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 579

Special Issue 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

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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 359
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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