Higher order ADI method with completed Richardson extrapolation for solving unsteady convection-diffusion equations

Ruxin Dai; Jun Zhang; Yin Wang

doi:10.1016/j.camwa.2015.12.007

Higher order ADI method with completed Richardson extrapolation for solving unsteady convection-diffusion equations

Ruxin Dai, Jun Zhang, Yin Wang

Computer Science

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

A higher order alternating direction implicit (ADI) method with completed Richardson extrapolation is proposed for solving unsteady two dimensional convection-diffusion equations. The method has sixth-order accuracy in space and fourth-order accuracy in time. Completed Richardson extrapolation is used to improve the accuracy of the solution obtained from the high-order ADI method in spatial and temporal domains simultaneously. Stability analysis is given to show the influence of Richardson extrapolation on the unconditionally stable ADI method. Numerical experiments are conducted to test its high accuracy and to compare it with Karaa-Zhang's high-order ADI method.

Original language	English
Pages (from-to)	431-442
Number of pages	12
Journal	Computers and Mathematics with Applications
Volume	71
Issue number	1
DOIs	https://doi.org/10.1016/j.camwa.2015.12.007
State	Published - Jan 1 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Ltd.

Keywords

ADI method
Higher order compact scheme
Richardson extrapolation
Stability analysis
Unsteady convection-diffusion equation

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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title = "Higher order ADI method with completed Richardson extrapolation for solving unsteady convection-diffusion equations",

abstract = "A higher order alternating direction implicit (ADI) method with completed Richardson extrapolation is proposed for solving unsteady two dimensional convection-diffusion equations. The method has sixth-order accuracy in space and fourth-order accuracy in time. Completed Richardson extrapolation is used to improve the accuracy of the solution obtained from the high-order ADI method in spatial and temporal domains simultaneously. Stability analysis is given to show the influence of Richardson extrapolation on the unconditionally stable ADI method. Numerical experiments are conducted to test its high accuracy and to compare it with Karaa-Zhang's high-order ADI method.",

keywords = "ADI method, Higher order compact scheme, Richardson extrapolation, Stability analysis, Unsteady convection-diffusion equation",

author = "Ruxin Dai and Jun Zhang and Yin Wang",

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year = "2016",

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T1 - Higher order ADI method with completed Richardson extrapolation for solving unsteady convection-diffusion equations

AU - Dai, Ruxin

AU - Zhang, Jun

AU - Wang, Yin

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A higher order alternating direction implicit (ADI) method with completed Richardson extrapolation is proposed for solving unsteady two dimensional convection-diffusion equations. The method has sixth-order accuracy in space and fourth-order accuracy in time. Completed Richardson extrapolation is used to improve the accuracy of the solution obtained from the high-order ADI method in spatial and temporal domains simultaneously. Stability analysis is given to show the influence of Richardson extrapolation on the unconditionally stable ADI method. Numerical experiments are conducted to test its high accuracy and to compare it with Karaa-Zhang's high-order ADI method.

AB - A higher order alternating direction implicit (ADI) method with completed Richardson extrapolation is proposed for solving unsteady two dimensional convection-diffusion equations. The method has sixth-order accuracy in space and fourth-order accuracy in time. Completed Richardson extrapolation is used to improve the accuracy of the solution obtained from the high-order ADI method in spatial and temporal domains simultaneously. Stability analysis is given to show the influence of Richardson extrapolation on the unconditionally stable ADI method. Numerical experiments are conducted to test its high accuracy and to compare it with Karaa-Zhang's high-order ADI method.

KW - ADI method

KW - Higher order compact scheme

KW - Richardson extrapolation

KW - Stability analysis

KW - Unsteady convection-diffusion equation

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U2 - 10.1016/j.camwa.2015.12.007

DO - 10.1016/j.camwa.2015.12.007

M3 - Article

AN - SCOPUS:84954025372

SN - 0898-1221

VL - 71

SP - 431

EP - 442

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 1

ER -

Higher order ADI method with completed Richardson extrapolation for solving unsteady convection-diffusion equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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