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Mathematics
Special Issues
Computational Mathematics and Numerical Analysis with Applications
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Computational Mathematics and Numerical Analysis with Applications

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

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 3035

Special Issue Editor

Dr. Bishnu Lamichhane

E-Mail Website
Guest Editor
School of Information and Physical Sciences, College of Engineering, Science and Environment, University of Newcastle, Callaghan, NSW 2308, Australia
Interests: applied mathematics; numerical analysis; finite element method; approximation theory; mathematical modeling; optimization; fluid mechanics

Special Issue Information

Dear Colleagues,

Recently, the role of computational mathematics has increased tremendously in different areas of science and engineering. This Special Issue will present recent research results in computational mathematics and publish state-of-the-art fundamental development for applied mathematics and advanced numerical methods, prospective research directions, and their applications. Original and survey papers on analysis, modeling, control, and optimization using advanced computational mathematics and numerical methods with applications to different areas of science, technology, engineering, and other disciplines related to computations are all welcome.

Topics include but are not limited to:

  • Numerical analysis of differential equations and integral equations;
  • Partial differential equations and their applications;
  • Finite element methods with applications;
  • Computational fluid dynamics and fluid mechanics;
  • Scientific computing and algorithms;
  • Computational mathematics applied to data science;
  • Applied mathematics in optimization problems;
  • Mathematical image and signal processing;
  • Numerical methods for problems arising in science, technology, and engineering.

Dr. Bishnu Lamichhane
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 analysis
  • partial differential equations
  • scientific computing
  • finite element methods
  • computational fluid dynamics
  • optimization
  • data science
  • image processing
  • signal processing
  • numerical methods in science, technology and engineering

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (2 papers)

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Research

19 pages, 392 KiB  
Article
A Linear Stabilized Incompressible Magnetohydrodynamic Problem with Magnetic Pressure
by Shahid Hussain, Ahmed Bakhet, Ghada AlNemer and Mohammed Zakarya
Mathematics 2024, 12(12), 1839; https://doi.org/10.3390/math12121839 - 13 Jun 2024
Viewed by 750
Abstract
The objective of this article is to examine, stabilize, and linearize the incompressible magnetohydrodynamic model equations. The approximate solutions are carried out through the lowest equal order mixed finite element (FE) approach, involving variables such as fluid velocity, hydro pressure, magnetic field, and [...] Read more.
The objective of this article is to examine, stabilize, and linearize the incompressible magnetohydrodynamic model equations. The approximate solutions are carried out through the lowest equal order mixed finite element (FE) approach, involving variables such as fluid velocity, hydro pressure, magnetic field, and magnetic pressure. The formulation of the variational form for the approximate solution necessitates the use of a pair of approximating spaces. However, these spaces cannot be arbitrarily chosen; they must adhere to strict stability conditions, notably the Ladyzhenskaya–Babuska–Brezzi (LBB) or inf-sup condition. This study addresses the absence of stabilization and linearization techniques in the incompressible magnetohydrodynamic model equations using the lowest equal order mixed finite element approach. The article introduces a stabilization technique to meet two stability conditions, proving its existence and uniqueness. This novel approach was not previously explored in the literature. The proposed stabilized technique does not necessitate parameters or computing higher-order derivatives, making it computationally efficient. The study offers numerical tests demonstrating optimal convergence and effectiveness of the revised approach in two-dimensional settings. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis with Applications)
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22 pages, 16614 KiB  
Article
Rectangular Cylinder Orientation and Aspect Ratio Impact on the Onset of Vortex Shedding
by Neelam Tahir, Waqas Sarwar Abbasi, Hamid Rahman, Mubarak Alrashoud, Ahmed Ghoneim and Abdulhameed Alelaiwi
Mathematics 2023, 11(22), 4571; https://doi.org/10.3390/math11224571 - 7 Nov 2023
Cited by 1 | Viewed by 1797
Abstract
Rectangular cylinders have the potential to provide valuable insights into the behavior of fluids in a variety of real-world applications. Keeping this in mind, the current study compares the behavior of fluid flow around rectangular cylinders with an aspect ratio (AR) of 1:2 [...] Read more.
Rectangular cylinders have the potential to provide valuable insights into the behavior of fluids in a variety of real-world applications. Keeping this in mind, the current study compares the behavior of fluid flow around rectangular cylinders with an aspect ratio (AR) of 1:2 or 2:1 under the effect of the Reynolds number (Re). The incompressible lattice Boltzmann method is used for numerical computations. It is found that the flow characteristics are highly influenced by changes in the aspect ratio compared to the Reynolds number. The flow exhibits three different regimes: Regime I (steady flow), Regime II (initial steady flow that becomes unsteady afterward), and Regime III (completely unsteady flow). In the case of the cylinder with an aspect ratio of 2:1, vortex generation, variation in drag, and the lift coefficient occur much earlier at very low Reynolds numbers compared to the cylinder with an aspect ratio of 1:2. For the cylinder with an aspect ratio of 1:2, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 120, 121 ≤ Re ≤ 144, and 145 ≤ Re ≤ 200, respectively. For the cylinder with an aspect ratio of 2:1, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 24, 25 ≤ Re ≤ 39, and 40 ≤ Re ≤ 200, respectively. The cylinder with an aspect ratio of 1:2 is found to have the ability to stabilize the incoming flow due to its extended after-body flatness. Generally, it has been found that a cylinder with an AR of 2:1 is subjected to higher pressures, higher drag forces, higher curvatures of cross-flow rotations, and higher amplitudes of flow-induced drag, as well as higher lift coefficients and lower shedding frequencies, compared to cylinders with an AR of 1:2. In Regime III, elliptic and vertically mounted airfoil-like flow structures are also observed in the wake of the cylinders. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis with Applications)
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