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Mathematics
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Advances in Computational Dynamics and Mechanical Engineering
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Advances in Computational Dynamics and Mechanical Engineering

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

Deadline for manuscript submissions: 30 November 2024 | Viewed by 2634

Special Issue Editor

Dr. Mostafa Mahdavi

E-Mail Website
Guest Editor
Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa
Interests: heat and mass transfer; CFD; fluid mechanics; boiling and condensation; nanofluid

Special Issue Information

Dear Colleagues,

The development of fluid flow models in recent years has provided powerful tools for researchers to obtain and visualize simulation results using computational fluid dynamics. One of the main advantages of such an approach is finding the details of the actual flow process which are difficult to measure in an experiment.

This Special Issue focuses on numerical simulation and mathematical model research with an emphasis on recent advancements and applications in many industrial/academic applications. We are interested in papers addressing topics ranging from the novel application of existing mathematical tools in fluid dynamics to the development of novel numerical schemes to solve existing problems with the involvement of heat or mass transfer. This includes but is not limited to the following topics: (a) the use of standard numerical tools (e.g., finite difference, finite volume, finite element, meshless methods); (b) mass and energy conservation using new numerical methodologies, including their validation with benchmarking cases; (c) high-performance computing, including new parallel computing algorithms; (d) extendibility to dealing with more multiphysics phenomena such as magnetohydrodynamics (MHD), electrohydrodynamics (EHD), non-Newtonian flows, phase changes, nano-fluids, etc.; (e) the extension of the aforementioned methodologies to three-dimensional modeling and massively parallel computing in order to handle real-life problems; (f) mathematical modeling of multiphysics phenomena. Research articles, review papers, and short communications are also invited.

Dr. Mostafa Mahdavi
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

  • numerical modeling
  • fluid mechanics
  • CFD simulation
  • process simulation
  • mass, momentum, and heat-transfer processes
  • porous media
  • acoustics
  • electrochemistry
  • multibody solid mechanics
  • fluid–solid interactions
  • nanofluid flows
  • multiphysic phenomena
  • boiling and condensation
  • particulate systems

Published Papers (4 papers)

