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Symmetry
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Symmetry in Numerical Analysis and Computational Fluid Dynamics
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Symmetry in Numerical Analysis and Computational Fluid Dynamics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 8705

Special Issue Editors

Dr. Dhananjay Yadav

E-Mail Website
Guest Editor
Department of Mathematical and Physical Sciences, University of Nizwa, P.O. Box 208, PC 133 Al Khuwair, Nizwa 616, Oman
Interests: carbon capture; storage and oil recovery; computational sustainability and environmental analytics; fluid mechanics; numerical analysis; hydrodynamic and hydromagnetic stability; nanofluids and fluid flow in porous media
Dr. Mukesh Kumar Awasthi

E-Mail Website
Guest Editor
Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, India
Interests: viscous potential flow; fluid mechanics; heat and mass transfer; hydrodynamic stability; numerical analysis
Dr. Rishi Asthana

E-Mail Website
Guest Editor
School of Engineering and Technology, BML Munjal University, Gurugram, Haryana 123106, India
Interests: vaporization; fluid mechanics; viscous potential flow; heat and mass transfer; soft computing; machine learning

Special Issue Information

Dear Colleagues,

Fluid flow, in various geometries, plays an important role in industry as well in our our daily life. In the case of cylindrical configuration, there are many applications of capillaries, such as water jets, film boiling, film-wise condensate, etc. The decay of any liquid cylindrical jet into different droplets is a complex and universal process that is useful both in nature and industry. The root cause of jet decay is the instability generated on the surface of the jet. When a liquid jet enters the atmosphere, the interface between the atmospheric air and the jet becomes unstable, resulting in liquid jet decay. The exact solution of the Navier–Stokes equation is not currently known, and therefore, general numerical- and symmetry-based numerical methods are very helpful for the computation of various properties of fluid flows required for industry.

The proposed Issue, “Symmetry in Numerical Analysis and Computational Fluid Dynamics”, will address the current developments in mathematical modeling and computations using general and symmetry-based numerical methods of various fluid phenomena arising in the biological, medical, and engineering sciences.

This issue will provide a comprehensive insight into the symmetrical and computational approaches to examine important emerging problems in the fields of fluid dynamics, including but not limited to:

  • Onset of convection;
  • Flow through porous media;
  • Characteristics of nanofluid flow;
  • Fluid–fluid interaction;
  • Fluid–solid interaction;
  • Instability arising in fluid flow;
  • Boundary layer theory;
  • Computational approaches;
  • Numerical techniques;
  • Flow through complex geometries;
  • Impact of complex fluids;
  • Symmetry and sensitivity analysis of fluid flows.

We invite contributions from authors on these topics.

Dr. Dhananjay Yadav
Dr. Mukesh Kumar Awasthi
Dr. Rishi Asthana
Guest Editors

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. Symmetry is an international peer-reviewed open access monthly 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 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

  • flow through complex geometries
  • complex fluid-flow and heat-transfer problems
  • flow through porous media
  • CFD theory and applications
  • numerical methods
  • symmetry analysis

Published Papers (6 papers)

