysis, and spectral methods) capable of leveraging parallel computational architectures, including CPU and GPU facilities.

We invite contributions that present significant advancements in mathematical modeling, numerical algorithm design, and computational implementation, particularly contributions tackling challenging applications in areas like aerodynamics, pipe and turbine flows, convection, MHD, and flow control, and which demonstrate the crucial interplay between applied mathematics, numerical methods, HPC, and impactful CFD simulations.

Dr. Roman Chertovskikh
Guest Editor

Manuscript Submission Information

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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-anonymized 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.

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Keywords

  • fluid mechanics
  • magnetohydrodynamics
  • convection
  • flow control and optimization
  • numerical methods
  • parallel computing

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Published Papers (3 papers)

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Research

21 pages, 442 KB  
Article
Fuzzy–Viscous Fluid Dynamics with Dynamic Interval-Valued Intuitionistic Fuzzy Sets
by Osama Ogilat and Abd Ulazeez Alkouri
Mathematics 2026, 14(16), 2895; https://doi.org/10.3390/math14162895 - 11 Aug 2026
Viewed by 258
Abstract
The rheological behaviour of complex fluids such as blood and polymer melts is governed by viscosities that are inherently subject to epistemic uncertainty arising from incomplete knowledge of evolving small scales rather than intrinsic randomness. Classical continuum models assume precisely known viscosity functions, [...] Read more.
The rheological behaviour of complex fluids such as blood and polymer melts is governed by viscosities that are inherently subject to epistemic uncertainty arising from incomplete knowledge of evolving small scales rather than intrinsic randomness. Classical continuum models assume precisely known viscosity functions, an assumption that is physically unjustifiable in such systems, while existing fuzzy approaches have failed to integrate rigorously with the full conservation laws of continuum mechanics. To address this gap, we introduce Fuzzy–Viscous Fluid Dynamics (FVFD), a novel framework in which dynamic viscosity is governed by Dynamic Interval-Valued Intuitionistic Fuzzy Sets (DIVIFS), with membership functions grounded in Coleman–Gurtin internal-variable thermodynamics and evolution equations derived from a Lyapunov dissipation postulate. Employing the parabolic comparison principle together with Galerkin–Leray–Hopf theory, we establish that intuitionistic ordering constraints are preserved over time and prove the existence of global weak solutions to the coupled fuzzy Navier–Stokes equations (FNSEs). An exact analytical solution for fuzzy Couette flow is derived, recovering the classical Newtonian limit and shown, via a structural argument, to be non-linear precisely because and only because FVFD departs from the purely local generalised-Newtonian closure shared by the Power-law, Carreau–Yasuda, and Cross models. Three governing dimensionless parameters, the Reynolds number (Re), Damköhler number (Da), and fuzzy number (Fz), are identified and justified to characterise distinct flow regimes. This framework provides a rigorous, physically grounded alternative to stochastic and data-driven methods for explicitly tracking epistemic uncertainty through interval-valued hesitancy parameters, enabling more accurate modelling of complex fluids whose internal aggregation states remain inaccessible to direct observation. Full article
(This article belongs to the Special Issue Advanced Computational Fluid Dynamics and Applications)
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22 pages, 4981 KB  
Article
Causal State-Space Reduced-Order Modeling of Sweeping Jet Actuators Using Internal Mixing-Chamber Dynamics
by Shafi Al Salman Romeo and Kursat Kara
Mathematics 2026, 14(10), 1694; https://doi.org/10.3390/math14101694 - 15 May 2026
Viewed by 455
Abstract
Sweeping jet (SWJ) actuators are widely used in active flow control, but explicitly resolving actuator-scale unsteadiness in full-configuration computational fluid dynamics (CFD) remains prohibitively expensive because of the small geometric scales and high-frequency oscillations involved. Existing reduced-order boundary-condition models constructed from exit-plane data [...] Read more.
