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Mathematics
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Numerical Methods and Simulations for Turbulent Flow
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Numerical Methods and Simulations for Turbulent Flow

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 4950

Special Issue Editor

Prof. Dr. Abdelkader Frendi

E-Mail Website
Guest Editor
Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA
Interests: turbulence; fluid structure interaction; computational fluid dynamics; numerical analysis

Special Issue Information

Dear Colleagues,

We are pleased to announce this Special Issue of the journal Mathematics entitled, “Numerical Methods and Simulations for Turbulent Flow”. Turbulent flows are common in nature, technology, and everyday life. The modeling and simulation of turbulent flows constitute a fundamental approach to providing in-depth insights into the underlying flow physics of various turbulence mechanisms and how to apply them in various engineering applications. This Special Issue welcomes both theoretical and applied studies, as well as interdisciplinary research that combines mathematical modeling, computational methods, and experimental validations. Potential topics for submission include, but are not limited to, turbulence modeling, high-performance computing for turbulence simulations, turbulence closure models, and validation and verification of numerical methods for turbulent flow.

Prof. Dr. Abdelkader Frendi
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.

Keywords

  • turbulent flows
  • turbulent boundary layer
  • turbulent channel flow
  • computational fluid dynamics
  • fluid–structure interaction
  • numerical simulations
  • numerical methods
  • direct numerical simulations
  • large eddy simulation
  • hybrid RANS-LES
  • Navier–Stokes

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Published Papers (3 papers)

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Research

23 pages, 8729 KiB  
Article
PSE-Based Aerodynamic Flow Transition Prediction Using Automated Unstructured CFD Integration
by Nathaniel Hildebrand, Meelan M. Choudhari, Fei Li, Pedro Paredes and Balaji S. Venkatachari
Mathematics 2025, 13(7), 1034; https://doi.org/10.3390/math13071034 - 22 Mar 2025
Viewed by 247
Abstract
The accurate, robust, and efficient prediction of transition in viscous flows is a significant challenge in computational fluid dynamics. We present a coupled high-fidelity iterative approach that leverages the FUN3D flow solver and the LASTRAC stability code to predict transition in low-disturbance environments, [...] Read more.
The accurate, robust, and efficient prediction of transition in viscous flows is a significant challenge in computational fluid dynamics. We present a coupled high-fidelity iterative approach that leverages the FUN3D flow solver and the LASTRAC stability code to predict transition in low-disturbance environments, initiated by the linear growth of boundary-layer instability modes. Our method integrates the ability of FUN3D to compute mixed laminar–transitional–turbulent mean flows via transition-sensitized Reynolds-Averaged Navier–Stokes equations with the ability of LASTRAC to perform linear stability analysis, all within an automated framework that requires no intermediate user involvement. Unlike conventional frameworks that rely on classical stability theory or reduced-order metamodels, our approach employs parabolized stability equations to provide more accurate and reliable estimates of disturbance growth for multiple instability mechanisms, including Tollmien–Schlichting, Kelvin–Helmholtz, and crossflow modes. By accounting for the effects of mean-flow nonparallelism as well as the surface curvature, this approach lays the foundation for improved N-factor correlations for transition onset prediction in a broad class of flows. We apply this method to three distinct flow configurations: (1) flow over a zero-pressure-gradient flat plate, (2) the NLF-0416 airfoil with both natural and separation-induced transition, and (3) a 6:1 prolate spheroid, where transition is primarily driven by crossflow instability. For two-dimensional cases, a formulated intermittency distribution is used to model the transition zone between the laminar and fully turbulent flows. The results include comparisons with experimental measurements, similar numerical approaches, and transport-equation-based models, demonstrating good agreement in surface pressure coefficients, transition onset locations, and skin-friction coefficients for all three configurations. In addition to contributing a couple of new insights into boundary-layer transition in these canonical cases, this study presents a powerful tool for transition modeling in both research and design applications in aerodynamics. Full article
(This article belongs to the Special Issue Numerical Methods and Simulations for Turbulent Flow)
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28 pages, 1350 KiB  
Article
A Simplified Two-Fluid Model Based on Equilibrium Closure for a Dilute Dispersion of Small Particles
by S. Balachandar
Mathematics 2024, 12(22), 3543; https://doi.org/10.3390/math12223543 - 13 Nov 2024
Viewed by 622
Abstract
Two-fluid formalisms that fully account for all complex inter-phase interactions have been developed based on a rigorous ensemble-averaging procedure. Here, we apply equilibrium approximation to particle velocity to simplify two-phase flow equations for the case of a dilute dispersion of particles much smaller [...] Read more.
Two-fluid formalisms that fully account for all complex inter-phase interactions have been developed based on a rigorous ensemble-averaging procedure. Here, we apply equilibrium approximation to particle velocity to simplify two-phase flow equations for the case of a dilute dispersion of particles much smaller than the flow scales. First, we extend an earlier approach to consider the rotational motion of the particles and seek an equilibrium approximation for the angular velocity of the particulate phase. The resulting explicit knowledge of the particulate phase translational and rotational velocities in terms of fluid velocity eliminates the need to consider the momentum equations for the particulate phase. The equilibrium approximations also provide precise scaling for various terms in the governing equations of the two-fluid model, based on which a simplified set of equations is obtained here. Three different regimes based on the relative strength of gravitational settling are identified, and the actual form of the simplified two-phase flow equations depends on the regime. We present two simple examples illustrating the use of the simplified two-fluid formalism. Full article
(This article belongs to the Special Issue Numerical Methods and Simulations for Turbulent Flow)
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12 pages, 17305 KiB  
Article
Unified Gas Kinetic Simulations of Lid-Driven Cavity Flows: Effect of Compressibility and Rarefaction on Vortex Structures
by Vishnu Venugopal, Haneesha Iphineni, Divya Sri Praturi and Sharath S. Girimaji
Mathematics 2024, 12(18), 2807; https://doi.org/10.3390/math12182807 - 11 Sep 2024
Viewed by 3539
Abstract
We investigate and characterize the effect of compressibility and rarefaction on vortex structures in the benchmark lid-driven cavity flow. Direct numerical simulations are performed, employing the unified gas kinetic scheme to examine the changes in vortex generation mechanisms and the resulting flow structures [...] Read more.
We investigate and characterize the effect of compressibility and rarefaction on vortex structures in the benchmark lid-driven cavity flow. Direct numerical simulations are performed, employing the unified gas kinetic scheme to examine the changes in vortex generation mechanisms and the resulting flow structures at different Mach and Knudsen numbers. At high degrees of rarefaction, where inter-molecular interactions are minimal, the molecules mainly collide with the walls. Consequently, the dominant flow structure is a single vortex in the shape of the cavity. It is shown that increasing compressibility or decreasing rarefaction lead to higher molecular density in the cavity corners, due to more frequent inter-molecular collisions. This results in lower flow velocities, creating conditions conducive to the development of secondary and corner vortices. The physical processes underlying vortex formations at different Knudsen numbers, Mach numbers, and cavity shapes are explicated. A parametric map that classifies different regimes of vortex structures as a function of compressibility, rarefaction, and cavity shape is developed. Full article
(This article belongs to the Special Issue Numerical Methods and Simulations for Turbulent Flow)
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