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Mathematics
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Numerical Advances in Computational Fluid Dynamics
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Numerical Advances in Computational Fluid Dynamics

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

Deadline for manuscript submissions: 31 July 2024 | Viewed by 1108

Special Issue Editors

Dr. Célio Fernandes

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Guest Editor
1. Center of Mathematics (CMAT), School of Science, University of Minho, Campus of Gualtar, 4710-057 Braga, Portugal
2. Transport Phenomena Research Center (CEFT), Faculty of Engineering at University of Porto (FEUP), Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal
Interests: computational and applied mathematics; difference and differential equations; engineering mathematics; mathematics and computer science
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Leandro Franco Souza

E-Mail Website
Guest Editor
Department of Applied Mathematics and Statistics, Institute of Mathematics and Computational Sciences, University of Sao Paulo, Av. Trabalhador Sao-carlense 400, CP 668, Sao Carlos 13560-970, SP, Brazil
Interests: numerical methods; high order approximations; computational fluid dynamics
Prof. Dr. Antonio Castelo Filho

E-Mail Website
Guest Editor
Department of Applied Mathematics and Statistics, Institute of Mathematics and Computational Sciences, University of Sao Paulo, Av. Trabalhador Sao-carlense 400, CP 668, Sao Carlos 13560-970, SP, Brazil
Interests: geometric processing; mesh generation; numerical methods; computational fluid dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue in the Mathematics journal aims to explore recent advancements in mathematical modelling and numerical methods in computational modelling. The efficient and accurate simulation of computational modelling is of paramount importance in various engineering and scientific applications. Therefore, this Special Issue invites original research contributions that focus on the development and implementation of numerical methods, code verification, and code validation techniques in the context of computational fluid dynamics or solid mechanics.

Topics of interest include, but are not limited to:

Mathematical modelling: Papers that propose new mathematical models or refine existing models for describing complex multiphase flows. These contributions should provide insight into the physical phenomena, interface tracking, and rheological behaviour of multiphase systems.

Numerical methods: Novel numerical methods, including finite difference, finite volume, finite element, and other mesh-based techniques, to efficiently solve the governing equations of multiphase flows. Emphasis should be placed on accuracy, stability, and convergence properties.

Code verification and validation: Studies that address code verification and validation methodologies in the context of fluid flow simulations and solid mechanics. Contributions should focus on assessing the accuracy and reliability of numerical methods, comparing with analytical solutions or experimental data.

Researchers and practitioners from various disciplines, including applied mathematics, mechanical engineering, chemical engineering, fluid dynamics, and solid mechanics, are encouraged to submit their original research articles, reviews, and case studies to this Special Issue. This collection aims to foster a better understanding of the numerical challenges in engineering mathematics and promote the development of innovative and efficient computational techniques for this important field.

Dr. Célio Fernandes
Prof. Dr. Leandro Franco Souza
Prof. Dr. Antonio Castelo Filho
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. 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

  • mathematical modelling
  • numerical methods
  • code verification
  • code validation
  • computational fluid dynamics
  • computational solid mechanics
  • finite difference method
  • finite volume method
  • finite element method

Published Papers (1 paper)

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Research

21 pages, 2271 KiB  
Article
Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm
by Aquisson T. G. da Silva, Célio Fernandes, Juniormar Organista, Leandro Souza and Antonio Castelo
Mathematics 2023, 11(18), 3900; https://doi.org/10.3390/math11183900 - 13 Sep 2023
Viewed by 757
Abstract
This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation is located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the [...] Read more.
This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation is located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the piecewise-linear interface calculation (PLIC) scheme of the VOF method is performed to solve the three-dimensional (3D) interface transport during the dynamics of two-phase flows. In this method, the interface is approximated by a line segment in each interfacial cell. The balance of forces at the interface is accounted for using the continuum interfacial force (CSF) model. To solve the Navier–Stokes equations, meshless finite difference schemes from the HiG-Flow computational fluid dynamics software are employed. The 3D PLIC-VOF HiG-Flow algorithm is used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation is evaluated by conducting two standard advection numerical tests: the 3D shearing flow test and the 3D deforming field test. Good agreement is obtained for the 3D interface shape using both the 3D PLIC-VOF HiG-Flow algorithm and those found in the scientific literature, specifically, the piecewise-constant flux surface calculation, the volume of fluid method implemented in OpenFOAM, and the high-order finite-element software FEEL. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm is found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. The volume fraction conservation absolute errors obtained using our algorithm are 4.48×10−5 and 9.41×10−6 for both shearing and deforming flow tests, respectively, being two orders lower than the results presented in the scientific literature at the same level of mesh refinement. Lastly, the 3D bubble rising problem is simulated for different fluid densities (ρ1/ρ2=10 and ρ1/ρ2=1000) and viscosity ratios (μ1/μ2=10 and μ1/μ2=100). Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and OpenFOAM, DROPS, and NaSt3D software. The 3D PLIC-VOF HiG-Flow algorithm predicted a stable ellipsoidal droplet shape for ρ1/ρ2=10 and μ1/μ2=10, and a stable cap shape for ρ1/ρ2=1000 and μ1/μ2=100. The bubble’s rise velocity and evolution of the bubble’s center of mass are also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with those software. The rise velocity of the droplet for both the ellipsoidal and cap flow regime’s is found, in the initial stages of the simulation, to gradually increase from its initial value of zero to a maximum magnitude; then, the steady-state velocity of the droplet decreases, being more accentuated for the cap regime. Full article
(This article belongs to the Special Issue Numerical Advances in Computational Fluid Dynamics)
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