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Research

26 pages, 13278 KiB  
Article
An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures
by Xiaoyingjie Huang, Jiabao Chen, Jun Zhang, Long Wang and Yan Wang
Symmetry 2023, 15(10), 1909; https://doi.org/10.3390/sym15101909 - 12 Oct 2023
Viewed by 700
Abstract
An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied [...] Read more.
An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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19 pages, 6138 KiB  
Article
Comparative Numerical Analysis for the Error Estimation of the Fluid Flow over an Inclined Axisymmetric Cylinder with a Gyrotactic Microbe
by Fuad A. Awwad, Emad A. A. Ismail, Waris Khan, Taza Gul and Abdul Samad Khan
Symmetry 2023, 15(10), 1811; https://doi.org/10.3390/sym15101811 - 22 Sep 2023
Cited by 1 | Viewed by 653
Abstract
The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of [...] Read more.
The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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23 pages, 8920 KiB  
Article
Bio-Convection Effects of MHD Williamson Fluid Flow over a Symmetrically Stretching Sheet: Machine Learning
by P. Priyadharshini, V. Karpagam, Nehad Ali Shah and Mansoor H. Alshehri
Symmetry 2023, 15(9), 1684; https://doi.org/10.3390/sym15091684 - 01 Sep 2023
Cited by 1 | Viewed by 1068
Abstract
The primary goal of this research study is to examine the influence of Brownian motion and thermophoresis diffusion with the impact of thermal radiation and the bioconvection of microorganisms in a symmetrically stretching sheet of non-Newtonian typical Williamson fluid. Structures of the momentum, [...] Read more.
The primary goal of this research study is to examine the influence of Brownian motion and thermophoresis diffusion with the impact of thermal radiation and the bioconvection of microorganisms in a symmetrically stretching sheet of non-Newtonian typical Williamson fluid. Structures of the momentum, energy, concentration, and bio-convection equations are interconnected with the imperative partial differential equations (PDEs). Similarity transformations are implemented to translate pertinent complicated partial differential equations into ordinary differential equations (ODEs). The BVP4C approach from the MATLAB assemblage computational methods scheme is extensively impacted by the results of these ODEs. The impact of several physical parameters, including Williamson fluid We(0.2≤We≤1.2), the magnetic field parameter M(0.0≤M≤2.5), Brownian motion Nb(0.0≤Nb≤1.0), thermophoresis diffusion Nt(0.1≤Nt≤0.9). In addition, various physical quantities of the skin friction (RexCfx), Nusselt number (Nux), Sherwood number (Shx), and motile microorganisms (Nnx) are occupied and demonstrate the visualization of graphs and tabular values. These outcomes are validated with earlier obtained results, displaying excellent synchronicity in the physical parameters. Furthermore, the physical quantities concerning the non-dimensional parameters are anticipated by employing Multiple Linear Regression (MLR) in Machine Learning (ML) as successfully executed a novelty of this study. These innovative techniques can help to advance development and technologies for future researchers. The real-world implications of this research are that bio-remediation, microbial movements in mixed fluids, and cancer prevention therapy are crucial. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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40 pages, 17062 KiB  
Article
Conjugate Heat Transfer Model for an Induction Motor and Its Adequate FEM Model
by Marek Gebauer, Tomáš Blejchař, Tomáš Brzobohatý and Miroslav Nevřela
Symmetry 2023, 15(7), 1294; https://doi.org/10.3390/sym15071294 - 21 Jun 2023
Cited by 1 | Viewed by 2504
Abstract
The primary objective of the research presented in this paper was to design a methodology for analyzing the thermal field of an induction motor that would be of higher fidelity but less time- and cost-consuming and that would deal with air-cooled induction motors [...] Read more.
The primary objective of the research presented in this paper was to design a methodology for analyzing the thermal field of an induction motor that would be of higher fidelity but less time- and cost-consuming and that would deal with air-cooled induction motors of all sizes. The complexity of the simulation is increased by the geometric asymmetry and by the asymmetric character of flow cooling the motor casing caused by the fan’s rotation. This increases demand, especially on computational resources, as creating a simplified numerical model using symmetry boundary conditions is impossible. The new methodology uses the existing findings from many partial articles and literature, which are modified into more accurate relationships suitable for predicting the external thermal field of induction motors. That way, we do not have to solve the thermal field by the conjugate heat transfer method, and it is possible to assess temperature gradients over the entire range. Furthermore, a new relationship between shear strain rate and thermal contact conductivity has been discovered that allows solving heat transfer of fluid adjacent to the internal walls of an induction motor at any location. That approach has not yet been published in the literature, so it can be considered a new method to simplify heat transfer simulation. An experimentally validated new methodology of the induction motor was performed. The so-called digital twin will be used for the virtual optimization of the new designs concerning minimizing losses and maximizing efficiency. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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10 pages, 284 KiB  
Article
The n-Point Composite Fractional Formula for Approximating Riemann–Liouville Integrator
by Iqbal M. Batiha, Shameseddin Alshorm, Abdallah Al-Husban, Rania Saadeh, Gharib Gharib and Shaher Momani
Symmetry 2023, 15(4), 938; https://doi.org/10.3390/sym15040938 - 19 Apr 2023
Cited by 5 | Viewed by 1006
Abstract
In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann–Liouville fractional integral operator. With the use of the definite fractional integral’s definition coupled with the generalized Taylor’s formula, a novel three-point central fractional formula is established [...] Read more.
In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann–Liouville fractional integral operator. With the use of the definite fractional integral’s definition coupled with the generalized Taylor’s formula, a novel three-point central fractional formula is established for approximating a Riemann–Liouville fractional integrator. Such a new formula, which emerges clearly from the symmetrical aspects of the proposed numerical approach, is then further extended to formulate an n-point composite fractional formula for approximating the same operator. Several numerical examples are introduced to validate our findings. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
15 pages, 4721 KiB  
Article
Analysis of a Squeezing Flow of a Casson Nanofluid between Two Parallel Disks in the Presence of a Variable Magnetic Field
by Reshu Gupta, Janani Selvam, Ashok Vajravelu and Sasitharan Nagapan
Symmetry 2023, 15(1), 120; https://doi.org/10.3390/sym15010120 - 01 Jan 2023
Cited by 6 | Viewed by 1257
Abstract
The present article deals with the MHD flow of a Casson nanofluid between two disks. The lower disk was fixed as well as permeable. The upper disk was not permeable, but it could move perpendicularly up and down toward the lower disk. Titanium [...] Read more.
The present article deals with the MHD flow of a Casson nanofluid between two disks. The lower disk was fixed as well as permeable. The upper disk was not permeable, but it could move perpendicularly up and down toward the lower disk. Titanium dioxide was selected as nanoparticles and water as a base fluid. The governing higher-order nonlinear partial differential equations were transformed into a set of nonlinear ordinary differential equations by using similarity transformation. The differential transform method (DTM) was applied to solve the nonlinear ODEs. The nature of the velocity profiles for the different values of the suction injection parameter, the squeeze number, the Casson fluid parameter, and the volume fraction parameter of the nanofluid are pictorially discussed in this paper. The coefficient of skin friction was tabulated for the novelty of the research. The comparison of the results was determined by the DTM and the numerical methods. The profile values were also compared with the literature work and found to agree. This comparative study proves the accuracy and efficiency of the method. It is concluded from this research that the flow properties behave oppositely for all parameters during suction and injection. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Computational Fluid Dynamics)
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