The absorbing boundary conditions of Newtonian fluid flowing across a semi-infinite plate with different velocities and pressures

Lin Liu; Jiajia Li; Jingyu Yang; Jihong Wang; Yu Wang; Siyu Chen; Libo Feng; Chiyu Xie; Jing Zhu

doi:10.1515/zna-2023-0258

Article

The absorbing boundary conditions of Newtonian fluid flowing across a semi-infinite plate with different velocities and pressures

Lin Liu , Jiajia Li , Jingyu Yang , Jihong Wang , Yu Wang , Siyu Chen , Libo Feng , Chiyu Xie and Jing Zhu

Published/Copyright: December 22, 2023

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From the journal Zeitschrift für Naturforschung A Volume 79 Issue 4

Abstract

The Newtonian fluid flowing across a semi-infinite plate with variable velocity and pressure is considered in this work. The dimensionless governing equation is obtained by introducing the dimensionless quantities. For infinite region, the artificial boundary approach by using the Laplace transform is applied to gain the absorbing boundary condition (ABC) in a finite region which we call the inner region. The approach differs from the traditional approximation method for infinite boundaries with large values and is first applied to the research. And the stability of the ABC is verified by considering the same point of the outer region and inner region. The numerical difference scheme by using the L1-scheme to approximate the fractional derivative is used to get solutions, and the feasibility assessments, such as stability and convergence, are developed. Three numerical examples are given. In the first example, the exact solution is gained by importing a source term. Through the comparison of numerical solution with exact solution verifies the accuracy of difference method. A comparison between the velocity distribution of the ABC and the infinite boundary approximated by a large value is also discussed and graphically analyzed. In the following two examples, by analyzing the fluid flow over the plate with assorted speeds or pressure gradient, the impact of correlative parameters on the velocity distribution and the flow mechanism are thoroughly analyzed.

Keywords: absorbing boundary condition; constitutive model; Newtonian fluid; numerical difference method

Corresponding author: Lin Liu, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China; and State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China, E-mail: liulin1020@126.com

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11801029, 12302326

Funding source: Open Fund of State key laboratory of advanced metallurgy in the University of Science and Technology Beijing

Award Identifier / Grant number: K22-08

Funding source: Fundamental Research Funds for the Central Universities

Award Identifier / Grant number: FRF-IDRY-22-014; QNXM20220048; FRF-EYIT-23-07

Acknowledgment

The author would like to thank the anonymous reviewers for their valuable suggestions, which have greatly improved the quality of this paper.

Research ethics: Not applicable.
Author contributions: LL Writing – review & editing (equal). JLWriting-original draft (equal). JY Formal analysis (equal). JW Software(equal). YW Software (equal). SC Resources (equal). LF Writing –review & editing (equal); CX Investigation (equal); JZ Investigation(equal). The authors have accepted responsibility for the entire contentof this manuscript and approved its submission.
Competing interests: The authors state no conflict of interest.
Research funding: The work is supported by the Project funded by theNational Natural Science Foundation of China (No. 11801029, 12302326),Interdisciplinary Research Project for Young Teachers of USTB(Fundamental Research Funds for the Central Universities) (No. FRFIDRY-22-014), Fundamental Research Funds for the Central Universities(Nos. QNXM20220048, FRF-EYIT-23-07), and the Open Fund of Statekey laboratory of advanced metallurgy in the University of Science andTechnology Beijing (No. K22–08).
Data availability: TNot applicable.

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Received: 2023-09-22

Accepted: 2023-12-04

Published Online: 2023-12-22

Published in Print: 2024-04-25

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Articles in the same Issue

https://doi.org/10.1515/zna-2023-0258

Keywords for this article

absorbing boundary condition; constitutive model; Newtonian fluid; numerical difference method