A high-order ADI method for parabolic problems with variable coefficients

Samir Karaa

doi:10.1080/00207160802217227

A high-order ADI method for parabolic problems with variable coefficients

Samir Karaa^*

^*Corresponding author for this work

Mathematics

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

11 Citations (Scopus)

Abstract

A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.

Original language	English
Pages (from-to)	109-120
Number of pages	12
Journal	International Journal of Computer Mathematics
Volume	86
Issue number	1
DOIs	https://doi.org/10.1080/00207160802217227
Publication status	Published - Jan 2009

Keywords

2D incompressible Navier-Stokes equations
ADI method
Driven cavity flow
High-order compact scheme

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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10.1080/00207160802217227

Cite this

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title = "A high-order ADI method for parabolic problems with variable coefficients",

abstract = "A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.",

keywords = "2D incompressible Navier-Stokes equations, ADI method, Driven cavity flow, High-order compact scheme",

author = "Samir Karaa",

note = "Funding Information: This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.",

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AU - Karaa, Samir

N1 - Funding Information: This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.

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N2 - A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.

AB - A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.

KW - 2D incompressible Navier-Stokes equations

KW - ADI method

KW - Driven cavity flow

KW - High-order compact scheme

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A high-order ADI method for parabolic problems with variable coefficients

Abstract

Keywords

ASJC Scopus subject areas

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