Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

doi:10.1007/s10483-023-2970-6

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (4): 669-692.doi: https://doi.org/10.1007/s10483-023-2970-6

• 论文 • 上一篇

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

M. HAMID^1,2, M. USMAN³, Zhenfu TIAN²

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2. Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China;
3. School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China

收稿日期:2022-06-13 修回日期:2023-01-02 发布日期:2023-03-30
通讯作者: Zhenfu TIAN, E-mail: zftian@fudan.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 12250410244 and 11872151), the Jiangsu Province Education Development Special Project-2022 for Double First-ClassSchool Talent Start-up Fund of China (No. 2022r109), and the Longshan Scholar Program of Jiangsu Province of China

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

M. HAMID^1,2, M. USMAN³, Zhenfu TIAN²

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2. Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China;
3. School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China

Received:2022-06-13 Revised:2023-01-02 Published:2023-03-30
Contact: Zhenfu TIAN, E-mail: zftian@fudan.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 12250410244 and 11872151), the Jiangsu Province Education Development Special Project-2022 for Double First-ClassSchool Talent Start-up Fund of China (No. 2022r109), and the Longshan Scholar Program of Jiangsu Province of China

摘要/Abstract

摘要： The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics (MHD) flows. The time derivative is expressed by means of Caputo's fractional derivative concept, while the model is solved via the full-spectral method (FSM) and the semi-spectral scheme (SSS). The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques. The SSS is developed by discretizing the time variable, and the space domain is collocated by using equal points. A detailed comparative analysis is made through graphs for various parameters and tables with existing literature. The contour graphs are made to show the behaviors of the velocity and magnetic fields. The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows, and the concept may be extended for variable order models arising in MHD flows.

关键词: higher-dimensional Chelyshkov polynomial (CP), time-dependent magnetohydrodynamics (MHD) flow, fractional convection-diffusion model, convergence, stability and error bound, finite difference and higher-order scheme

Abstract: The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics (MHD) flows. The time derivative is expressed by means of Caputo's fractional derivative concept, while the model is solved via the full-spectral method (FSM) and the semi-spectral scheme (SSS). The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques. The SSS is developed by discretizing the time variable, and the space domain is collocated by using equal points. A detailed comparative analysis is made through graphs for various parameters and tables with existing literature. The contour graphs are made to show the behaviors of the velocity and magnetic fields. The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows, and the concept may be extended for variable order models arising in MHD flows.

Key words: higher-dimensional Chelyshkov polynomial (CP), time-dependent magnetohydrodynamics (MHD) flow, fractional convection-diffusion model, convergence, stability and error bound, finite difference and higher-order scheme

中图分类号:

M. HAMID, M. USMAN, Zhenfu TIAN. Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 669-692.

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Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

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