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Mathematics
Special Issues
High-Order Numerical Methods and Computational Fluid Dynamics
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High-Order Numerical Methods and Computational Fluid Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 20 January 2026 | Viewed by 790

Special Issue Editor

Dr. KyungSung Kim

E-Mail Website
Guest Editor
Department of Mechatronics Convergence Engineering, Changwon National University, Changwon, Republic of Korea
Interests: particle-based simulation; high-order numerical applications; fluid–structure interaction

Special Issue Information

Dear Colleagues,

In this Special Issue, we aim to present the recent developments in the theory and applications of high-order numerical methods and computational fluid dynamics including conventional and particle applications. This special issue will accept high-quality papers containing original research results and review articles of exceptional merit in the following fields: particle-based simulation, high-order multiphase instability, hydrodynamics, computational fluid dynamics with Neural networks.

Dr. KyungSung Kim
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

  • high-order numerical method
  • computational fluid dynamics
  • particle-based simulation method
  • neural network in CFD
  • numerical schemes and algorithms
  • high-order hydrodynamics

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Published Papers (1 paper)

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Research

26 pages, 43661 KB  
Article
Numerical Investigation of Atwood Number Effects on Shock-Driven Single-Mode Stratified Heavy Fluid Layers
by Salman Saud Alsaeed, Satyvir Singh and Nouf A. Alrubea
Mathematics 2025, 13(18), 3032; https://doi.org/10.3390/math13183032 - 19 Sep 2025
Cited by 1 | Viewed by 357
Abstract
This work presents a numerical investigation of Richtmyer–Meshkov instability (RMI) in shock-driven single-mode stratified heavy fluid layers, with emphasis on the influence of the Atwood number. High-order modal discontinuous Galerkin simulations are carried out for Atwood numbers ranging from A=0.30 to [...] Read more.
This work presents a numerical investigation of Richtmyer–Meshkov instability (RMI) in shock-driven single-mode stratified heavy fluid layers, with emphasis on the influence of the Atwood number. High-order modal discontinuous Galerkin simulations are carried out for Atwood numbers ranging from A=0.30 to 0.72, allowing a systematic study of interface evolution, vorticity dynamics, and mixing. The analysis considers diagnostic quantities such as interface trajectories, normalized interface length and amplitude, vorticity extrema, circulation, enstrophy, and kinetic energy. The results demonstrate that the Atwood number plays a central role in instability development. At low A, interface deformation remains smooth and coherent, with weaker vorticity deposition and delayed nonlinear roll-up. As A increases, baroclinic torque intensifies, leading to rapid perturbation growth, stronger vortex roll-ups, and earlier onset of secondary instabilities such as Kelvin–Helmholtz vortices. Enstrophy, circulation, and interface measures show systematic amplification with increasing density contrast, while the total kinetic energy exhibits relatively weak sensitivity to A. Overall, the study highlights how the Atwood number governs the transition from linear to nonlinear dynamics, controlling both large-scale interface morphology and the formation of small-scale vortical structures. These findings provide physical insight into shock–interface interactions and contribute to predictive modeling of instability-driven mixing in multicomponent flows. Full article
(This article belongs to the Special Issue High-Order Numerical Methods and Computational Fluid Dynamics)
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