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Article Open Access November 05, 2021

Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion

Zhenwei Zhu 1 and Junjie Chen 1,*
1
Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China
Publihed in: Current Research in Public Health (Volume 1, Issue 1, 2022)
Page(s): 1-10
DOI: 10.31586/ujpr.2022.155
Received
September 30, 2021
Revised
November 01, 2021
Accepted
November 04, 2021
Published
November 05, 2021
Keywords
Runge-Kutta methods; Compact finite difference schemes; Convection-diffusion equations; Stabil-ity analysis; High-order accuracy; Crank-Nicolson methods
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright: Copyright © The Author(s), 2022. Published by Scientific Publications
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Cite This Article

APA Style
Zhu, Z. , & Chen, J. (2022). Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion. Current Research in Public Health, 1(1), 1-10. https://doi.org/10.31586/ujpr.2022.155
ACS Style
Zhu, Z. ; Chen, J. Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion. Current Research in Public Health 2022 1(1), 1-10. https://doi.org/10.31586/ujpr.2022.155
Chicago/Turabian Style
Zhu, Zhenwei, and Junjie Chen. 2022. "Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion". Current Research in Public Health 1, no. 1: 1-10. https://doi.org/10.31586/ujpr.2022.155
AMA Style
Zhu Z, Chen J. Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion. Current Research in Public Health. 2022; 1(1):1-10. https://doi.org/10.31586/ujpr.2022.155 
@Article{crph155,
AUTHOR = {Zhu, Zhenwei and Chen, Junjie},
TITLE = {Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion},
JOURNAL = {Current Research in Public Health},
VOLUME = {1},
YEAR = {2022},
NUMBER = {1},
PAGES = {1-10},
URL = {https://www.scipublications.com/journal/index.php/ujpr/article/view/155},
ISSN = {2831-5162},
DOI = {10.31586/ujpr.2022.155},
ABSTRACT = {The convection-diffusion equation is of primary importance in understanding transport phenom-ena within a physical system. However, the currently available methods for solving unsteady convection-diffusion problems are generally not able to offer excellent accuracy in both time and space variables. A procedure was given in detail to solve the one-dimensional unsteady convec-tion-diffusion equation through a combination of Runge-Kutta methods and compact difference schemes. The combination method has fourth-order accuracy in both time and space variables. Numerical experiments were conducted and the results were compared with those obtained by the Crank-Nicolson method in order to check the accuracy of the combination method. The anal-ysis results indicated that the combination method is numerically stable at low wave numbers and small CFL numbers. The combination method has higher accuracy than the Crank-Nicolson method.},
}
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%A Zhu, Zhenwei
%A Chen, Junjie
%D 2022
%J Current Research in Public Health

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%M doi:10.31586/ujpr.2022.155
%U https://www.scipublications.com/journal/index.php/ujpr/article/view/155

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AU  - Zhu, Zhenwei
AU  - Chen, Junjie
TI  - Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion
T2  - Current Research in Public Health
PY  - 2022
VL  - 1
IS  - 1
SN  - 2831-5162
SP  - 1
EP  - 10
UR  - https://www.scipublications.com/journal/index.php/ujpr/article/view/155
AB  - The convection-diffusion equation is of primary importance in understanding transport phenom-ena within a physical system. However, the currently available methods for solving unsteady convection-diffusion problems are generally not able to offer excellent accuracy in both time and space variables. A procedure was given in detail to solve the one-dimensional unsteady convec-tion-diffusion equation through a combination of Runge-Kutta methods and compact difference schemes. The combination method has fourth-order accuracy in both time and space variables. Numerical experiments were conducted and the results were compared with those obtained by the Crank-Nicolson method in order to check the accuracy of the combination method. The anal-ysis results indicated that the combination method is numerically stable at low wave numbers and small CFL numbers. The combination method has higher accuracy than the Crank-Nicolson method.
DO  - Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion
TI  - 10.31586/ujpr.2022.155
ER  -