Fluid Dynamics: Mathematics and Numerical Experiment

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

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 2890

Special Issue Editors


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Guest Editor
1. I. I. Vorovich Institute for Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-na-Donu 344090, Russia
2. Southern Mathematical Institute of VSC RAS, Vladikavkaz 362027, Russia
Interests: non-linear dynamics; stability and bifurctaions; asymptotic analysis; averaging and homogenization; fluid mechanics; perceptive and chermosensitive motions; populational dynamics; mathematical modelling

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Guest Editor
Department of Mathematics, DCC-KFUPM, P.O. Box 5084, Dhahran 31261, Saudi Arabia
Interests: mathematical modelling; computational fluid dynamics; modeling and simulation; numerical analysis; applied mathematics; engineering, applied and computational mathematics; computational simulation; numerical simulation; numerical modeling; numerical mathematics

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Guest Editor
Vorovich Institute of Mathematics, Mechanics and Computer Science, Milchakova Street 8a, Southern Federal University, 344090 Rostov-on-Don, Russia
Interests: mathematical modeling of convection-diffusion problems; iterative methods for solving linear algebraic equation systems; preconditioning of the linear systems of algebraic equations; constrained optimization problems; iterative methods for saddle point linear systems of algebraic equations

Special Issue Information

Dear Colleagues,

We cordially invite you to submit your research to this Special Issue. Despite the considerable recent advances in mathematical theory and numerical techniques for fluids, a multitude of challenging issues remain. Given the existing high-intensity investigations, it is very important to present every achievement to the research community, and a logical way to do so is by taking advantage of open-access publishing. This Special Issue in Axioms aims to provide such an opportunity to a wider range of researchers working in Fluid Dynamics. That is why it is our intention to set a wide scope for this Special Issue. We encourage the submitting of high-quality studies of boundary-value problems; developments in the numerical schemes; numerical, asymptotical, and exact solutions to concrete problems, analytical and numerical analyses of stability problems; and research into instabilities, bifurcations, and any other matters of such a kind with applications in Fluid Dynamics. Our scope covers but is not restricted to vortex dynamics, free boundary flows, water waves, shallow water and thin films, viscous incompressible fluid, stratified and compressible fluid, electro/magnetohydrodynamics, fluid–structure interactions, hemodynamics, microfluidics, and coupling the Keller–Segel systems to hydrodynamics.

Dr. Andrey Morgulis
Dr. Muhammad Adil Sadiq
Dr. Tatiana S. Martynova
Guest Editors

Manuscript Submission Information

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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

  • fluid dynamics
  • microfluidics
  • hemodynamics
  • fluid-structure
  • numerical methods
  • reasonings asymptotics
  • exact solutions
  • simulation
  • wellposedness
  • stability
  • bifurcation
  • nonlinear dynamics

Published Papers (4 papers)

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Research

25 pages, 5968 KiB  
Article
Analyzing Richtmyer–Meshkov Phenomena Triggered by Forward-Triangular Light Gas Bubbles: A Numerical Perspective
by Satyvir Singh and Ahmed Hussein Msmali
Axioms 2024, 13(6), 365; https://doi.org/10.3390/axioms13060365 - 29 May 2024
Viewed by 260
Abstract
In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded [...] Read more.
In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded by nitrogen gas. Three different shock Mach numbers are considered: Ms=1.12,1.21, and 1.41. For the numerical simulations, a two-dimensional system of compressible Euler equations for two-component gas flows is solved by utilizing the high-fidelity explicit modal discontinuous Galerkin technique. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The numerical model explores the impact of the Atwood number on the underlying mechanisms of the shock-induced forward-triangle bubble, encompassing aspects such as flow evolution, wave characteristics, jet formation, generation of vorticity, interface features, and integral diagnostics. Furthermore, the impacts of shock strengths and positive Atwood numbers on the flow evolution are also analyzed. Insights gained from this numerical perspective enhance our understanding of RM phenomena triggered by forward-triangular light gas bubbles, with implications for diverse applications in engineering, astrophysics, and fusion research. Full article
(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)
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24 pages, 393 KiB  
Article
Steady Solutions to Equations of Viscous Compressible Multifluids
by Alexander Mamontov and Dmitriy Prokudin
Axioms 2024, 13(6), 362; https://doi.org/10.3390/axioms13060362 - 28 May 2024
Viewed by 267
Abstract
For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are [...] Read more.
For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are shown to exist with weak constraints on the types of viscosity matrices and constitutive equations for pressure and momentum exchange. Full article
(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)
19 pages, 1539 KiB  
Article
Numerical Simulation of Flows Using the Fourier Pseudospectral Method and the Immersed Boundary Method
by Laura Augusta Vasconcelos de Albuquerque, Mariana Fernandes dos Santos Villela and Felipe Pamplona Mariano
Axioms 2024, 13(4), 228; https://doi.org/10.3390/axioms13040228 - 30 Mar 2024
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Abstract
The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high [...] Read more.
The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high accuracy and low computational cost inherent in pseudospectral methods, thanks to the utilization of the Fast Fourier Transform algorithm. IBM is employed to impose non-periodic boundary conditions in the Navier–Stokes equations, addressing the requirement of periodicity at boundaries for FPSM convergence and to accurately represent the immersed slender airfoil in the flow. The aerodynamic behavior of the analyzed profiles was assessed by calculating lift and drag coefficients, which were then compared with existing literature results. Consistently favorable outcomes were observed, particularly in flows at lower Reynolds numbers, demonstrating the effectiveness of the IMERSPEC methodology for simulating complex flows computationally. Additionally, weight functions, fundamental to IBM, are employed flexibly for aerodynamic force calculations. Specifically, within the same simulation, a Cubic function is utilized for drag calculation while a Hat function is employed for lift calculation, yielding results more closely aligned with the literature’s findings. This approach offers an alternative to previously proposed methods for IBM implementation. Full article
(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)
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18 pages, 2633 KiB  
Article
Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes
by Alexander Chupakhin, Alexander Mamontov and Sergey Vasyutkin
Axioms 2024, 13(1), 65; https://doi.org/10.3390/axioms13010065 - 19 Jan 2024
Viewed by 929
Abstract
This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are [...] Read more.
This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel’s central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas. Full article
(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)
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