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Axioms
Special Issues
Mathematical Modelling of Fluid Dynamics
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Mathematical Modelling of Fluid Dynamics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 677

Special Issue Editor

Dr. Xi Deng

E-Mail Website
Guest Editor
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Interests: computational fluid dynamics; numerical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The mathematical modelling of fluid dynamics plays an important role in understanding fluid physics in various industrial applications such as aerospace engineering, chemical engineering, etc. However, the mathematical modelling of fluid dynamics with high accuracy and high fidelity remains challenging as fluid dynamics involves multi-scale and multi-physics problems.

This Special Issue welcomes the submission of research and review articles that address the development of novel mathematical modelling and its applications. Topics of interest for this Special Issue may include, but are not limited to, the following subjects: numerical methods in fluid dynamics, multiphase flow modelling, reacting flow modelling, compressible and incompressible flows, fluid–structure interactions, and machine learning. Any work relevant to these topics is welcome to be submitted.

Dr. Xi Deng
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. Axioms 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

  • numerical methods
  • multiphase flows
  • combustion
  • high-speed compressible flows
  • incompressible flows
  • fluid–structure interactions
  • machine learning
  • aerospace engineering
  • chemical engineering

Published Papers (1 paper)

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Research

25 pages, 2819 KiB  
Article
Explicit Numerical Manifold Characteristic Galerkin Method for Solving Burgers’ Equation
by Yue Sun, Qian Chen, Tao Chen and Longquan Yong
Axioms 2024, 13(6), 343; https://doi.org/10.3390/axioms13060343 - 22 May 2024
Viewed by 435
Abstract
This paper presents a nonstandard numerical manifold method (NMM) for solving Burgers’ equation. Employing the characteristic Galerkin method, we initially apply the Crank–Nicolson method for temporal discretization along the characteristic. Subsequently, utilizing the Taylor expansion, we transform the semi-implicit formula into a fully [...] Read more.
This paper presents a nonstandard numerical manifold method (NMM) for solving Burgers’ equation. Employing the characteristic Galerkin method, we initially apply the Crank–Nicolson method for temporal discretization along the characteristic. Subsequently, utilizing the Taylor expansion, we transform the semi-implicit formula into a fully explicit form. For spacial discretization, we construct the NMM dual-cover system tailored to Burgers’ equation. We choose constant cover functions and first-order weight functions to enhance computational efficiency and exactly import boundary constraints. Finally, the integrated computing scheme is derived by using the standard Galerkin method, along with a Thomas algorithm-based solution procedure. The proposed method is verified through six benchmark numerical examples under various initial boundary conditions. Extensive comparisons with analytical solutions and results from alternative methods are conducted, demonstrating the accuracy and stability of our approach, particularly in solving Burgers’ equation at high Reynolds numbers. Full article
(This article belongs to the Special Issue Mathematical Modelling of Fluid Dynamics)
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