A New Method for Solving Convection-Diffusion Equations

Wenyuan Liao; Jianping Zhu

doi:10.1109/CSEW.2008.27

A New Method for Solving Convection-Diffusion Equations

Wenyuan Liao
, Jianping Zhu

University of Calgary

Research output: Other contribution

Abstract

When solving convection-diffusion equations using the finite difference schemes, the convection term is usually discretized by the upwind schemes to avoid oscillations. A method to eliminate the convection term from convection-diffusion equations is presented in this paper. The new approach makes it feasible to solve convection-diffusion equations using central difference schemes without oscillations. It can also be easily combined with the Pade approximation to achieve fourth-order accuracy. Numerical examples involving one-dimensional equations are presented in the paper to demonstrate the accuracy and robustness of the new approach.

Original language	American English
DOIs	https://doi.org/10.1109/CSEW.2008.27
State	Published - Jul 1 2008

Keywords

Central difference schemes
convection-diffusion equations
upwind schemes

Disciplines

Applied Mathematics

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10.1109/CSEW.2008.27License: CC BY

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title = "A New Method for Solving Convection-Diffusion Equations",

abstract = " When solving convection-diffusion equations using the finite difference schemes, the convection term is usually discretized by the upwind schemes to avoid oscillations. A method to eliminate the convection term from convection-diffusion equations is presented in this paper. The new approach makes it feasible to solve convection-diffusion equations using central difference schemes without oscillations. It can also be easily combined with the Pade approximation to achieve fourth-order accuracy. Numerical examples involving one-dimensional equations are presented in the paper to demonstrate the accuracy and robustness of the new approach.",

keywords = "Central difference schemes, convection-diffusion equations, upwind schemes",

author = "Wenyuan Liao and Jianping Zhu",

note = "Liao, W. and Zhu, J. (2008), A new method for solving convection-diffusion equations, in Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, 107 – 114, IEEE Computer Society, Los Alamitos, CA.",

year = "2008",

month = jul,

day = "1",

doi = "10.1109/CSEW.2008.27",

language = "American English",

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T1 - A New Method for Solving Convection-Diffusion Equations

AU - Liao, Wenyuan

AU - Zhu, Jianping

N1 - Liao, W. and Zhu, J. (2008), A new method for solving convection-diffusion equations, in Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, 107 – 114, IEEE Computer Society, Los Alamitos, CA.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - When solving convection-diffusion equations using the finite difference schemes, the convection term is usually discretized by the upwind schemes to avoid oscillations. A method to eliminate the convection term from convection-diffusion equations is presented in this paper. The new approach makes it feasible to solve convection-diffusion equations using central difference schemes without oscillations. It can also be easily combined with the Pade approximation to achieve fourth-order accuracy. Numerical examples involving one-dimensional equations are presented in the paper to demonstrate the accuracy and robustness of the new approach.

AB - When solving convection-diffusion equations using the finite difference schemes, the convection term is usually discretized by the upwind schemes to avoid oscillations. A method to eliminate the convection term from convection-diffusion equations is presented in this paper. The new approach makes it feasible to solve convection-diffusion equations using central difference schemes without oscillations. It can also be easily combined with the Pade approximation to achieve fourth-order accuracy. Numerical examples involving one-dimensional equations are presented in the paper to demonstrate the accuracy and robustness of the new approach.

KW - Central difference schemes

KW - convection-diffusion equations

KW - upwind schemes

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/88

UR - http://ieeexplore.ieee.org/xpl/articleDetails.jsp;jsessionid=HYm2PK5Zw1ytPHlY5Zd6nDGw1G7nhcHKdYnFvqwwjVcMXtBLTNCc!397391424?arnumber=4625048&contentType=Conference+Publications

U2 - 10.1109/CSEW.2008.27

DO - 10.1109/CSEW.2008.27

M3 - Other contribution

ER -

A New Method for Solving Convection-Diffusion Equations

Abstract

Keywords

Disciplines

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