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Research

19 pages, 10024 KiB  
Article
A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method
by Maciej Leszczynski, Przemyslaw Perlikowski and Piotr Brzeski
Mathematics 2024, 12(7), 987; https://doi.org/10.3390/math12070987 - 26 Mar 2024
Viewed by 330
Abstract
This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase [...] Read more.
This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems. Full article
(This article belongs to the Special Issue Advances in Computational Dynamics and Mechanical Engineering)
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21 pages, 3224 KiB  
Article
Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields
by Yao Ma and Zhong-Min Wang
Mathematics 2024, 12(6), 840; https://doi.org/10.3390/math12060840 - 13 Mar 2024
Viewed by 556
Abstract
In this study, the Kevin–Voigt viscoelastic constitutive relationship is used to investigate the vibration characteristics and stability of a functionally graded viscoelastic(FGV) fluid-conveying pipe with initial geometric defects under thermal–magnetic coupling fields. First, the nonlinear dimensionless differential equations of motion are derived by [...] Read more.
In this study, the Kevin–Voigt viscoelastic constitutive relationship is used to investigate the vibration characteristics and stability of a functionally graded viscoelastic(FGV) fluid-conveying pipe with initial geometric defects under thermal–magnetic coupling fields. First, the nonlinear dimensionless differential equations of motion are derived by applying Timoshenko beam theory. Second, by solving the equilibrium position of the system, the nonlinear term in the differential equations of motion is approximated as the sum of the longitudinal displacement at the current time and longitudinal displacement relative to the position, and the equations are linearized. Third, these equations are discretized using the Galerkin method and are numerically solved under simply supported conditions. Finally, the effects of dimensionless temperature field parameters, dimensionless magnetic field parameters, thermal–magnetic coupling, initial geometric defect types, and the power-law exponent on the complex frequency of the pipe are examined. Results show that increasing the magnetic field intensity enhances the critical velocity of first-order mode instability, whereas a heightened temperature variation reduces the critical velocity of first-order diverge instability. Under thermal–magnetic fields, when the magnetic field intensity and temperature difference are simultaneously increased, their effects on the complex frequency can partially offset each other. Increasing the initial geometric defect amplitude increases the imaginary parts of the complex frequencies; however, for different types of initial geometric defect tubes, it exhibits the most distinct influence only on a certain order. Full article
(This article belongs to the Special Issue Advances in Computational Dynamics and Mechanical Engineering)
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16 pages, 728 KiB  
Article
Mathematical Modeling of Collisional Heat Generation and Convective Heat Transfer Problem for Single Spherical Body in Oscillating Boundaries
by Kwon Joong Son
Mathematics 2023, 11(22), 4637; https://doi.org/10.3390/math11224637 - 14 Nov 2023
Viewed by 725
Abstract
The application of high-energy ball milling in the field of advanced materials processing, such as mechanochemical alloying and ammonia synthesis, has been gaining increasing attention beyond its traditional use in material crushing. It is important to recognize the role of thermodynamics in high-energy [...] Read more.
The application of high-energy ball milling in the field of advanced materials processing, such as mechanochemical alloying and ammonia synthesis, has been gaining increasing attention beyond its traditional use in material crushing. It is important to recognize the role of thermodynamics in high-energy processes, including heat generation from collisions, as well as ongoing investigations into grinding ball behavior. This study aims to develop a mathematical model for the numerical analysis of a spherical ball in a shaker mill, taking into account its dynamics, contact mechanics, thermodynamics, and heat transfer. The complexity of the problem for mathematical modeling is reduced by limiting the motion to one-dimensional translation and representing the vibration of the vial wall in a shaker mill as rigid boundaries that move in a linear fashion. A nonlinear viscoelastic contact model is employed to construct a heat generation model. An equation of internal energy evolution is derived that incorporates a velocity-dependent heat convection model. In coupled field modeling, equations of motion for high-energy impact phenomena are derived from energy-based Hamiltonian mechanics rather than vector-based Newtonian mechanics. The numerical integration of the governing equations is performed at the system level to analyze the general heating characteristics during collisions and the effect of various operational parameters, such as the oscillation frequency and amplitude of the vial. The results of the numerical analysis provide essential performance metrics, including steady-state temperature and time constant for the characteristics of temperature evolution for a high-energy shaker milling process with a computation accuracy of 0.1%. The novelty of this modeling study is that it is the first to obtain such a high accuracy numerical solution for the temperature evolution associated with a shaker mill process. Full article
(This article belongs to the Special Issue Advances in Computational Dynamics and Mechanical Engineering)
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15 pages, 308 KiB  
Article
Decay of a Thermoelastic Laminated Beam with Microtemperature Effects, Nonlinear Delay, and Nonlinear Structural Damping
by Hicham Saber, Fares Yazid, Djamel Ouchenane, Fatima Siham Djeradi, Keltoum Bouhali, Abdelkader Moumen, Yousef Jawarneh and Tariq Alraqad
Mathematics 2023, 11(19), 4178; https://doi.org/10.3390/math11194178 - 6 Oct 2023
Viewed by 676
Abstract
This article deals with a non-classical model, namely a thermoelastic laminated beam along with microtemperature effects, nonlinear delay, and nonlinear structural damping, where the last two terms both affect the equation which depicts the dynamics of slip. With the help of convenient conditions [...] Read more.
This article deals with a non-classical model, namely a thermoelastic laminated beam along with microtemperature effects, nonlinear delay, and nonlinear structural damping, where the last two terms both affect the equation which depicts the dynamics of slip. With the help of convenient conditions in both weight delay and wave speeds, we demonstrate explicit and general energy decay rates of the solution. To attain our interests, we highlight useful properties regarding convex functions and apply a specific approach known as the multiplier technique, which enables us to prove the stability results. Our results here aim to show the impact of different types of damping by taking into account the interaction between them, which extends recent publications in the literature. Full article
(This article belongs to the Special Issue Advances in Computational Dynamics and Mechanical Engineering)
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