Sweeping jet (SWJ) actuators are widely used in active flow control, but explicitly resolving actuator-scale unsteadiness in full-configuration computational fluid dynamics (CFD) remains prohibitively expensive because of the small geometric scales and high-frequency oscillations involved. Existing reduced-order boundary-condition models constructed from exit-plane data alone can reproduce the observed switching waveform, but they treat the actuator as an input–output black box and provide limited insight into the internal dynamics that generate the response. This work develops a causal state-space reduced-order modeling framework that links internal mixing-chamber dynamics to time-resolved exit-plane boundary conditions. Proper orthogonal decomposition (POD) is used to obtain a low-dimensional representation of the internal flow, and a data-driven linear evolution operator is identified in the reduced space by least-squares regression of successive snapshot pairs. A POD truncation rank of r=60 is selected from cumulative-energy and validation-error sensitivity analyses, capturing well above 99% of the fluctuation energy while lying within the converged performance regime. A corresponding reduced operator is identified for the exit plane, and spectral comparison reveals near-neutrally stable oscillatory modes in both regions. Using a ±1% relative frequency-matching tolerance, the dominant reduced-operator modes exhibit a 28.3% frequency overlap, providing operator-level evidence that exit-plane oscillations are dynamically linked to internal coherent structures. This correspondence is further supported by cross-spectral coherence analysis between representative internal and exit-plane probe signals, which shows strong coherence at dynamically relevant frequencies. A delayed causal output mapping is then formulated in which the internal reduced state drives the exit-plane response after an identified lag of 149 time steps, corresponding to 2.98×10−3 s. This delay provides a physically interpretable convective transport timescale from the mixing chamber to the actuator exit. Over the validation interval, the model maintains a mean relative L2 error below 0.02, with maximum normalized errors below 0.04 for most of the prediction horizon, and localized increases are confined to rapid jet-switching events. Field-level reconstructions of streamwise velocity and total pressure show that the model captures both phases of the jet-switching cycle, with errors concentrated primarily in high-gradient shear-layer regions. Compared with exit-only reduced-order models, the proposed internal-driven formulation improves amplitude and phase fidelity over extended prediction horizons. The resulting framework provides a compact, interpretable, operator-based representation of SWJ actuator dynamics suitable for use as a CFD-embeddable dynamic boundary condition. Full article
(This article belongs to the Special Issue Advanced Computational Fluid Dynamics and Applications)
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29 pages, 16683 KB  
Article
Numerical Study of Amplitude-Driven Flow Dynamics in Shocked Heavy-Fluid Layers
by Ahmed Hussein Msmali, Satyvir Singh and Abdullah Ali H. Ahmadini
Mathematics 2026, 14(1), 82; https://doi.org/10.3390/math14010082 - 25 Dec 2025
Viewed by 817
Abstract
In this study, a comprehensive numerical investigation of amplitude-driven flow dynamics in shocked heavy-fluid layers is presented to focus on the evolution of the Richtmyer–Meshkov instability (RMI). A high-order mixed local discontinuous Galerkin scheme is employed to resolve the complex interactions between shock [...] Read more.
In this study, a comprehensive numerical investigation of amplitude-driven flow dynamics in shocked heavy-fluid layers is presented to focus on the evolution of the Richtmyer–Meshkov instability (RMI). A high-order mixed local discontinuous Galerkin scheme is employed to resolve the complex interactions between shock waves and perturbed interfaces within a compressible viscous flow framework. Impacts of the initial interface amplitudes are systematically examined through a series of single-mode configurations with amplitude–wavelength ratios ranging from a0/λ=0.025 to 0.4. The simulations capture the complete transition from early linear growth to nonlinear roll-up and subsequent mixing. This investigation illustrates that increasing the initial perturbation amplitude enhances baroclinic vorticity generation, intensifies interfacial deformation, and accelerates the onset of secondary instabilities. Low-amplitude interfaces maintain nearly symmetric deformation with delayed nonlinear transition, whereas high-amplitude cases exhibit pronounced spike–bubble asymmetry, stronger curvature, and rapid Kelvin–Helmholtz roll-ups. Quantitative diagnostics of the circulation, enstrophy, and kinetic energy demonstrate that both baroclinic torque and mixing intensity scale directly with the initial perturbation amplitude. This study offers new physical insight into amplitude-dependent shock–interface interactions and elucidates the mechanisms governing vorticity amplification and energy redistribution in RMI flows. Full article
(This article belongs to the Special Issue Advanced Computational Fluid Dynamics and Applications)
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